# Full text of "The Grinder's Manual A Complet Peter Clarke"

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. ■ ■ 1 H DOUG HULL JJDUg J'lLII L ^ Introduction There is a mathematical backbone of poker, and it can be learned. Much of the math that you need at the table is simple, but you need to practice away from the table so that you know what is important and ean do what is needed when needed. Ibis book gives you hundreds of practice problems so that the mental math of poker becomes as automatic as simple addition. These practice problems are presented as worksheets that you will till out for each kind of problem, with an answer key in the back to check your work. By practicing these worksheets over and over, you will remember the procedures for calculating important percentages and numbers when you need to do this math at the table. 1 also include my own mental dialogue that 1 have when I am working out these problems. You will notice that there is rarely more than one or two numbers we need to remember at any given time. Kach operation is made as simple as possible. For example multiplying 37 by 4 might be too taxing, instead 1 would advocate thinking along the lines of, ' Double 37 is 74, 74 is basically 75 and double 75 is 150.” Is it absolutely correct? No. Is it close enough? Yes. in this batik we will be calculating equities of specific hands versus specific hands. You might say, “But this donkey could show' up with K7o after re-raising pre-flop!” You are right, he very well might, Ihis book is about calculating the winning chance of one hand versus another or one hand versus a set of several possible hands, ft is up to you and your poker sense to decide what those hands might be. Because of the inherent uncertainty in poker, we are not worried about calculating winning chances out to something like 73.1% on the flop/1 hat level of accuracy is meaningless in the face of other larger uncertainties. If the exact math were to come out to 73.1% but we just estimated to 75% that would be plenty good. [here is no need to measure with a micrometer if you are going to mark with chalk and then cut with an ax. With practice, you will be completely capable of doing these calculations at the tables when you need them. We will be quite liberal with the simplification of problems and that is quite acceptable. My grandfather, fapaw, often said, “Close only counts in horseshoes and hand grenades.” I would argue it is also true for the mental math of poker. These problems can also be used to get better with computer tools like Flopzilla, Equilab, Poker Cruncher, and the like. I he solution key for this book was made with these tools, and there is an appendix of which tools I recommended using. The focus of this book is on mental math so we will not be talking about the tools much here. I here will be companion videos for this book on ht tp j /Re dC hi pPoke r. com the answer key for this book is not just a list of answers without context It is a complete re print of the problems with the answers written in. This allows you to read the answer key as a way of reviewing the correct answers and building up intuition, and it saves you the trouble of flipping back and forth to the key later. The answer key is exact where it can be. Do not hope, or try to get your mental math as exact, if you are within 5% either way of the answer, you will be a monster at the tables. All of this math is used to enhance your poker sense. The problems in this book all tell you what the Villain holds. Doing the math in this ideal situation allows you to estimate better when the Villains holding is unknown. Will the Villain show up with unexpected hands? Yes. Will your rive red pair of Deuces actually put you ahead in unexpected situations? Yes. All of this math will be done in an uncertain environment, but we practice it here to better deal with that uncertainty. Contents Introduction 5 P re-Flop All- In Mat h 11 Pre-Flop All-In Percentages 13 Turn Math 23 Equ ity on t h e I u rn, H and Ve rsu s Han d 25 Equity on Turn Hands Versus fype of Hand 35 Calling Odds 48 Ratios and Percentages 52 Hunting Method and Bracketing 53 You r P e re entage of the P ot M e t ho d 54 Caldilating Percentages and Odds 57 Drawing Decision on Turn: Percents or Odds 62 i nipii ed Odds on th e 1 'urn 6 7 Coun ting Combos 77 Hand Versus Range, All-In 83 Hand Versus Range, implied Odds 94 Flop Math 105 Equity on the Flop 106 Hand Versus Hand Type 113 Hand Versus Hand Facing a Flop Shove 121 D e c is ion Ve rsu s a Hand Type Sh ov e on the FI op 127 Hand Versus Range After a Flop Shove 132 Hand Versus Hand on the Flop with Implied Odds 140 Hand Versus Range on Flop with implied Odds 153 Fold Equity 163 Real Hands 173 Folding Nut Flush Draw on the Flop 174 Folding Middle Set on the Flop 177 Flop Call on Paired Board 18t) Facing a Massive Donk Ship on the Flop 183 Fold ing l op P air Gp e n En de r 186 Nut Flush Draw Against “Same Bet” 189 Big Draw Versus I urn Check Raise 192 Answer Key 199 Appendix 285 Combinatorics You Can Use at the Table. 286 C om pute r Tools 2 96 Obligatory Silly Painting 297 About the Author 298 Pre-Flop All-In Percentages if all the money goes in before the flop, there is no more action and the cards just run out. there are eight basic ways two hands can relate to each other, they are show r n on the following pages. A common match-up is for one person to have two overcards and one person to have a pair, this is commonly referred to as a race or a coin flip because each person will win essentially 50% of the time. A second typical match-up is pair versus pair. The lower pair will only w r in 20% of the time. The percent chance of winning is also known as your equity. So if there was SI 00 in the pot, on average the lower pair would win S20 because 20% of S100 is S20. Pre-flop equities are not calculated at the tables, they are remembered. All of the equities that are listed on the next pages w r ere calculated w r ith Equilab, but any of the tools in the appendix of this book would do the same. We only need an approximation of the percent chance of each hand winning, and w r e can round the equities off to make them easier to remember. As with most of this book, we are only trying to get close. Ihese equities are important when calling a shove or making a shove pre-flop. A simple example would be if you raise to SI 0 with Ace King and someone shoves all-in for S50. You have seen this player do this kind of thing w r ith small pocket pairs quite often, and you believe that is w r hat he has now. You are being given the opportunity to call S40 to win a total pot of S100. Your Ace King wins 50% of the time versus his assumed holding of a small pocket pair like 77. Since you expect to walk away with 50% of the $100, that is S50. If you put S40 into the pot and expect to win S50, this is a good bet and you should calk Later in the book we consider more complex (and realistic) situations, like the fact that the Villain might also hold AQ, KK, or something like 78s. In the following diagrams, notice that the cards are not haphazardly placed, they are higher or lower in the space based on their ranks so it is easier to see their relationships. For instance, in the diagram below, the King is higher up than the pair of Queens and the Seven is placed lower. Also using Equilab, we know that the Queens are a 70%-30% favorite over K7o, and this statistic is mentioned above the pairs of cards. 'Ibis basic percentage will hold whenever a pair is matched up against an over card and under card with slight bonuses for the possibility of a straight or Hush by the unpaired cards. Pair versus over/under Note that in a dominated situation (a hand like A7 versus AK below) the actual equities can vary quite a bit from the stated 35%-65%. This is because in a dominated situation like K3 versus K2, frequently neither the Deuce nor the Trey will play, so the equities are much closer to 50%-50%. In other situations like A7o versus 78s is 35%-65%. Hands that share a small card, like Q2o versus K2o are more like 25%-75%. It is not worth doing a lot of work to remember all these possibilities. Pair versus pair Pair versus unders 30% 70% r A \ ( - m a l * ' 1 L + , 90% 10% r a Q fl 1 > 1 , A 7 vj Pair versus single over Pair versus single under 50% 60% Pair versus overs Two live ones Pair versus over/under Dominated (Percentages vary much more) These first exercises are very straight forward and based off of the percentages mentioned above. Hie point of tills exercise is to get you thinking about the possible variations of the type of hands described above and begin to develop an intuition on your own of how mathematically good your hand is versus other possible hands. For the first set, circle the hand that is ahead if all the money goes in pre-flop. The second set of exercises are tougher but more useful. Write the percentages in for each hand. Just find the applicable case in the prior page and fill in the percentages. To further refine the estimates, the hand that is behind gets an equity boost for being suited and/or connected. For instance: * KK versus 92o is 13%, * KK versus 92s is 17%, * KK versus 98o is 19%, * KK versus 98s is 22%. Add 4% for suitedness and 4% for connectedness and that is a good approximation. Add 4% for suitedness and 4% for connectedness and that is a good approximation. Just about any poker calculator will be capable of this kind of calculation. Look for the video accompaniment to this book on RedChipPoker.com to see how to use compute tools to solve these. See the appendix for recommended too Is. vs. vs. vs. vs. vs. vs vs vs. vs. vs. 'k' 'Kl vs. 'k' r K % vs. fo. vs. f i A '4' JL A' A *** vs. % vs. vs. % vs. % vs. 2 2 wt- y. vs. vs. k' t -* 3 VS. r 1 K ,*j ’2 ♦. % VS. r- 1 10 + 9 vs. io 2 -o (71 ITI VS. r -^ 10 fol ra fji LL jL- L±J LL vs 10 ? r” "i 3 T r™ ^ 9 Jl ? ITI [T| Li Li vs. 9 VS. fo Equity on the Turn, Hand Versus Hand Pre-flop is the easiest street to calculate. It is not even calculating, it is looking up pre-calculated numbers. Calculating equities on the turn is the next easiest street because there is only one card to come. Outs are cards that make the hand that is behind take the lead. On the turn there is only one thing to do, count outs and use the Rule of Two (explained soon). Remember, the guy counting outs on the turn is the one behind. Some of these problems are tricky with some false outs that actually improve both hands so they are not really outs. Don't worry if these tricky situations trip you up. At the tables, even if you miss these, you are rarely going to be oft by more than a couple of percent. The Rule of Two says multiply the number of outs by two to get the percentage chance of winning after the next card. Hie reason this rule works is that there are 52 cards in the deck and we know where six of them are on the turn, that leaves 46 unseen cards. If there were 50 unseen cards, each one would be exactly two percent of the deck. In actuality (because there are slightly fewer cards than 50), on the turn each unseen card represents 2.17% of the deck. Since we are usually calculating our hand versus an assumed holding, we can refine this rule further. If we pretend to know the Villains cards also, there are only 44 remaining cards so each is really slightly higher — 2.27% of the deck. We can add 1% bonus equity for every four outs to account for the extra 0.27%. This is becomes more important when the number of outs increases. In this book we will add the bonus percentage if we think it will matter. However, usually the simple multiplication of outs by two is enough. If we are not assuming we know the Villain's cards, we can account for that extra 0.17% by adding a bonus percent for every six outs. Add these bonus percents in if you like or not as you choose. (Note that the answer key is as accurate as possible and does account for this.) 31 Add-ons to the Rule of Two 13 Multiply outs by two to get the percentage to win on the next card. Think you know their cards? One bonus percent Tor every four outs. Not sure? One bonus percent for every six outs. Rule of Tw r o applies on the turn since there is one card to come, but you can use it on the flop also if you expect to face another bet on the l urn. *1_ P Let's work an example of the kind of problem in this section: f -1 9 — 8 r-' 3 -s 2 .♦J ♦ J l *J f A 9 VS. io r- -< J 4 ♦ -___j # putts fo __ VS. $ In this hand, JTs has no pair, and A9s does have a pair. This means A9s is ahead, so we will be counting outs for JTs. Start by counting the most powerful draws—the flush. Any of the remaining nine Diamonds makes a winner. Next, any of the four Queens or four Sevens will make a straight. We already counted the Diamond outs that are among the straight cards, so be careful to not count them twice. We get three of each of the Queens and Sevens as outs instead of four each. We have the luxury of knowing that our overcards to the pair of Nines are good also. That means we also win if a Jack or Ten comes, so we can also count three outs for each rank. When doing these problems, space is provided to w r rite down the number of outs. Notice that in the example below we wrote out all the outs separately, 9+6+3+3=21. (You may find it beneficial to adopt this trick for this kind of counting if keeping all the numbers in your head before adding is tricky. You might want to count up each time or do some other strategy to keep the mental dialog simpler. This will make sure the math gets done right. This book allows you time to practice this and find something that works for you away from the table.) Once 21 outs are counted, double 21 to get 42%. If we want to be more accurate, we can add the bonus percentage of 5% because we get a bonus percent for every four outs. 21 divided by 4 gives us 5% to add in as a bonus bringing 42% to 47%. The actual equity is 47.7%. This was a damn fine estimate considering we did this in our head. f % 9 / -> 8 3 2 , * , . ♦ . 'a [9l VS. id r j * ♦ JL. # pw.ts '£+5^5*2*/ fo 5? vs. % ^7 Some people do these exercises with computer tools to get used to using the tools. This can be helpful in learning the tools and building intuition. You can use these tools and get as accurate as you want, but the estimating we do here is going to be just fine at the tables. At the tables, if you think you know what your opponent has, just round 47% equity up to 50% for ease of calculations. If we want to be more conservative because it is hard to know exactly what your opponent has (maybe it isn’t exactly A9 without blockers), we might discount a few outs and call it 40% for easy calculations. Do not be overly concerned about the errors in your calculations because of small adjustments for uncertainty and ease of mental math. Remember that it is the approximations we are looking for. Being oft by a few percentage points doesn’t matter if it means you comfortable doing the math at the table when necessary. * <"-1 7 J 2 a ±J JL /-" Q J vs. ^—> A r -■p 3 Ls LL JL JL # outs vs. % # outs * VS. 70 J [ 2 ] fa] . *. ±J t J vs. t -1 A t - 'i 8 LL JL L*. # outs VS. 7fl 31 9] ^ ■> K r -\ K - > [3 / ' [9 c —^ [7 r ■- 2 — ™\ 3! fll ±J * .._*_ j L ♦ , ♦ A L + , [♦, VS. A 7 r ^ 3 2 VS. r A 7 I 7 7 VS. A r 1 K l±J L±J LL Ll L±J L±J jlI A LL #■ outs # outs # outs vs. o vs. vs. Answers: page 203 Doug I-Iull y 1 > K r 10 f^ J 3 J JL , ♦ , K r A * vs. 9 * 8 + # outs vs. % # DutS # 0U±£ o vs. vs. r-> r-1 r -^ J o 1 —\ 8 6 { * , , ♦ , [a' A VS. 'k' [a| •T* A 'fio fel 131 fa] (Id fsl fel A ♦. JL k ♦ , JL , ♦ . I a VS. 9 8 i a A VS, 9 A J[ ± J * ± J i±j liL Li, A a ♦ 10 ♦ 8 ¥ v._:_ 6 ♦ A * A vs. 9 + A * # outs # outs # outs vs. % vs. ?- vs. N/-- \/' •\/-N/' -\ - \r 9 8 3 4 9 8 3 3 9 8 3 3 4 L- ± - 4 A 4 >— •*• ^ > + , J 4 L - A - J >+, < > 9 t * 8 vs. < > J < > 10 * > 9 >• * 8 vs. t > J < > 10 ^ > a r-1 a VS. 7 t > 6 4 k. A ^ 4 ^ ^ > + , JL y. ,+J JL # outs # outs # outs % vs. % % vs. % % vs. % L L L -' 9 8 r > 8 3 9 r * 8 t y 8 r > 3 ^ > 19 r > 7 f > 5 f > 3 jL > + , , + J > + , y, t > a ^ > a VS. t N J ^ >k 10 >* > A t > A VS. < n J < > 10 r -> 9 * y 7 VS. f > 8 < > J A •I* 4* k- ^ JL 4 ^ ^ [ + , 4* JL L 4* k— 1 —- y. >- *■ * 4 i ^ # outs # outs vs. % vs. % T 4 6 *3U * > 5 * K [* 4 f -N 6 5 A f - 1 K f > 6 4 f -N 6 5 r i K k + . f -' 1 A '6' VS, ^^ 7 /-' : 8 /- - 19 '6' VS. ? -i 7 f -> 8 f -^ 7 6’ VS. f - 1 4 f -i 3 JL V JL ¥ L±- JL ¥, L±. # DU.tS # O UtS # PUtS vs. %. vs. to vs. r-' 10 K I T| r -> 5 [♦, 4 J ¥ J / -1 10 io VS. r - > J t i fl ♦ S___ 4 Jk. A L+. 9 ^-\ 8 3 4 2 4 9 L± - \r 8 3 4 3 + K ¥ K * vs. Q 4 J 4 K ¥ K * vs. Q 4 ■\ y J 4 # PUtS # PUtS # PUtS vs. %. vs. % vs. * -' 9 / -\ 8 f -' 3 t -> 3 /-i 19 r > 8 5 3 t \ A f -> 10 /-' 3 2 4* ^ -A - 4 4 1 ^ + , > + , L + j 4 >- x y t J 4 ^ 1 ^ 4 ^ 1 > A 9 VS. r ^ a r ~ j r ^ A 9 vs. A r ^ 7 r ^ A r ^ A VS. r ^ K Q y, JL 4 l * 4 ^ a - y. y t l + . 4- # outs, # outs # OUtS VS. fo VS. fo t > A ^ > 10 J -> A ^ 1 ^ r ^ 2 L * a <■ > A 10 J /-> A Lil f > 2 L- A^i t > 2 r > 3 4 <- A —j < > K JL /-' 7 »* > A < > J VS. t > K ^ > a < > A t > 3 VS. t > K < > a t y 13 < > 3 VS. < > 4 < > A .v, y. l + . 4* JL .v, ! 4* J l + . l + . # OUtS # outs # outs ? vs. ^ ? vs. ? % vs. $ t \ 5 f -> 4 /-' K f * J /-i 19 / -\ 8 t' 3 2 /-> [9 /-■> 8 r ^ 3 f 2 y. LL A i - — l*\ y t l+. L±, L- 1 -J r -> A t > K VS. < *< 7 ' > 6 < > A r > 9 VS. f > 10 t > J a t > a vs. 10 f > J l*, [♦, u. i 1 ^ [♦, # ou.ts # outs # 0u±s T° VS. % % VS. % % vs. % L L f > 9 f > 8 r > 3 f * 2 r > 9 <-> 8 t > 3 r > 2 < ■> 9 f > 8 f y 3 f ) 2 l+- Ub v _ 1 J l + , JJ y f Li- f -> A t > A VS. t > 10 ^ ■» J < > 9 f > 8 VS. io < > J f > 9 r > 8 vs. f > 10 t > J l+. l±- l*. A x ^ y. LL # outs # outs # outts T° VS. fo % vs. t vs. $ 32 Poker Work Book for Math Geeks /-\ -\ r 9 00 4 a 3 3 ♦ L- 1 -i 9 8 3 L±- 3 ♦ L-*- A 9 8 6 ♦ ^ L a 6 J < > A < > A VS. ^ > 10 < N J 1 A < > A VS. t > 10 r -i J < > A * > A VS. < > K < > 7 1 + J l + , k±- # outs vs. % ■\ - \t - \r # outs * vs. % - \f - \r # outs % vs. % 9 ✓-\ 8 * 6 t > 6 9 /-\ 6 /-\ A / -\ 3 r ^ 9 /-\ 6 f ^ K 9 k— 1 —- ♦ * L-1- A <> V_ 1 _/ LL A L-*-J k+. ^ ^ k*, < > A ' > A VS. > K < > 7 9 f > 9 VS. ^ > 7 t > 8 < > A t > 9 VS. ^ > 7 t > 8 1 + l—1—j ^ A ^ + . 4» ^ ^ 4 ^ X A # outs # outs # outs vs. % vs. vs. % Doug Hull IT] 3 /■ - 6 f - -V 7 . *, -___ i A k' VS. 10 JL JL L±J Q * \ 7 k" _ X _^ 8 A a 4 k _;_, 7 l*. ♦ 00 2 10 4 a J ♦ . VS, 2 * 2 4 a i*. J ♦ VS. 2 * K ♦. # OutS, VS. % -■\/ r # outs vs. ~\ s - \r # outs, VS. 7 ♦ 8 ♦ a ♦ j ♦ ^ ^_:_ J VS. 2 * 2 * / v 3 ♦ #0Ut£ # oucts # owts vs. % VS. fo_ % vs. % 34 Poker Work Book for Math Geeks (Tl iti f i 8 [k] fsl IT] * V ” J l ___- . V. [♦, ♦ t * 8 r ^ 8 V-S. - " K - ' 7 ^ n 8 t —^ 8 A Li i Li i ♦ <s___> # OLitS VS, % VS. r - > 3 . ♦, r -' 7 r* ■> 8 * T *, /-i 3 Li t -i A L !L VS* —' K Li -' K # outs % vs. % # OUtS VS. fo. r-> A r > 7 A r i 8 •f. . 1 T rr -^ 7 [♦, 3 IjL 2 4- L 1 - r--' 13 A vs. r"-' K -' K r ^ 7 f -- 7 VS* f -" A * -" 2 JL JL Li jt. L±, L±* f -•> f -"> *- ■> /- A A 2 5 [♦, •f* „ A r K VS* r i A a L±- Li Li Lsl # ou.ts # cuts # o^te ?■ vs. %. vs. % vs. # 0U±S VS. % # outs, vs. % # outs vs. % # outs # outs # outs vs. % vs. % vs. % Equity on Turn Hands Versus Type of Hand In this section, we are considering an instance where we have a specific hand (like AQo) and we guess that the other player has a certain kind of hand (like a set). We will now practice calculating our equities against these guesses. In the two empty rectangles where you calculate outs, you can write a specific hand for the other player. Some of the time, all the hands of a given description have the same equity against our hand. Other times, the specific hand matters quite a bit. As an example, when we have top two pair and the unknown hand has a set, the different sets will have different equities. Top set versus top two pair is an unbeatable hand on the turn, but bottom set can lose if the top two pair gets a full house. When you are writing down a specific hand for the unknown hand, just choose something that seems realistic. Do not be concerned if the answer key chose a different hand. A a N -‘V 2 10l * 0 4 V ^ J\ v, VhS. OV-trpflir # outs A A £ - # cuts AA_£ # puts A A Z~ * VS. fcj£ _ fc ft vs. fo$I _ % + vs. %2k _ A VhS. OvwfQ'ir K J V3. cvemptr 3 r-■> 3 L * * J ♦ vs. VS. vs. .set vs. # # OUtS VS, % VS. set set # Dl^LtS a 3 2 10 . 4* . + ♦ V vs. OJtr pair # outs VS. fo. VS. overpaid # outs VS. % (Tl ITI i ♦ j VS. Overpaid # 0U.t£ vs. vs. OVirpalr # outs VS. % ♦ 4 4 VS. straight # outs vs. % t *\ t > A 6 + ^ 1 ■< Ter p T VS. Tpp pair # outs ?■ vs. $. Opea e^der VS. + Flush draw # outs vs. % vs. % VS. fo . Top pair Pair VS. + CpfiiA- guv^gr opgw girder VS. + Flush draw # outs # outs ♦ ♦ ♦ vs. Straight # outs # outs VS. % f y A /■-N A vs. Top pair P # outs VS. % vs. tw o Pair VS. 7o vs. opea cadcr + Flu^h draw # cuts VS. 7o \s V 4 ^ 4 4 VS. st.r&.l&hx # %■ VS. 7a nr fsl ll L4J # Obt.tS VS. Jo VS. TW0 PfltK # DU.t<> VS. 7b VS, T“dTp. "pdLr Pft ly VS. + Oft ia- euu^r Ope^ £iA,rfer VS. + Flush draw # puts # outs # outs VS. 7a VS. % VS. 7o I N ♦ \r 4 "N * ♦ K ^ Ppcfeet pfl Lr fcfilow Tp # DW.ti VS. % VS P^feetfsnir toe Low Tp # outs VS. % T| [A ve -, POfifeet fifltir JL A beLow rp # £>u±s VS. %. y.._ Poftfeet pa Lr toeLow rp v s Pctfet pnV toeLow TP Pocket pnLir bdLow rp # outs # OKtS # outs vs. %. vs. £ VS. fo. "\ 4 4* 4- k' K vs. <^ut shot # outs vs. vs. ^ut shot # outs vs. $. vs. <^ut shot # outs vs. V * a' V 1 J vs. <qnt shot » # DRtS K a vs. £}ut shot vs. e^wt shot # outs # outs vs. fo. vs. vs. £ VS. Full f+cLise # ou. ts VS. ?o. Thru &f a r^iv^d # vs. %, VS. Fi'j&vi VS, # 0 W±£ VS. % vs. VS. QverptUr # DKlS VS. % VS. ovfircfiireU # DRtS VS. % ¥ ♦ ¥ VS. Fu.LLHpn.i2 # ou .ts vs. % vs, # VS, fo. VS. cvfirpnw # £>U.tS ?■ vs. vs. FL.if,fl ft raw VS, VS. cvftnMir^s # outs # OwtS # DRtS VS. % vs. $. vs. % ¥ ♦ ¥ •I* fTI (161 VS. Fw.Lt h-f?Li5C VS. overpair 4 # outs. vs. %. A r i A VS. TWO V’tiU jL # OUtS vs. % vs, VS. $. VS. Over jjficr VS. vs, qut s h ct + o^ercftKd # puts # # Dl/LfS VS. % VS. % VS. ■ m • # i t 4 t t K.J LL £—) L. Ill U - \ ♦ 4 vs. set # ORtS vs. % Q 1 J VS. L J # ORtS % vs. vs. two 'Pair # oixts vs. $. VS. T(?J)-pfUr # DRt£ vs. %. CA/firptftr VS. Ope Vt, eerier <q.Kt sJirt. VS. + Dvcrcia # ORtS # outs VS. % VS. % « • * # set k' 10 vs. tavo pair l*J # outs. Y r 10 VS, ovfirpfltr ♦ j # DU t£ Y 10! opew- vs. . » . jlJ # DU t£ i-lHt Allot VS. + averts rd # DRtS ovtr \pair 8 r- 1 7 *T* t j VS. f VS, overpaid # DRtS VS. fo [8] |8] VS. i_J # ORtS * VS, 5 r-^ 5 vs. V L ♦ , # DRtS ? vs. 4 * overpfltr VS. GvfirpflLr VS. % CVfirpflLK VS. % VS. 7 ± VS. Nixt FP> 5 JL 5 i VS, VS. # outs # DKtS ft _vs. ft vs. ■ i ■ i’ 6 4 . V V — ± —J Nwfc Ft> r i if > VS. Nwt Ft> # £>W.tS £ % vs. % L L- Ni/tt FE £ K 10 5 g> 0 * . ♦. ♦ 4 - vs. set # outs vs. r 1, K K K | vs. two pair # outs VS. % Y K JL L*. # OKtS VS. % VS. T/P/TKU K v K ♦ e Ad w VS. + Plush iarcTW VS. # 0wt£ # outs # outs vs. $ VS. % VS. % vs. % 8 * i 7 VS. T.P.T.k.. jt] # oucts VS. fo 8 r i 7 vs. CJ T >e ‘^ u, # VS. fo VS. % Calling Odds In poker there are good bets and there are bad bets. The real art is setting up bad bets for your opponents while only taking the good bets offered to you. There are two components to any bet, the odds of winning and the pay off'odds. In order to decide what to do when presented with a bet, we need to know both. We might calculate that we will win a given bet only one time for every nine losses, but if we get one hundred times our bet when we win, this is a bet we should take every time. Let s look at an example: BET OF 2 (ALL-IN) POT OF 4 In the above example, the Villain bets his last two chips into a pot of four chips. We can see that we are getting a chance to win all six chips for the two we are asked to pul into the pot. This is a ratio of six in the pot to two in the call. We would write this as 6:2. In the interest of simplicity, we can simplify this 6:2 ratio to 3:1 to keep the numbers smaller. All that matters is the ratio. We could do this same simplification for a bet of $200 into a $400 pot or even a bet of $ 133 into a pot of $266. BET OF 1 (ALL-IN) POT OF 2 For Ihe rest of the example, we will think in the reduced or simplified ratio because keeping the numbers simple allows us to more easily do the mental math. Even though we only play out a given situation once, we really care what happens on average. An easy way to think about these situations is to imagine that we call the bet several times in a row and we win or lose in the exact proportion to what the odds dictate we should. Alter playing out the hand several times, we add up all the wins and losses. Let’s pretend we know we will win this bet exactly 25% of the time. This is 75%-25% or a ratio of 3:1. This says we will lose three times and win once on average. We will look at four trials in this case. We use four trials because it is the smallest number that lets us keep the ratios of wins and losses right. If we were to call this bet four different times, we would lose three limes for a total loss of three chips. On the fourth time, we win, and we would get three chips from the pot. This one win of three chips would pay for all three of the losses. Because on average we neither win nor lose, this is our break even chances of winning. Playing out the scenario four times is illustrated below. 3:1 ODDS (25% WIN) We just saw that getting 3:1 on our call, the break even percent of winning is 3 losses to 1 win, or 75% losses and 25% wins. What if we actually won this hand 50% of the time? 1:1 ODDS C50% WIN) Looking above illustration, if we win 50% of the time, our ratio is 50%-50% or 1:1. The smallest number of trials we can do to keep the ratios right is two. Play it out twice to see the results: once losing and once winning. We will suffer a single one chip loss and also get three chips from the pot for our one win. Over the two trials we win more than we lose. Profiting two chips over the two trials means this is a great bet. We should take it every chance we can get. What if we only win this hand 2G%? We know this is less than our break even percentage (25% was break even). Looking to the ratio, 80% losses and 20% wins means 4:1 odds. We should play this out five times to keep the ratios right. Illustrated below is four losses to one win: 4:1 ODDS (20% WIN) CALL AND LOS CALL AND LOS CALL AND LOS CALL AND LOS Over Lhe five trials, we lose four chips and only win three. We can see that we are slowly losing money because the payoff does not justify the risk. We are losing one chip over five trials or on average losing 0.2 chips ever)' lime we make this call. These small losses are often disguised in the luck of Holdem, but they are silent killers. Avoid these small losses and instead inflict them on your opponent and you will win at poker. Ratios and Percentages We often need to convert the pot-to-call ratio into a percentage. This is easiest when the numbers in our ratio are both whole numbers like 3:1 (which is 75%:25%) or 2:1 (which is 66%:33%). These two ratios act as milestones when trying to calculate ratios like 2.5:1 and other less friendly numbers. Here is a chart with lots of common ratios in poker. The conversion to needed outs is also listed. In the first grouping, the whole number ratios 5:1 through 1:1 are listed. The second grouping shows the percentages in increments of 10% from 90%-10% through 50%-50%. The final grouping combines the two tables. S : l 8 4 %— 16 ( 7 outs ) 9.0: 1 -1 ( 5 outs) 9.0:1 3055-10% ( 5 outs) 4:1 ( * outs ) 4.0: l 0DS4-2Q5S ( 9 outs) 5,0:1 C 7 outs ) 3 : 1 755i-Z5* ( 12 outs ) 2.3: l 7034-303S <14 outs) 4-0:1 eo%-20% c ^ outs) 2:1 66%-33SS (IS outs) 1.5: l 6091-4Q5S <18 oute) 3-0:1 7S%-25% (12 Outs ) 1:1 so%-50ss <23 outs ) 1 . o: l 5QS4-5Q3S <23 outs) H ■+ in 70%-30% C14 outs) i-ifa- 2-0:1 CIS outs) 1-5:1 €0%-40% CIS outs) 1-0:1 50%-50% C23 outs) Knowing these whole number ratios like 2:1 or 70%-30% allows us to guess at ratios like 2.5:1 when they occur. Since 2.3:1 is 70%-30% and 3.0:1 is 75%- 25%, we know 2.5:1 is in between 70% and 75%. You can pick either one depending on how optimistic or pessimistic you want to be. The actual answer is 71%, so both are very reasonable approximations. Hunting Method and Bracketing A second way to think about calling odds avoids having to do much math with the bigger numbers that occur in large pots. Look at the amount you are asked to call, and start hunting for that amount of money around the table. In this example, we are asked to call $75. We look around ihe table for piles of $75. There is one pile of $75 that we always have: the bettors $75. Next we look at the pot. There is another $75 pile in there. In fact, once we find one $75 in the pot, there is about $50 in change. This $50 is two-thirds of a $75. We have found 2% on our call. We now know we are getting 2%: 1. What is that as a percentage? We can use a bracketing method. If we round 2%:1 up to 3:1 we know that is 75%-25%. If we round 2Vy.l down to 2:1 then we know that is 66%-33%. Our ratio of 2 Z A:1 must be between 25% and 33%. Since 2% is closer to 3 than to 2, our final percentage should be closer to the 25% than the 33%. Estimate this to “just under 30%..” The actual number is 28%. Most of the time, we will be able to bracket around the simple-to-remember ratios of 2:1, 3:1, and 4:1. This puts easy milestones at 33%, 25%, 20% and covers everything from pot-sized bet (2:1) through 'A pot-sized bet (4:1). Your Percentage of the Pot Method The final technique is asking ourselves, “What percentage of the final pot call?” Remember that the final pot includes our call. Let s do an example with realistic numbers. POT: $170 BET: $70 In our head, we say the bet of $70 plus our call of $70 is $140. The original pot was $ 170 so that sum is about $300. We want our call of $70 as a percentage of$300. If you can divide $70 by $300 in your head, then just do that to get 23%. If you can’t easily do that math in your head, an estimation technique would be to think four times $70 is $280. This is pretty close to $300 so we will use $280. We now have a ratio of $280:$70 or 4:1, and we know that is 80%-20%. Our call is 20% of the final pot. Even though we rounded the pot from $310 to $300 and then down to $280 for convenience, we got within 3% of the actual value. Do not be afraid to make these convenient estimations. In the following exercises, fill in the blank. The answer key is exact, but feel free to round your answers to convenient numbers. Pot ts: 1 OO villa tiA, bets: so call ls> °(d £5 of totcil Pot Is: 100 villain bets: so : 1 oia, the call Pot Is: 100 villaliA/ bets: y-s : 1 oiA/ the call Pot Is: 100 villal ia, bets: 20 : 1 oiA/ the call Pot Is: 100 villaliA/ bets: 100 : 1 oiA/ the call Pot Is: 40 villain bets: 30 : 1 oiA/ the call Pot Is: S ’s villa liA/ bets: 35" : 1 oiA/ the call Pot is: y -0 villa iiA, bets: oo _: i oia, the call Pot is: Jo villain bets: &s _: l oia, the call Pot is: 5 villain bets: ±o : l oia, the call Pot is: villain bets: 41 : 1 oiA, the call Pot is: villaiiA, bets: ±0 : 1 oiA, the call 3 Pot is villa iiA, bets 300 ? ± 0.5 : ± oiA, the call pot is: ±00 Pot IS: ±00 villain bets: so villain bets: y ~5 ca ll is fo of tot#l ca ll is f of totfll Pot is: ±00 Pot is: ±00 villaii^ bets: 010 villain bets: ±00 ca ll is f of totoi L ca ll is fo of tot# L Pot is: so Pot is: 55 villain bets: so villain bets: 35 ca ll is fo of totfl L call is fo of totct l pot Is: TO Villain bets: Q.0 call is f _of total Pot Is: Jo villain bets: os call is f of total Pot is : s villain bets: ±o ca ll Is f of tota l Pot is: oo villain bets: 41 ca Ll Is f of tota L Pot Is: 12 villain bets: 12 ca Ll Is f of total Pot Is: 300 villa Iia, bets: 12 S ca ll Is fo of total Calculating Percentages and Odds The next exercise is not introducing any new skills, it is only combining them. We are counting outs and writing down the equity percentages and the wins to losses ratio. The wins to losses ratio is rarely round numbers. Try to get it into X:1 form. Getting X so it is a nice round decimal like: 0.5, 0.33, 0.8 is ideal. In this example, we start at 24%:76%. We recognize this is very close to 25%:75% and then divide each side by 25 to get the 1:3 ratio. t \ 10 y\ t - % 10 4* L- 1 - J / -\ 3 t > K t > Q vs. t > K t > 10 y\ y . # putts 7/ v.s / Sometimes, it is easier to use the hunting technique tor division. If we start with 70%-30% we would start hunting for “30s.” We see two of them in 70 and then there is 10 left over. This 10 over 30 is l A or 0.33 so we can say 2.33:1. ; J 6 v vv 9 * Q ♦ vs. 10 9 # oucts vs. %. a ♦ A ¥ ^ Vi V K ♦ 8 ♦ K vs. # outs vs. r n K A [ 4 * * 1 K .♦J 4 k,_-_ J <-s a J vs. / - ^ 6 7 4 ^_ t _ j LL 4 V " ^ .♦J # cuts f \ J /■ \ 9 r i a F 1 K ♦ V_ t 'y 9 /-\ 10 vs. A r-- a IL (D A 4* \_ 1. _H /*-' 3 /— 8 * 10 r \ 10 ,♦ J [♦J ♦ s ___ J 4* v_ J t \ J VS. A t -' K IL l±J LL r—■* 4 t \ J p F K A p t 2 ♦ L _-_ J t i. L J 'a' VS, 4 LL # outs # outs # outs vs. % vs. $ 7 * —-=>/■- _ J ♦ 4 4* A J ♦ j 4* vs. 6 4* r \i 9 4* # o Lite vs. & f©' ’6' r > 1 t 1 5 M ♦ dJ 4* t -' 18 * - 9 VS. f -^ J r- J JL ♦ JL # DLttS ?■ vs. f f -" 6 10 4 I 21 I* J M Jj l*. 10 J VS, 4 4 _J _ JL ♦ # Puts ¥■ vs. %. # outs VS. % t ' 10 [8 6 v * y, ffll f - J vs. r -- A t - 4 a 4 ^_i__ L*J # outs vs. %. # outs vs. %. f -^ J , ♦ J F - - ^ 9 L*, r- 4 JJ r -^ 13 l*, a 10 VS, f -- A J L^J JL LL # outs. % _. vs. % r-> 10 "-™\ 10 J r 1 ^ 3 JL ^ — ■* A r ■* K fii VS. r -1 K /-^ 10 ul l*J # OiitS _ VS. fo # oixts % __ vs. % 6 5 r - '1 5 10 V-—-—- L + J JJ r - A > 10 vs. 's' 9 JL ♦ s.____J. v * . # OktS f° - vs - 1° 4 J — 8 ♦ L_ 1 r 9 .♦J A K Li — K L±J VS. A ^^ a l*J 2 .♦J 2 9 j*J f - A .♦J r a' + v_ i 'a' i_j VS. A 4 A 8 l + J r *> 4 4 ( - * A J a VS. 8' < - \ 10 Jt. # cuts # outs # outs $_vs. ^ fo _ VS. fo 8 [3] v V i___ j 3 . *, K fl] VS. J io l*J ♦ s_1_^ # outs _ VS. Jo id ’8' 3 id ♦ ■. _:_ j •*• 4 _:_ j JJ 'jl f~ -i 8 VS. —^ 10 K JJ * s __ J A # outs. %_vs. % # outs $_vs. $ # outs VS. fo. r ' 9 >J 5 Q _ J [ 9 ' l*. y-- 10 Ul f-\ J vs. /-1 A LL 9 # P^tS VS. fo. f 5] /■-■s J r 1 ^ 6 F 1 K H_^ [(f io VS. K L±, , ♦ # outs VS. fo. r ~-——' 2 - - 7 l+J ' 1 5 f i 8 f - 6 L±J ♦ oo vs. ■■-- A A f-* A # outs _ VS. fo /-\ 3 f~——n 7 K f y 4 ,*J JlJ f -V 7 7 VS, f-i A t i Q # outs, % __ vs. % r ' 4 r-- 2 ♦ ^i Q| F \ 6 r-x A Ul, f-> A LLI vs. p*-*i 7 8 # outs :_ . VS, % F F 10 ♦ J /*- 7 M f i 3 JJ r i 5 id M F 1 A > e r-^ >00 ^^ f 1 2 J F ' 7 /- "S A M t \ Q L*J F F 10 r-' 8 ♦ ^_*_J /-' 9 4 l T * VS. 10 _ f-> 10 r- 8 -' 10 vs + /- f A JL "- K JlI r-\ K t - J 4 vs. r \ 8 . ♦ „ f -F 9 # 0U±£ # £>W.t£ # D W.t£ VS. % ?- VS. $ ?- vs. fo Drawing Decision on Turn: Percents or Odds In this exercise, we use these odds and equity percentages for something that is critical at the table: a call or fold situation. In all of these cases, we are on the turn and the Villain has shoved into us. We assume we are behind but that we have a certain number of outs that will win for us. Each problem is a mini worksheet to draw attention to the numbers that dictate the answer. Pot: 41 Q.0 Vlllfllu, Shoves: 4 Pot OO lots: : 1 pot would be:_ your call would be %_ of the flyu?l pot. Outs: -4 equity f _ Return, fron/i pot:_ Odds: : 1 <^ut shot Call □ Fold Here we find ourselves with a gut shot, that means we have four outs. There are two ways to solve this problem, we need only do one. For ihe first method, we calculate our pot odds, which are the darker boxes towards the middle of the problem. In the problem above, we are being asked to call $80. Using the hunting method, we find one “$80” in the Villain’s shove. We find a second “$80” in the pot with $40 left over. That $40 is another half “$80” so we found 2.5 for our pot odds. Are we going to win once for every two and a half losses? There are about 50 unseen cards. This is more than ten losers for every one of our four winners. Do not bother calculating this at the table since this is already a clear fold. For practice away from the tables, we might work out these numbers to the brutal end. At the tables, once you know what your decision is, stop and take the action. ’Hie second way of doing this problem is asking what percent of the final pot is our call? Our call of $80 out of a final pot of $280 would be a lot easier to calculate if the final pot was $240, so round the pot down. The rounded pot is three times the size of our call so our percentage is 33%. The pot was actually bigger so our call is a lower percentage. We nudge down to an even 30%. The actual percentage is 29%. Next we compare our contribution to the pot to our equity. We have four outs, so that is about 8% plus 1% bonus for every four outs. Lets call it 10% because it easier to work with. We are being asked to put 30% of the money into the pot and collect 10% of it at the end. This sounds like a terrible idea. We should fold. Notice that the two relevant numbers to this decision are the lighter boxes on the right. Most people prefer the percentage method, but both are on the worksheet. Use what you like or practice both to help decide. There is a new calculation in this exercise: return from the pot. This is tells us how much you would win or lose on average if you made the call. This number gives us an idea of how good or bad the call is. Pot: #120 villain Shov 1 ££: $ so Pot odds: £-5 ; t FLu-al pot would be: ' $00 your call would be % m JO of the fiwal pot. Outs: 4 equity ^ IQ Eftum frovu. pot:_ OoldS: }}Q : 1 £ju± shot Call * Fold Using the percentage method, the return from the pot is easy. In this case the final pot is about $300. We will bring back 10% of the final pot: $30. Since we are putting in $80 and only getting back $30 on average, calling is a terrible idea. Every time we make this bad call on average we are losing $50. wt 4120 <^wt: shot villa lit Shoves :-4 SO Pot DdotS: £-3 : 1 call * Fold i'V' FikUll ~pot would b£: _ your call would be of the flwtf L ■pot. Outs: E^Litty ^ R£tum -fVoito, Odds: ^lQ : 1 100 10 4 10 For now, this number is just a curiosity, but it will be come essential later. If this return is greater than the amount of the shove, we should call. If it is exactly equal, it is just a gamble where you don’t really lose or win over time. OpgiA, tv^dtr + FlixsVi draw C-all Fold Return from, pat: 2/5 villain ShoVte: # ^-00 Pot Odds:_: 1 FlrUal pot would be;_ your tall would be % _ of the fuiiflL pot.. Outs 15" equity g_ Odds*: : ± Poo feet ^alr be Low TP Pot: t ±O 0 v£XLg t vl S h 0 ves; 4 30 Pot OddS: __ : ± call Fold Return from pot: FLaftl pot would be:_ Your call would be % _ of the ftwJil pot. Outs: 2 Faulty g_ Odds: ; 1 r^ut shot Pot: 4 ± 2.0 VlLU*lu*-Shores: 4 so Pot Odds:_: 1 call Fold Return- from, pot: FlwflL pot would be:_ Your cnlL would be % _ of the fulfil pot. Outs: ^ equity j£_ Odds; : ± P0t: #120 Flush draw vtlLou^ shoves: # 30 Pot Odds.: _: 1 FerUll pot would be: _ Your oflLL would be % _ of the ftwai, pot. □ Fold Outs: ^ Faulty g_ Return from pot:_ odds:_: ± Pot: 42.00 Flush draw vlllam shoves: 4 £>0 Pot Odds: _: 1 call Fold R£twhrt, from, pot; Fulfil pot wonld be:_ yowr tciLL would be g_ of tke fln-ftl pot, OutS: ^ Equity g_ Odds,: : i opew tv^dtr + Flush draw coll Fold Return* from pot: Pot: 425 villain, Sko'yes: 4 jo Pot Odds:_: 1 FmAl pot would ht: _ y duy &all would be g_ of tke fin-flL pot. Outs.4 5" Bqyity g_ Odds: _ ; i Pocteet pair below tt C£?ll □ Fold Return from, pot: pot: 4 55 vlLLaln, shoves: 4 35 Pot Odds:_: 1 Flwfllpot would be:_ Y^ur &aLL would be g_ of the fln-fll pot, OutS: 2 equity g odds: ; 1 Pot: $ ^2 Flush draw vlLLam shoves: 4 &0 Pot Odds:_: 1 Coll Fold Return, from pot: Fl^Lpot would be:_ Y our call would be g._ of tke fln-fll pot, OutS: ^ equity g_ odds: ; x Pot: $2.00 Flusk d raw villain -Skoves: SO Pot Oddi: __ ; ± call Fold R£tw.rirt* fTOVW pot: Flu.fl L pot would bd:_ Your tali would be _ of tkfi fufl.nl pot* Outs: ^ Fc[ud.ty odds: ; i T** 4 .SO villa lu. 3 In 0 V££: 4 4 * 0 Pot Odds,: _; 1 Flri.nl pot would be: __ Your call would bt % _ of the fufl.nl pot. outsil^ Faulty j£_ Figturirt, froru pot:_ odds,: _ : i Pair + Flush draw call Fold Pot: 4 ±20 vCllflUt Skioves; 4 "40 Pot Odds: __; 1 Final pot wonLd bet_ Y our call would be _ of tine final pot. OutS: J \- Gqutty g_ Return from pot:_ Odds: _: 1 C^ut shot call F old tvtdtr Ppt: 4-400 -)- villain shoves: 4 ^- 50 Flush draw pi * — ;1 FtnaL pot Would be;_ Your ealL wouLd be % _ of the final pot. QUtS 1 5 Eqwty fo_ Return from, pot:_ Odds: _ : i Pot’ 4300 villain Shoves: 4125 Pot Odds: __ : 1 Filial pot wouLd bet,_ Your edit would be % of the final pot. Outs: 8 Return from. pot:_ odds: 11 Open, ender Call Fold Pot: 4-4-00 viiLfli-w, sho'/ts.- 4 100 Pot DddS;_: i Filial pot would be:_ Your t£ill would be % _ of the final pot. outs: 2 Return from pot:_ odds: _: 1 Pocket -pair below tp call □ Fold opeu, e^der call F old Return from, pot: Pot: 4320 villain. shoves: 4200 Pot Odds.: __ ; 1 FluflL pot would be:_ Y^ur CALL would be %_ _ of the flufll pot. Outs: & equity jg_ Odds: : ± ^t: 4 J~Q Flush draw vlllaU shoves: 4 +0 Pot Odds: _: 1 Flirt.flL pot wouLd be:_ Y our call would be % _ of the fLu-fllpot. [ Fold Out£: ^ equity ^_ Return. from pot:_ Odds: _: ± CfU.t shot + Flush draw call [ ] Fold Return frpt'u pot: Dvercdrots Pot: 4320 villain shoves: 4 2 00 Pot Odds: _: i FluflL. pot wouLd be:_ Y our cflLL would be % _ of the fUvfll pot. Outs:l3 equity ^_ odds: i ± Pot: 4 Jq villAln, Shoves: 4 ^0 Pot Odds:_: 1 Pi.irt.flL pot wouLd be:_ Y^ur caLL would be % _ of the flufii pot. [ ] Fold OutS: &> equity jg_ Return frowt pot:_ odds: _: 1 N Lit Ft> call □ Fold Return from pot; Pot: f±DD villain shoves: -f 5 0 Pot odds:_: i FtVLfll pot would be: _ Your GflLL wouLd be % _ of the flwaL pot. Outs: 12 Faulty g_ Odd s: ■ i Pot: + 45 villa iia , shoves: 4 2 :0 Pot Odds:_: 1 FliAjil pot would be;_ Your oall wouLd be % _ of the ftufll pot. Outs: 4 Faulty ^_ Rieturu- from, pot;_ Odds: _: ± ^jut shot □ call Fold Implied Odds on the Turn We have been making decisions on ihe turn where the opponent was all-in. Most bets on the turn do not leave either player all-in. When there is still money left in the stacks, the player who is drawing to the best hand can make a call with the hope of getting more money into the pot when he hits his outs. There is no mathematical answer to “If I hit my flush, will Villain call my shove on the river?” The only thing math can do is ensure there is enough money in the stacks so it is possible for Villain to pay us off. Inducing this payoff and knowing how often it will come is the art of poker. We only do the math here to know if it is possible to get paid off. Here is an example, The Villain makes a pot sized bet and has four times that bet left in his stack. POT VILLAIN BITS REMAINING STACK AFTER CALL One way to look at this is as follows. If we are on a draw that hits 20% of the time, roughly a flush or straight draw, then we will lose four bets chasing this draw for the one time it hits. When we hit, we will get the two units in the pot for sure. Over the course of these five trials, that means on average we are losing two chips, or 0.4 chips per try. 4:1 ODDS (20% WIN) We need to make up those two chips when we hit just to break even. The Villain sometimes will give us the remaining four chips in his stack when we hit. If we can get those four chips more than half the time when we hit, we are going to profit. To state this a second way, if we call, the final pot will be three chips and w r e have 20% equity in the pot. We are putting in 33% of the final pot. Because we put 33% of the money in and only collect 20% back, w r e lose 13% of the three chip pot. Doing the math exactly we see that three times 0.13 is 0.4 chips. We are losing 0.4 chips per trial. We have five trials so we are losing two chips over the five trials and we need to make that up. The four chips left in the stacks will do that, if we can get Villain to put them in when we hit. Let's do this a third way, this time with the hunting method. We would say that we know our draw will brick four times for every hit. We look around for four times our call. We see twice our call hi the current pot and four times the call in the remaining stacks. This means we can profit two units when we hit if we get it all. These are all different ways of saying the same thing. Use the thought process that is easiest for you. The size of the pot and the actual numbers will dictate what is easiest for you to do at the table. Here is out next worksheet: 2 ' f ’S j | _, K * J f s a i * vs. f -‘'S A J t 1 3 v y Pot: 4 100 Villa bets 4 £0 AkV^K^t bdhlwd 4 200 Pot Odds:_ : 1 Tlru*L pot would be:_. Your call would bd % _ of the, fiMl pot. Outs:_ Equity J_ Odds: ___ : 1 PKO-flt: f_Mfltedwp:£ call Fold We already know how to fill in most of the parts of this worksheet, but we will work through it again. First the pot odds: $180 for S80. We find two “S8Cf for SI 60. That is $20 left over and $20 is a quarter of the call of S80. So we found 2.25 times our call in the pot. We enter that number. Hie final pot will be $80 times two. SI 60, plus the original pot of $100 for S260. Now we want to get our call of $80 as a percentage of the pot of $260. We know calling a pot sized bet means we put in 33% of the pot. This was a little less than a pot sized bet, so we can round it down to 30%. The actual number is 31 %. Counting our odds versus top pair top kicker, we have all the flush outs and pairing our kicker. That is nine plus three or twelve outs. Turning outs into equity, we us the Rule of Two to double twelve and add a bonus percent for every four outs. That is 24% + 3% bonus for 27%. Calculating the drawing odds, there is 73% losses for our 27% wins. This means there is about three losses for each win giving us odds of 3:1. f > A O T / > If it , + , Ca l*J J 11 f - A t \ fl NAS. f ■> A r \ 3 4 j l±J L j PDt: 4 1 00 ViLlfhtA, bets 4 Av^Qui^i behind 4 200 Pot Odds: Z- £-5; I Fulfil pot would be: ^ Z-^Q Your call would be % 30 of the fu^l pot. Outs: tZ- ^Cjulty Yo ^ Odds: ? : i Profit : i _M£te£up:4_ Call =ev Fold Iliis is actually a really close call. We are putting in 30% of the final pot and collecting 27%. Stated the other way, we are getting 2.25:1 on our money and the odds against are at 3:1. At the table, we would likely say our return from the pot is essentially what we are putting in: $80. Doing the math away from the table we are more precise and see it is $70 return since 27% of $260 is $70. Since we are putting $80 in and collecting $70, this means we are losing S10 on this call immediately. The odds, located just above that, say we will suffer three losses for every one win. We take that loss of S10 and multiply it by the number of trials we are working with: three losses and one win. We get what we call makeup of $40. When we hit our outs, we have to makeup $40 to pay for those four $10 loses. We look at the amount behind, $200. This $200 is bigger than our required makeup of $40, so calling is at least an option. When we were doing problems earlier the Villain was all-in, so the amount behind was zero. This meant they could not pay our makeup when we hit. Sometimes there is money behind, but the amount behind is not enough to pay our makeup so it is a clear fold also. The question of us being able to make that $40 on the times we hit is beyond math. Knowing the math gives you the numbers; poker sense can make the assessment of the likelihood of getting paid off. Check the box if you would call or fold or if you think it does not really matter because you will break even. This is a judgment call in situations where there is enough money left to pay your makeup. In this specific example, if we put Villain on a top pair with better kicker, then ask, “If we spike our two pair on the river will we get at least an additional $40 considering that the pot is already $260?" Most people would say this a virtual guarantee. We would also ask, “If we hit our flush, will Villain pay us oft?” Some Villains would actually check-fold to a rivered flush, so this is less of a guarantee. If we bet SI DO when our flush conies, will the Villain call at least 40% of the time? Most players would think so. If we bet S200 will Villain call at least 20% of the time? Again, most players would think so. f > A . * , 2 l*J f J K , , t r— \ A f > t ' A fl VS. A 3 4 , 4 4 , + V___/ V___ J V_ S \ _ Pot: 4 VlLUuia, bets 4 behind 4 2.D0 Pot Odds,: 2- B-3 ; i_ Filial -pot would be: your call would be % ?fl of the -fmal pot* Outs: e^wt-ty odds: 5 : 1 PrD'fut: $~f6 Mak&it'fi:^_0 x call Fold The next questi on should be will we pay him oft" if we miss. We don’t have the action leading up to this decision, but under most circumstances that would have gotten us to this place, we would not pay oft" with top pair no kicker. Because we will know when our hand has improved but Villain will not, we would make this call. Without knowing the action to this point, the math can only tell us if this is a dear fold because there are not the implied odds to justify a call. The math can only tell us the proper implied exist, but not if they justify a call. Let’s do a second problem. In this case we are going to put up our draw versus the best possible hand for this board. If we can justify a call against the current nuts, then it is usually worth making the call no mater what Villain holds. ( \ 3 . ♦! \ a ♦ L ^ J /-\ 5 L— ^ J J .*J r-■> Q JJ f -> a VS. A A t 1 _ * K il Pot: 4 BO VlUtfUi eets 4 Ts behind 4 y~ 5 Pot Odds: _: 1 Pliant pot would bo:_ y our call would bo % _ of tho fli^nl pot, Okts:_ ^wtty ^_ odds; _ : ± Profit: f_M«leewp:4__ call f old Lets calculate pot odds first. The Villain is betting essentially pot, so we are getting 2:1 on our call The final pot is S230 and the call would be 33% of the final pot. Counting flush outs, we have only seven since the board pairing flush cards are false outs. Then we also have the non-flush Tens for another three outs. These are all nut draws that can overtake even the strongest hand on the current board. A total of ten clean outs is 20% plus two bonus percent is 22%. It is easier just to call this 20% though. This is a conservative estimate and makes the math easier. For the odds, if we are 20% to win, we are 80% to lose. This is a 4:1 ratio. Since we are putting in 33% of the money and only taking out 20%, we are losing money on this deal immediately. We might be able to get a win by calling this bet and making a hand and then getting more money in the pot. In a real situation, we might also consider making a raise here. That is a different kind of math, and we will get to it in something called fold equity. 3 1 Q » f \ 5 t 1 J ' J ' . v. 1 r— r 1 -> c * Q \ 0 VS. A K * - _ / HJ Pot: 4 20 viiln Ln fcets 4 y -5 Amount behind 4 7~5 Pat Odd s: ? : 1 Ft^flLpot would hi: Your c$LL would hi % ^ of the fiMl pot Puts: 10 e^wtty g.g odds: ^ : 1 ; Profit: ^0 Makeup: ^/5fl call =ev x fold To find out how much we are losing on this call immediately, we know we put in 33% and take back 20%. That means a loss of 33% - 20% or 13% of the final turn pot. Thirteen percent is not a nice number to work with. We will do this calculation in two easier pieces: 10% and 3%. Ten percent of $230 is $23. The remaining 3% is about a third of this $23. That is about seven dollars. Add that on, and we are losing about S30 on this call. We will miss four times for every win. Tliis means over the five trials, we have to make up $150 (5 * $30 = $150) on that one time we hit. The Villain only has $75 left, that means even under the best scenario where we get paid off every time we hit, we are taking the worst of it against this particular holding and should fold if we knew this is what he had. 2 J ♦ K ♦ f - “*1 m '-\ I -^ A Q vs. A 3 l±) Pot: 4 100 vUimn bets 4 Avu . au iA,t behind 4 200- Pot Qrtsk:_: 1 tlruaL pot WOK-W bfi:_ Youtr cot LL would be % _ of the flkW^lpot, Outz : Ddd£>: : i Profit : 4_Makeup:;!_ call =ev Foil 10 ? -'—\ 4 l V - 1 10 vs. '-\ J A \ Q * 1 * v 1 J *f* , Pot: 4 7~5 villain bets 4 75- Avuouwk behind 4 15"O Pot Odds: _ : 1 Fu/UtL pot would be: _ Y our tali would be % of the fL^Lpot, QutS: Drifik: _: x eopj-ty Profit: 4_ _ Mflte£up:j;_ Call =EV Harold A ^ V A \ R r- ■* it .♦J Ji V L vj o t vj /-N /-*\ -^ -\ A J vs. K Q , ♦, J V T > Pot: 4 35" VilLatw, bets 4 20 Awiouvrt behind -4 1 5D Vot OMZ: _ : 1 FLyuiLpot wokld be; _ Y our call wpwid b t % of the fiktflLppt Ow±S : Odd%\ : l Bo[uLtQ Profit : 1_ _ Call =^v Mftte£wp:+ Fold * > A 4] f 71 f m \ 5 * ♦ , L _$J * i 1 J r-\ <<> / -\ a VS. K .♦J f " K v_±^ m : 4 y-5 vUXft'uA, bets 4 45" AmouiA* behind -4 ±20 Pot Ddd^: _: 1 FLi/uiLpofc would be: _ Y our call would be % of the fmat pot. Outs: Odds: : 1 Profit : i _Mflteeup:4. call =ev Fold Answers: page 2 it) vs Ppt: 4 &0 Viliam bets 4 &0 Aw&uiAfc behUuJ 300 Ppt Odds: __ : ± FLi/utL pot would be: _ yputr chLL would be % of the fmflLppt. DutS: Odds,: _ : x Equity -profit : J_Mfiteeupi _ call m=ev □ Fold K *, 10 ♦ — < 4^ K \ K Y VS. /- A Ppt: 4 l: Villain, bets Amount behind Ppt odds,: 4 To 4 3 DO : 1 Plvutl ppt would be: _ ypur &aLL v/ould be % of the, filial pot. DutS,: Equity ^ Odds: : 1 Profit 11 _Mflteeu.p:£ call EV FoLd f - V C^* 4- k_ 4 '2' ♦ i* V J 4 / \ 3 .*J r ^ /-\ 7 7 VS. A K JJ 4, JL 1 l*J pot: 4 ^ villain, bets 4 ^5" behind 4 Pot Odds:_: 1 FwutL pot would be: __ your call would be ^_ of the filial pot. Outs:^__ equity ^_ Odds; __: i Profit: jf_Mftteeup:4 Call =^v Fold ■\ r 9 7 4, .*j JU t 1 j 4 . t j 7 ] '8] vs. r 8 fibl LLI 4 1 *._i_/ lii Pot; 4 y-o villain bets 4 45” Awm unit behind 4 Pot Odds: : 1 FmaL pot would be:_ your octLl would be % _ of t Vie fiw& L pot. DutS:_ equity ^_ Odds; __ : i Profit; ^ MCI fee up: 4_ Oct It =ev fold Counting Combos We know what our hand is, but we do not know what the Villain has. We can guess that he holds certain hands, like a set or top pair. Some hands are rare, like sets, and some are relatively common, like top pair. We count combos to estimate the likelihood of each holding. The set of likely hands for the Villain to hold is called his range. This book is not about constructing a range for the Villain. It is about doing the math after you have decided on that range. Read How to Read Hands by Ed Miller (buy it at http://RedChipPoker.com) for ideas on how to construct ranges. Out of necessity, we will be constructing ranges to work with but do not claim them to be realistic. We just need something to work with. For simplicity in these exercises, we will assume Villain has only hands from tliis range: [XJtj | KTtj K^| ;^i |K T i| Kfl*JjK5j |K4sJ:X3*j|K2*. [QflsjQTsj(Q&||Q3s [Q4=| Q3sj|Q2 j u KJe QJa U™J£I |JSi «4[ Jto H J3,j [J7s lATo KTo QTc Ills |T7s 16: T5* ;T4s| I3*j|T2»i jASo KSo.QSo J9 d|&9q y pft 5 97s S5s L 9 H Mil 92e jAflo QSa 3So TSo m 37* |S4s | 53* \*'* (AToj K7d Q7o ""o 7 - f? r* f'p Ud [74s- 1 [g»j A 6 c i.6c Q6 q 36o tfs? S6o !&6o j 76a u &5s iFJ! 63» 6Il (A5fl K5ej Q5o: J5o Tic- 95a :■ r o [ 75c* 450 55 H FiF A4d ,K4c‘ Q4c . r 4o T-c £4: £4d 74a 64a ?4d i(*j 25.1 42s A3? KJlvQAj; 23o jT3o 93a 5.3 o ;73o 43a 23d 43o 33 [kTj : A2o K2o!Q2o • [no T2o 92* &2o ,KoJ jZr 42 0 ?2o VI 1 — :*S C0Djbe5 IE pfEdcp njiff 0 % n.«i Tills is Ed Millers opening range from the early positions as outlined in his video How to Beat S2-S5 Anywhere . This can be found at http://RedCliipPoker.com in the May 2014 Pro archive. Remember the suited cards are above the diagonal. Here is the new worksheet. A 'k' - 3 j’ M 4* _* M 0 0 vs. t 1 A 10 • k _ J ■ k_ J 4* s,_ : _, 4* \_ s FLutsh draw ___ Combos Str & Lg ht pair + shot 5£t combes Combos Combos We need to count how many of each hand type is possible for Villain to have. Lets look at the Club flush draws. We are looking for any flush draw in that range that does not have an Ace, King, Ten or Trey {since they are on the board). The Ace and King are in most of the flush draws, so there are actually not that many, just five. Heart flush draws are a little more numerous because King high flush draws are not blocked. There are eight flush draws in Hearts for thirteen total. Flush draw combos are the hardest to count. In the Appendix there is a method for counting combos quickly that is a decent approximation. This appendix is a reprint from the strategy book Poker Plays You Can Use , also available at http://RedChipPoker.com Straights are easier to count since there is only QT. The stated range only includes suited QT so there are four combinations. We hold a blocker, meaning Villain can not hold QcTc, so there are actually only three suited combos for him. This is only one combination blocked, but that was 25% of the possible straights. Finding the pairs plus gut shots is a bit more challenging. Any hand with a Queen or a Ten and another Broadway card has a gut shot plus a pair. Looking at a computer tool, there are 39. Sets are easy to count. If the board is unpaired and we hold no blockers, there are three sets per card on the board. If we hold one of that cards rank, then there is only one way for Villain to have a set. This means there is one set of Aces, three of each of the other sets. The only wrinkle here is we don’t think the Villain would play pocket Treys, so there are just seven combos of sets on this board. Flush ctirflw ft straight pair + shot set J 7 &DkVLb£>£ Combos CdwOqd$ If we think Villain could have any pair plus gut shot draws* there are lots of them. We will rarely be concerned about an accurate count* but getting an intuition by counting combos over and over is important. Since this counting of combos is difficult to do exactly, consider a computer tool like Flopzilla to count the combinations. Fill in the worksheets with FlopziUa to get the intuition of the relative frequency of each part of the range. r -— 1 > 9 9 vs. A io ■ ^_> L-L •f* -.^ Flush draw Combos Straight Pair + £|Wt shot Combos Combos Combos uus Is* -i91 KJd IQJo; ATo ETb.QTtfl AJs i .ATs : A9i liAflillA ■ i! A6 b |. AS ■ j| A4s j«A5iI A2s I KJ*j^KTa[K&aJ QJj: QT&l QPe :qSj QTs Q6: Q5i Q4v Q5s QZi A*> K&o Q&e iPc T3p QBdli&cj TSq no ASo tSo U |p 8 i. ■ - ■■ 93 s|pjj U Fv Tp 91o S T ( Fsl 36s S1 e Ui fi.'s $2s 7fo| 75, |74l|j73*| 72* K"o Q 7 p Aflc: SCfio QGo ,-fic jj5l? 96* Sfo k-.-iiSjs, 64s 1 43i 62a [A_1o K2c Q3c J5-o T2c 95o E3c ‘5a fi5o 5' 1 54s 53s i-32s A4o K4o Q4c J4c T4o 9 4c i-r '4o 54g 54a 4-! 43s | 42? |A3o EJ Q3flj|.J3o|i'nft|.-93bi|jWiiJ[73*J|©& 53oj[43* 32s |A2o K2 d QIC- ;:c T2oj 92c £Id "2a 62 u 52 d :2 c I 1combos ie preflop nmfc i2o 21 _ _ Va :i 6*'* FlM-sh Ptrflw Combos Three of a fet^d ope^i Combos Combos Two Pmr Combos VS, 9 ■ * 1 * ♦ Full House Combos Combos Three of n felr^i Combos TWO Patr Poo feet pfllr below tp Combos Answers; page 232 I AX* £*§ Kiij Xli •. Q^j| KJ^j[KT*J t K 9 ij v - :< f - ?:■ :<•■• lM|S|Q9a |QS*j | Q7»j | Qlaj |Q ^: QZs KJcl QJc yaa JSl !l^l, Jfa |l J3s :I |j I ^ ^ Jjpij ■;• :•• t ' jA9oj K9d jQPp t ;pp 9^5J Mij| 55ij(*U| [93>] - 93» :TBo 9So A Sc KSo 97sJ S5: S3: - bJ E 9_’s $2: -V Qo v'd "■- -"•- * r '- "■ - "■' Xfio.lQSii’IJfioi-TGa. Me £ 6 all Tfol SffM fiSiJfiAil!* 5 s j 62 s Lfio ■A3dX5u ( Qio: J3 d ||T3u! Mo |S3o "3a 63q 33 i 5Js 33s 32s t,-Sc K-d 0*p .'-c T-io 9-Po £-k> *4-3 -&Jo :-o 4J 43s j 42s |A3o|K?> ' :.’t °l# .Sjo)["jp|:C3o i3*| 33 32s |A2o| J£2 d. :Q2o. f pc T2o Mo . S2o j | T2o| [Co 32o 142oj |. |2oj I i!Y& combos id preiSop nm=e _ VS. C^kubpS Combos CtffttbPS Combos, r i 4 l + J r 1 4 , , 10 l*j r ’i 5 J f -*N 0 ■ t-J /■ -s 0 V L- j vs. /■ - J ♦ _W t *, J Jl. Fwll H-ow.se Combos overpair _combos Top pfltr _Combos Three of o feew-d _Combos Fwll Howse Co mbos Overpatr Combos FwLL hfowse Combos Three of a tetw-ol Combos Hand Versus Range, All-In We can estimate the value of our hand versus any given holding. We know how to count the combinations of hands in the Villains range. Now we combine the value of each hand and frequency of each hand to choose our action. In these problems die Villain has shoved so we are not concerned about implied odds. To accomplish this section you will need to fill out the familiar forms that calculate the profit of a hand versus a hand. For instance the first hand versus hand in this section will be AJo versus KQs. Hie small worksheet calculates that this is a break even scenario with SO profit. We would then enter this profit on die separate combo counting worksheet on the facing page. Next we find the profit versus a set and versus two pair. Once combos and profit are both calculated, we multiply diem out. Once multiplied, we sum. This final total represents die profit or loss if we played out every possibility once. If this total is positive, we should make the call. If it is negative, we should not., It can happen that some hands in the Villains range give us a win, some a loss., We want to know what happens overall. Top pair set TWO Pair 3 K k A l *J j 9 " - > 0 ■ L A * -> V k,_ J VS. f - K f -^ Q JL V) 7 // Combos Combos Combos X X X 0 Profit "^0 Profit ^ Profit CflLL =EV Xfold Total: "W We see that we lose $610 taking this line if we play against every hand in the range once. This means over the 48 possible combinations, we on average lose about $13 on an $80 call. This loss is small enough relative to the size of the pot that players do not notice it in the natural variance of poker. These small losses add up. Players that call with the flush draw in this situation do not lose because “they never get there.” They lose because it is a bad bet and the odds are against them. A simple short cut was the possible here. If we expect this is likely to be a fold, start with the weakest part of the range. If we can not profitably call against the weakest hand, then the rest of the math does not matter, just fold. If our intuition is such that this is likely to be a call, start with the strongest part of the range. If we are good to call against the strong hands, the weak hands they might show up with are just a bonus. What about bluft’s? If we want to factor in bllifts and semi-bluffs into the Villain's range, the math is exactly the same as any other holding. If we spend the rest of our low limit poker career assuming that big bets on the turn and river are never bllifts, we will do just fine. Remember Rule two from Miller’s The Course : Stop paying them off. K vs>. Pot: 4 ±00 villa E-ia, s hovasi 4 Sio Pot Odds: _ : 1 Pw/UlL pot would be:_ your tall would ba %_ of tha ftkUil pot. Outs:_ ^_ odds.: ___; i Profit : f_ Call =ev Fold ’3' 1*. / - \ K 1 t A JL / > 9 4 f - ■y f \ f -\ tt 3 3 v<s. K Q UL y . y < P0t: 4 ±00 vtllflE-k, Shoves: 4 So Pot odds: _: 1 PIia-aL pot would be:_ y our tall would ba % _ of the fivuzl pot. Outs:_ Equity *£_ odds: ___ : I Profit : +__ call =^v DFold f ■* ** \ V A Q o V, A ♦ , L T J A jl w A 1 J r-s A ( \ K vs. t ■> K r"-\ a + . l + J l*J JL Pot: 4 ±00 villain Shaves: 4 Pot Oddi: _: 1 P'ua&L pot WOW.LM bf:_ your call would be % _ of thd ftaffL pot, Outs:_ Equity ^_ DddS: _: 1 Profit : i CflLL =^v Fold Atti Uffi, 1 p£J££ 234 KJs .TsiHBsllKgs, K7* k 6s K5s &4s K3s K2s _J •_- -_ K _■ k_• ■_ J •._• gajgj^^iy|Q9s QSs |QTs Q6 s Q5s Q4s Q3s Q2ji KJ c [QJoi F% J4a J2s ATc KTo QTc JTo I9&I TSe T6s T5s A9o •,_■ K9c Q9o J9o |T9o k ilggsj ASc KSc QSo JSo TSp 9$o 9 |A7o| *• _J &7o VkM0 Q7e Fl T"o 97o - -J S"d T4s T3s T2s J \_L_ * 95s 94s 93s 92s 19$ combos m prsflop rang? —i—nirrfliwi or: 2i.6% 3 .*J K L * J '-^ '9' ♦, * --— J 0 ■ * > 0 ■ vs. Y Q Top "pair _Combos • x - C0Hd30£ X Corw.bo£ x set two Pa lr 'Profit Profit Profit — ORli — 6 V FoLd Total: f y 4 /-^ 3 { 9 / -V 3 *$• l. J f - A f ‘N J VS. f % fl f -\ a •f* J L- 1 J POt: 4 ±50 villain Shoves: 4 $?0 Pot Oddi: _: 1 FmtfL pot WOW.Ld lfl£: _ Your oaLL wokLrt be % of the pot, Owts:_ E^ity ^ Ddd$>: : 1 Profit : i__ call n=ev Fold A f •z -“'S Q •z Ft o L J y •I* L - J O k *J f -\ f / - r-\ K K vs. 0 0 JL l±J i*j POt: 4 150 vtlLfltn. Shoves: 4 Pot _: 1 FLia,aL pot would be:_ yoixr call would be % _ of the fLi/uiipot. Dwts:_ equity ^ _ odds.: _: i Profit : t _ call = ev Fold Pot: 4 i. 50 Villain 3 il 0 V£S: 4 Pot Odds: : i Flia-^L pot would be: _ y our call would be % of the ftkvfll pot, Outs:_ Equity ^ Odds: : 1 Profit : +_ call =^v fold f 4 3 9' /-N 3 4 t J L 1 j * t j r - K f \ 9 V<S. f fl r“- a 4 1 4 4 1 1 v Pot: 4 ±50 vtllaL^ shoves: 4 ? O Pot odds:_: 1 FmaL pot Would be:_ your geLL would be % _ of the pot. Outs:_ equity ^_ Odds: _: 1 Profit : +_ C-flll =ev Fold KJo QJo ATc KToj[QToj[JToj ^ A9c Oo Q9c J9o 79 c J 6i I T9sl TSs T7s 98s I 9-s 96s 95s XU KSc QSo JSc TSc A7c K7 o Q^o Pc T7c J6c _-i6c K6c Q6o |Kis| J K45 k_ f [K3s] [K2s V M Q3s| Q4s [q3|] IQ2sI J5a L J i7.l J3s 1 J2s T5s . j |T4s| T3s K, _ J T2s 95s L J 94s l93sj B5s 84s S5s l J 75s 74s j 73s j 72s k. J L 2_J 64s A5o K5o Q5c J5o i5o 95 o S5o 5c 65c 53 54s 63s 55s 64s 52s A4c IUo Q4o J4c 14o 94o $4o "4c 64c 54c 44 4;s 42s ,45c K3o A2o K2c Q3c Pc T3o Q2o J2c T2o 55c 45c 55 52s 0 42c 32c ry I9S combos m preflop ranf* W//////A n.6*< 4 4- J 3 / \ 9 4* ■ 3 ' V, * - > /* - \ * \ / ' 0 v<s. Q Q ■ h.__ i * t_ d l*. l*J fLw£^ rfrflW Combos X Profit = ovtrpftlr Com bos X Prof^ , = Weuteer Dvtrpftir X - Profit = Top pdtr Combos X . Profi-t = □ < 3a ll — 6V fold Total: 4 /* ^ 8 if \ 10 / \ 2 4 4 , , * ; 9 f \ J v<s. /■ \ 8 / \ 10 1 J * pot: 4 ^ y~o Villa iKSh oves: 4 ^-20 Pot Odds: _ : ± plKRl pot would lc£: _ Your call would be % of the fivuzl pot. Outs:_ tqul ty f Q odds*-, : 1 Profit : +__ call n=ev Fold 4 v. f ^ 8 4 10 L ^ i f \ 2 + , ^ > 10 v. / ■> j i vj vs. f ^ 8 f \ 10 k j Pot: 4 i^o ViLlflLkv, shoves: 4 ^-20 Pot Odds: : 1 FuA^aL pot would be: Y our oall would be % of the ftkual pot. O0MS: Outs: equity ^ : i call Profit : + = 6V Fold f 4 / \ 8 id r- 2 v. ♦ , •I* ^- Q fl vs. / s 8 r \ 10 4 I *f* L J Pot-. 4 ±y-o Vill&M shoves: 4 Pot Ddd&: _’ ± fiviai pot would be:_ your u all would be % _ of the fLv^aL pot. Outs:_ equity *% _ odds*; m _: 1 Profit : +_ call =ev fold 4 L 4 j Ljl r“-\ 8 — 8 vs. /* - s 8 f - 110 . * , •f* Vl J Pot: 4 1^0 villain shove s: 4 120 Pot Odds:_: i Fulfil pot W Quid be:_ Y our cM would bt %___ of tbs pot. Duts:_ equity _ Orfds: _t 1 Profit : *_ call =ev Fold A s Kfts lKSs tos K6s! X5s K4s K3s |K2s T*j Q9s QSs Q'i Qfe Q4s Q3s Q2s J9s JS5 .175 J6s J5s J4s J3s J2s 1 _*_ 1 _J T9sl TS> :6s Tjs T4s T3s T2s .■^o j |K9oj |Q9o j j J9o iT%|^|9Ss| r, 96sj [95aj[»hj[»3s 92s A So KS^ilQ&o J$o 7Su 9&o 87* U& §5? S4s S3s A7o K7t> AGo K6c Q6c A5o too 83 ‘) S2s b J 173*1 L J V-— J hi 625 :js 52s Usil 4; s j IL J l J 33 52s l i 32o *>■1 '■■I % / 19S ccrabos m: preftop range _ 0 % il.6% opeiA. t\A,dtr TOf fair ovtYfalr Si t 4 81 r i 10 p' ■ 2 ♦ ^ X J f 0 r-^ vs. <-"i 10 * i d • V__> * t> ■f* ^__ J ComboS X Profit — Combos x Profit Combos X Profit = Combos X Profit — call =ev Fold Total: f o -\ A ft /-*\ A u •f* u u u 4 1 j r“-\ 6 /■- A v<s. — ol fll 4 L d * j L J v J 4 1 Pflfc 4 140 Villaivi & hoves: 4 100 Pot OddS: _: 1 plvttfl pot WOUld be:_ your call would be % _ of the pot. Outs:_ equity ^_ odds: __; i Profit : +__ CflLL I =ev Fol d O /- A A /-N A u 4 U U _ U 4 1 j ^ \ 7 r y 7 VS. f -\ fll f -\ a 4 >J V. J 4 J Pot: 4 140 villain shoves: 4 loo Pot odds: _: 1 Flvu*L pot would be:_ your call would be % _ of the filial pot. odds: Outs:_ equity ^ : 1 call Profit : +. = 5V Fold f 0 A A A M 4* L J O M U __, L) 4 x J k Y vs. J q' a + l j L±J L HE* V J 1 4 . \___j Pot: 4 1+0 villalui shoves: 4 100 Pat Odds:_: 1 Ptvuzi pot would be:_ your mil would be % _ of the ftvvflL pot. DutS:_ Equity f a _ Odds: _: 1 Profit : i call =^v Fold O / - \ A f -\ A /■ - A u + v V U M u LLI U 4 s- A K VS. a f a UL ♦ V A * L J 4 v_ x _> Pot: 4 1+0 VILLhli/l Shoves: 4 100 Pot Odds:__: l Fulfil pot would be: __ your call would be %_ of the fiw&l pot. Outs:_ Equity g_ Odds: : ± call Fold A5s A4s A3 s kcs : os Os Os K7s Kfe K5s K4 S Os A2si K2‘ |^p|mp| Q?s||QSs| Q"s !Q6sj|Q5s||Q4s| Q3sj[Q2i J9s! JSslIrs J6 j i J5s , J4s J3s J2s AjO K5o Q5o J3o i:c 95 a S:*o 15 c 65o 55 A4o X4c Q4o J4o T4 p 194o AM K3o Q3o J3o T3c 93o A2o K2v Q2o J2o 72 d 43s 42s 53c 43o 33 32s ‘Jo 42 o ■n 19S combos In pt^rlop range 0* . & 31.6% Mobster weaker Overpaid overpair Nut No Pair /-> o A A u t 1 J u U .. Jl { -^ f-V r 0 ■ 0 m vs. ^_> K _ S Combos -*- Combos ^ Combos X _Combos X cal i =ev a _/ _Profit — Profit ~ _ Profit = _ Profit = Fold Total: Hand Versus Range, Implied Odds In this section we are using a very similar worksheet as before. In the earlier sections, the Villain shipped all of his money in on the turn. In this section he bets but has more money left for a river bet. The caE decision is more complicated when there is still money left to bet on the next street. Hie money left behind after the bet and caE is referred to as implied odds. We never know if Villain is willing to put that money in the pot later, so we need to guess. Here is an example of a completed worksheet for the next section. We will use this to estimate the profit or loss of this hand versus hand match-up including the implied odds. f CO / rj s 9 /■-' 5 -' 3 * „ L ^ > * V. 1 , f y A z'-^ 1 9 9 vs. A 7 li_ ^ . POt: 4 &Q villa'un. bets 4 45 Av^ou^t bthivui 4 Put Odds: ^3.i- : 1 Fwa.£iL put wuwtpi be: - - :i o Your ofrll would be % 3£- 0 ^ the fiMtl put. Puts: 13 equity 3 Q Odds: 233 : 1 Profit : call = 5V Fold The SO profit means we are breaking even every time we make this call. If the Villain were all-in, this would be a pointless call since we neither win nor lose on average with the call. However, after we make this call, there is $120 in implied odds. Because the Villain has such a strong hand, we think we will get the remaining S120 most of the time when we hit our hand. Let’s be a little conservative and say that sometimes he will fold to the obvious flush. Discount J and sav we will only make SI00 when we hit. We hit 30% of the time, so on average we make S30 with this call in implied odds. 'Ihis is our average profit for this match-up of set versus combo draw r . We put this guessed number in the profit for the combo counting sheet. f -1 6 f - \ 9 ♦ J f -> 5 l _ _ t -*i 3 .♦J ^ 0 U t- -J f -h 0 * U. -J VS. A * -^ 7 . ♦, Dverpoiir CdrwJo£>£ ^ Cov Rtlos X ■Strflkght set CcmbtfS X Co pubes X LCflU =^v Profit Profit — _ Profit = FoLflt Total: We need to be realistic about this guess. Sometimes you will hit your draw and the Villain will not have a strong enough hand to pay you off. In this case, your profit from implied odds might be zero. Lets look at another hand for Villain on the same board. Pat'. 4 villain bets 4 45" behLi^o! 4 Pi± Odds: ^,33 : i Ftv'vftL pot wqu.UA be: 1*5fl Y&vtK fi-flLL wouUt be ~-% 3g of the fmflL pot. Ou t&; _ 3g equity g& Odds: ai& : i Profit; ~ M0le£LHLp; 4 --v xCflLL H=ev DFolri In the above match-up, the Villain bet into us with a dominated draw. Because we have such huge equity here, this S45 call into a SI05 pot already profits us S84. Barring bluifs, the only way more money is likely to go in is when the flush comes on the River. 'lhe flush will hit about 15% of the time and we will get the Villains entire stack every' time.lhis 15% of the remaining $120 is about S20 more oil average. In the combo counting worksheet we will note that this match-up is worth about SI 00 ($84 + S2G} on average. When making these estimates, be sure to account for situations where you will pay off the Villain and count that as negative profit. Note that when we are ahead, the number of outs is huge. It is often better to calculate the outs from Villains point of view' in these cases, but the answer key will show' the large number of outs. 8 2 ♦ . 3 T 4 L-£- J f -^ J *F \. j f -^ J ♦ VS. r > A UlJ f - 1 7 Pot: -f 5^ vLLLflEri^ bets 4 2-5 Amount bibL^ 4 i2£i Pet Odds*. _: 1 PuiA-flt. pOt WC'W.Lol bgl Yeur call would bt% _ of the flrtAl pet. Ou:t£i_ Equity £_ Odds: : i Profit : 4_ Mflfeewp:J_ Call =^v F old ft O *5? r 7 O , ♦ Li 4 ♦ , / 4 s___ J vs. Pcti 4 5S vLLUiu/i, bets 4 25 Amount behind 4 2-20 Pet Odds: _: i FunjaL pet would b£L your edit would be % _ of the fLifl-pL pet. Outs.: _ odds; : i Equity Profit : 1 □call Mflte(Up:£. = 6V fold STfr f N y r -i 8 ♦ r i 2 . *, r" 1 3 IL r ^ 7 .*J f - 'S 3 . v. f-> 3 ^iL, VS. f - \ A . ♦ f -1 7 ♦ Pat: 4 && vLLUs£la htti 4 25 Am^wn-t bibl^d 4 3 - 3.0 Pet Qdd&: : 1 Fua^L pot would b£: _ Your e-tiLL be % 0f thft fllAXjl 'pot. Du±£: DoWs: : 1 Profit: +_ cm ll = ev Fold f- r*-\ A r-^ /- 8 . ■* . vs. A * 7 ♦ Pat; 4 55 VtLLflm. bits 4 AnmHftt bc^Li^d 4 Pot Qddn _: 1 pIiaaL pet would be- _ your 6 hLL would be % of the fUvaL pot, Dut£: Odds: __ : ± Profit : f_MfffeMp;*_ Call =^v Fold b equity KJd QJr >,!>: K?»j [Kfej |Kjs tLAi U,sJ(K2 * QJsflQTsj Qfc Q8s:; Q7aj|q6a||Q5sj|Q4 s.,Q 3sj|Q2a| JTsliJSai JSsliJ7*ll Jfell J5*llJ4il)l3sl|j2» |AT»jjKT<j QT • A3 ,K3o Q9o J3o 73o . I 9 ‘h A3c KSo QSc JSo Tio ySo S7s| 85i Siii Mj 33s 92s L_ S lS E4; 83i S j> 76*1 n 5s ||74s j|73s||72i fj?5 6Jj JL _ 1 Gh\\m _ A3 a •K5& Q5o J5o T5o SJo £5 d 75o- 65a u :■}[ • Jt JL Ji- w jl Jaiv 51 54s 53$ 52$ .-.4c K4o Q4i5 J4 g m. A3o■ Kjc Q3e Jjc T3oi ?3<t S3 o 73c : 63o !3o 43o 33 32s I 31 T-o 9Ao S4o 6-e :4o 44 41* 42$ Alajpo Q7o J2*j 'nojpu j ^ajpoj S9S combs? £ tn prfftop rar,fe 5:0 4io 32o :: __J ■ 1 » J . _ f -> 8 f ^ 2 k___> f y 1 3 I ♦ 0 m r 1 ■ VS. Overpaid Combos X To p pair Ct>VH.b&S X set Combos X TWO Fair Ccmops X call £V Profit Fold TCtfiL: n r vs. Pot: 20 villa Li*, iiits 4 y-s behtp-ct 4 y~ ^ Pot Odds: : 1 Filial -pot wokW be: _ Your call would be % of tJ nt fii'vflLpot. Ou ts:_ Odds.: 1 1 Profit: i_Makeup-4_ Call =ev FdLpI x / Pot: 4 #3 vLLUabv bets 4 y~^ A^ouiAt belun,i?l -4 _? S Pot Ddcta:_: 1 Fu/l£iI pot '//ouL^ be: _ Yowl r tali. would be ^ of the ftvL^L pot, Dut£;_ e^ccltLj J Orfds; : i Profit: 4_Makeup 4_ □ Call =^v F old Pet: 4 VtLLfliA bets 4 y~ 5 bebZ-iA-d 4 ?5 Pet Odds:_: 1 Pistil pot would be: _ yei^r ohLL would be % of the ■flj'tflL |n7t. oddz: Du ts: equity ^ call =^v L ] Fold f -\ 3 . ♦ r i a' r -\ 5 l±J J JrJ t - \ K r — ] i VS. t - / 1 k' \JL + 4 ^ j 4 1 \. —j Pot: 4 SO Viliam bets 4 y^> A^uouWt belui^d 4 y5 Pot Odds*: _: 1 FlM\i pot would bfi:_ your tflU would be _ of the fivwl pot, Dut$>: _ e^wiLty £_ Dddsi _: 1 Profit - 1 _ M^fec^p:f_ □Call =ev Fold i£l ;ATv ASifefAAi A?* I A&j:A^i| A4&i A3*j A2s £7s Kfc K5s K4s K3s K2s J t JL_J L Jl Jl J ■ . JQIi|jQTi| Q=s \QU [Q7i Q6^yQ5s||Q4ajjQ3^lQ2sj KJ& QJo iJTi! JPi l! Jfis r* J&5 J5 j iJs JSi Jl% _ / JL k jATo KTo OToJ| jT'i |A9o K&c- Q9oj| j9o jjT9r |T7s T6i lis T4? T3i T^s j II , . JL 9Ss 9 ; 3 9fe 95s A8ff KSc QS?||j^p ISf 93c j t y /i 3fo S5s Ps ■A?o R7o Q?oi J o T-q 97o S~tf ' &i| 5s A5* A4o K4* I *| If !% roD 5 c 65c 55 H 92s 83 s L _ J 82a In ZJ to 72s L n J 63 s \62s FJ * i 43s IL 42s 33 32 s 32c fej ccmfces in pr-:':?p crtn^ _ _ 1 1 . 6 % Top ptf ir Coiubos x - set cc*ubp^ ■ x - TWc Pair CtfHA.b££ x cverpetLr C^^vubos X call — EV J VJ A * h K 4 j Profit Priflt- - Pmfut = Profit — Foie 1 ! Totfli,: ^ s r -i /■ \ 6 9 5 3 L±J , ♦ , , ». j f \ J VS. Y ’7' ±j LLI LtJ LL pot 4 &o Villain btfs 4 4^ An^pui^t behlud 4 '-L 3.0 Pot Oddz. _■ if Fti^nLppt would he-_ your daIL would be % _ of thi fungal "pot. Outs:_ e^ity y p _ Odds,: ; i Prefit : f_ Mfll££up: + call =bv Fold (¥1 (¥1 ¥1 fsl •f* l * j , ♦ , k_L> ^_Z_j 7 ' 8 vs. ' a ' 7 L 4» , *f* ± Pot: 4 &0 villain, bets 4 4 S Amtot behLud 4 1^20 Pot Odds,: _: 1 Flb-vClL fOt WOuLd hi;_ your tfliLL would he % _ of thi flirtjjLfsfit. Outs:_ equity ^ odds,: _■ i Prefit: 4 __ Call =ev Fold fel f9l f^ 5 [31 Lb *- ■• j f~ -"A r-> ' -^ f -A 9 9 VS. A 7 y J , 4 , ♦ Pot: 4 &D YiLUtlvt beti 4 45" Am.cw.Kut behtwd 4 l^LD Pot Odd s:_: 1 FwHlpGt would bfi:_ Y our geLL would he %_ of tbs flmal put OutS:_ E^uLty *g Odds: _; i Profit : 4_ _ Call =ev fold r-> 6 r -^ 9 f^ 5 f-^ 3 ■f* L J * , ♦ A >> ■ ^ ' E ' a VS. ' A 1 ♦ lb .♦J \ / Pot: 4 &O vULrIku heti 4 4 5 A m. o u w-t b t h. i w rt -f 1-2 O Pot Qdd£: : 1 Fii^Pl pot wdwLp! bz: _ YpuK £3 LI WOwlpf hi of the. fiviRl pot. DwtS:_ Equitlj % odds: : i Profit - £_MP^wp:+_ Cfl LI =£v Fold A-o K7o Q-q Afoip^tofiojjjfio : T6o 96q Sfopfid |b Q5o J5o T5o= 330 I 85-0 A-3& KJd Q4c J4o T-3* 34o 84o No I (No 54$ >1o: 1 6*0 5JC- jA3c X3o Q3ej|J3o 13 d 93»j| S5o| ' T2o 92 q j 82o j j ~ 2 q 62 g '?S :-:ral'C! if pr^Vp ^nrr A2o K2o - Q2o J2o ^‘j K4i K3i X_L Q4 S 03 i 01: L It J J4| e Jr J^t j:i 74!: © T2s 9-i 93s 84s L J M '4s : m 72s i. 64s | s _ / i63s| 62s 54s 53s |52a 44 43s 42s 43 o K j \JJ j 32:. 4 2o }2o 21 _ 31.6% Dv't'f^aLv .Strm-0 hi set draw G-om.h&Z X CoMA-bps X Cembtfs X _Cembps X CflLL =ev A ♦ Profit - TVfrflt Profit = _ — Fold TfltflL: Equity on the Flop ! he equities on the flop are calculated with the Rule of Two or Rule of Four depending on if a turn bet is expected. If you expect to face a bet on the turn, use the Rule of Two as we have been doing already for turn math. If you expect to get the next two cards for the calling the flop bet, use the Rule of Four. Ihe Rule of Four says to count your outs and multiply by four to get your percent chance of winning. I he re are refinements to this rule that we will cover later. Calculations on the flop are more complicated than on the turn because there are two chances to hit the needed outs. If the needed out comes on the turn, there is still a chance for the river to change things again. I here are cards that can come on the turn that will add more outs on the river, these are often called outs to outs” or back door equity. Mathematically they are just a few percent change in equity, but strategically they can mean a lot more. As an example of back door draws, imagine there are three different suits on the flop. Matching one of the suits on the turn and then again on the river makes a flush possible. This flush is called a back door flush. You can also have back door straight draws, if your hand combined w T ith the board makes three to a straight, the turn and river can combine to make a straight. So if you have pocket Sixes on an A57 board, you still can get a straight. We simplify back door draws by saying there is a bonus 4% for back door flushes and 2%-4% for back door straights. Three cards to a straight get the 4% bonus, for instance 456. Ihree cards that have one gap that must be filled gets a 3% bonus, for instance 679. Three cards that have two specific gaps that must be filled get a 2% bonus, for instance STQ or AKJ. On most boards there is chance for the turn and river to bring three of a kind or other perfect run outs. These are very rare and do not change equities enough to be worth accounting for. We will only look for the major back door draws of flushes and straights. These bonus equity amounts are only for the hand that is behind and counting outs, not for die hand in the lead. If we ate drawing to a straight or a flush and suspect that the Villain could get a full house with a single card then we need to account for that. 'Ihis ’would happen w r hen a player has three of a kind or two pair. "Ihis player is said to have a redraw. A set ins seven redraw outs on the turn and then an additional ten on the turn to get a fill I house. We need to discount our draw's equity to account for the redraw. Reduce the draws equity by 30% of the total equity. To do this, calculate your draws equity versus a simple top pair or overpair and take the 30% off for being against a set. Note that you do not subtract 30%, you reduce by 30%, Similarly, the draw' loses 13% of the total equity 7 versus two pair. If you suspect the made hand has either two pair or a set, reduce by 20%, Some outs are only a marginal improvement, like making a single low pair or a single pair becoming two pair, Ihe Villain usually has similar redraws against these small improvements. Because of this, we give back 4% percent. Ibis is a small adjustment that does not apply to strong draws like straights and flushes, only to two pair and pair outs. If a set is against a straight or a flush, they have seven outs on the turn and then ten on the river since they might pair the turn card also. I his can be thought of as 17 outs and use the Rule of Two to arrive at 34% equity. ^ Add-ons to the Rule of Four ^ Back door flush draws add 4% to their equity Back door straight draws add 2% to 4% to their equity Draws give back 30% of their equity to sets Draws give back 15% of their equity to two pair Draws give back 20% of their equity to sets and two pair range Small improvements should discount 4% at end Sets that need to boat have 7 outs on the flop then 10 on river. Call this 17 outs and use Rule of Two to say 34% to boat by the river. Pocket pairs that need to boat or pair the board are similar to the sets. H_P Lets give these a tty. f ^ 10 f -^ 7 f^ 9 JL A 10 VS. 7 8 V_I_r 1 * JlI L # outs. % _ vs. % in the above, we have all the straight outs for eight outs. Trip outs are another wo outs, and two pair outs are three more outs. Thirteen outs times four is 52%. the two pair outs are not strong, so we should give back 4% making our equity 18%. The actual equity is 46%. We can keep it simple by rounding this to 50% equity. Fifty percent equity is 1:1 odds. / --s 10 L_i 9 JL A 10 VS. 7 + 8 .+ # outs /? * 50 VS, *5$ K r- 8 f h_ 4 — 7 K K VS, 9 10 # Ihis is a best draw versus best hand situation, there is the added feature that the set has aback door flush against our draw. More importantly, the King of Clubs also acts as a blocker to the flush. We will compensate for the blocker and redraw. Our outs are eight flush cards plus six straight cards. We have the luxury of knowing our flush is blocked. I his is fourteen outs, the Rule of Four says to multiply by four. Our 14 outs is 56%. Against a set, we need to give back 30% of our total equity, thirty percent can be a challenge to calculate, so we can break it down into a simpler problem, fen percent of 56% is 5%. We need to give back this 5% three times. I his is a discount of 15%. I hat takes us from 56% to 40% equity. The actual equity is 41%. ( -v-v-"i r~ - K * L ^ J |l ■ 8 L. “ , , -i i*-^ 7 * <• - ■> (*■ 1 K l" > E V*5. f ^ 9 10 4* l_£_j A jt. 0 0Lit£ /*#" f. W V5. f *0 IS . / ■ Here is one more below. r — \ 7 L *7" , f \ K v L J r — 5 * L_-_J A K VS. 17' 8 1 + . ♦ , f 0 . _ vs. % The pair of Kings is ahead, so we count outs for the 78s hand. Our outs are two Sevens and three Eights, 1 hat is five outs or 20%.'l he two pair outs are weak, so we need to give back a couple of percent, call it 16%. Flopzilla puts us at 18%. A ♦ -% /" 6 ♦ A * K * 7 4- e * # OUtS vs. ?. r 1 -h. 10 — 7 '9' y. .♦J V r -^ A t 1 10 vs. .♦J /■-’Vi^ T a 8 # OWt£ «. vs. % 6 A ■S -y r' _r-' ' h . 4 4- J * J vs. 7 * 7 ¥ # 0Ut£ VS. 7o A •f. “t, -^ f a „_ j + 7 JU K ¥ 3 7 A " % ' I /- \J r .J*,, 10 ♦ A A K vs. Q 9 * A 4* K 4* vs. 7 ♦ 8 ♦ 7 4* 8 ♦ vs. 8 9 v, JL f outs # euts # outs vs. %. vs. vs. % s I f -** 9 EE VS. 8 # £>kt£ % __ V -S- % i*-1 J *-\ 7 *-H 7 J A H Q ♦ l._ rJ VS. /-*1 A / -> K A w_ : _ j \f OWtS % J A 7 7 ♦ a ♦ vs. # £>Wt£ % A . *. K % r*-“i K JL r - •>. 8 A b... ■ _d r-*i 7 K _;_ J (¥1 j 1 * - —*i K VS. [91 r i 10 A t_:_ i u_:_j * L_J •f* i_ j # OKtS _ V*S. % f -h 6 y. r -^ A ±- I 1 - K A 'el ’? 1 VS. ■ i a ?** > j L_._J A ^___ $ # OU.t£ b_j * l_:_j % _ VS. % f - •> 6 y r =—i A 1 % _:_/ f -*1 K + l x j ^—*t. 6 F 1 "" ”■ 7 VS. a' fl i L ^ ^ L ___ J # DMltS % _VS. % Hand Versus Hand Type In these exercises, we know our hand and guess the Villains hand type. Sometimes all the hands of a given guess will have the same equity, sometimes th ey will 110 L Choose whatever specific hand for the Villain you want. Do not worry if it is a different choice than the answer kev makes. As before, write the j j hand in the two empty boxes on the line marked “outs*' Let s do an example; f -s Q f -^ f -\ 4 L + A s - <c o vj / - \ 9 r -^ 9 iJv.de.- J* “j L 4 fiJvLi 'n Hr-flw # outs_ Our set is the current nuts, but we want to know r how it does against a combination draw: 4h5h. Counting outs, it is nine flush outs plus six straight outs for 15 outs. Rule of Four says to multiply by four to get 60%. Ibis draw is against a set, so we need to discount this 60% by 30%. Ten percent of 60 is 6. Triple that to get the full discount of 18%. That puts us at 42% for the draw. Flopzilla confirms this for 5h4h_ The other hand of this description, 7h8h, has 40% equity. The 5h4h has a little more equity because it can make a straight flush that will not b e beaten by a redraw. f -^ 9 t i Q y VS. 4- ■!* l_ ■■ ft Will w # out& 7Shh /5 g 5S vs. ***£» Calculating our hand versus a variety of hands on the same board will give us an idea how our hand holds up against a variety of possible holdings by the Villain. \ Q A <3 * A -J U i *J v) Cntv 1 * tjwAir VS. + F-U*£h yy # Obits %■ VS. f. [ 9 ] f9l 4* L * J v.s, CTpfiH. evader # out s *. VS. %. VS. FliJt'i ■! draw # owts *■ vs. ?£, VS. OvlerpaLr r 1 -S 9 r-' 9 i. * j ,,_ Pfl&teet y.fl i-r bfrlcuv TP VS. S£t # owts # $ OKjtS vs. g, vs. vs. £ M M M * # * ■9 1 * * * * * 'IP ■•■####### Hand Versus Hand Facing a Flop Shove ki this section, we are making a call or fold decision when facing a shove on the flop. Draws have a lot mote value on the flop because the) will get both cards for the same price. /-\ 4 /-s K fel l±J /-\ 6 f -\ 6 VS, f -V A 9 L L Vtfc 4 30 villa ttv 3 h &v &£: .f 50 Pot oddii___ : 1 Ftafilpot would be:_ Your &hLL would be % _ of the fu/usL -pot. OwtS:_ Equity odds: _^; i Profit : i_ Call =ev Fold The set is ahead and the draw can only w r in with a flush. Notice this is an Jr overbet, one of the few times so far that we will be getting less than 2:1 on our call. Find the pot odds first. When we start hunting for “$50” we find only our Villains bet. There is S30 in the pot. What percentage is S30 of S50? Double each and we have 60/100, That is 60% or 0,6 times the bet. This means we hunted up 1,6:1 on our call. The final pot will be SI 30, What percent is S50 of the final pot? The fraction 50/130 is ugly to work with. Lets change the final pot to be SI 25 instead of SI 30, We can divide everything by S25. That makes S50 divided by S2r> into 2 and $125 divided bv 25 into 5. This 2/5 is 40%. j Because we are going to discount our equity for being against a set, we get to count all nine flush outs. Nine outs using the Rule of four gives us 36%. Because we are against a set, we need to give back 30% of the full amount. This is just the way the math works out. Calculating 30% of 36% might be too difficult. Lets discount 33% instead. One third of 36% is a J 2% discount leaving 24% total equity. The exact equity is 25%. this puts our odds at 75%-25% or 3:J on the call. Ihese odds are much worse than the payoff of 1.6:J, so it is a clear fold, in the same way, we look at the fact that w r e put 40% of the money into the final pot and we only collect 25% of it back. We must fold. Even though we already know we will fold, w r hat is the profit or loss on calling? Since we are donating 40% to the pot and collecting back 25%, that means we are losing 40%-25% or 15% of the final pot. Id do the final calculation of profit by calling, S120 is a nicer number than S125. Id get 15% of SJ20 we will use two steps: Calculate 10% then 5%. Our 10% of SI20 is SI 2. lo get the 5% we take half of this SJ2. We add Si2 and S6 to get SIS. We are losing about S20 on average when we make this call against the set. r A 6 L*J Pot: 4 30 villa 1*4 £. km/gs; 4 5"0 Pot Odds;_: 1 Fulfil pot would b£:_ Y&uk ceLI would be %_ of the ftMil pot. Outs:_ ^wky^_ _ Odds: _; i Profit :i__ CflLL =ev Fold X r Pot: 4 55 Villain. .Skovgs^ 4 40 Pot Odd$: : 1 FlirvflLpot would be: _ your geLL would be % of the ftvutl pot. Outs: _ equity ^ Odds: : i Profit :£_ Call =ev Fold t * 2 . * , 4 ' 9 ' f \ J r- \ j ► vs. '-^ a + -^ a V, Pot: + ±2.0 vtLLa in. s k-sves: 4 i 3 0 Pdt ©rids:_: 1 FmaLpot would be:_ your kfliL would be % _ of the pot. Dwts:__ f 0 Odds: ; 1 Profit : £_ call =^v Fold /■ ,B 'l 4 [6 [3l .♦J > + J f - \ { - \ 6 A VS, 5 5 LLI A Pot: 4 &Q VtLLa m. Sk©V£s: 4 ^0 PCt Oddis.: : 1 Ftirt-flL pot wowLci be;_ Yd«k ectlL would be %_ of the f£n.«L pet. OwtST_ f a _ oeidsr _; i Profit :±_ call Fold I 11 l- r ■•■'L • nrjiTi 1 ■'-L i. \ 6 5 6 * J L ♦ , JL >._;_J 5' f 1 5 vs. f -1 7 5L 4 1 jr. Ppt: 4 15" £3 vLUfl t-a £ >10 V£s: 4 ISO Pet Dl^dS: : I HvutL pot would bsi_ Y our would bt % _ of the flvual pot. OwtS,_ ^_ Odds; _: ± Profit : +_ call =ev Fold V ^ Petr 4 25 vU La i\& s Si oves i 4 20 Pet Odofs:_: i pot woiiLd be:_ Y^ur kHll would bt % _ ofkht fmfll pot. Outs:_ Equity £ Odds: _: ± Profit : i _ Call = ev Fold f ' 10 111 6 VS. A K jL JJ Pat; 4 75 Vi lla in, o\/t&: 4 00 Pat Odds: _: 1 Fmal pot WQlA.ld b£;_ Y our cnll wouLd he % _ of the flkuU pot. Ontsr_ % Ddd£: _: 1 Profit : * __ call =ev Fold \ r ’ 0 ’ r *\ Q J .* J ♦ k--J 2/ li id lio VS. f - a ■j' 'JL Ijl JL Pat: 4 ±20 vli La U 4 - s *1 0 ves : 4 S' 0 Pat Odds: : 1 FmaL pot waw-Ld bt: _ your cpril would b£ % _ of the fl^uU pot. outsr_ Equity £ Odds: _■ i Profit : *__ Call =w Fold vs. Pot: 4 ±05 vt-L La inn ,3 kcves: 4 35 Pot Odds; _: i Fb^flLppt wpulri be:_ Your &£tU would be % _ of tke fwftL pot. Orfdsr Ou ts:_ Equity % : 1 call "Profit : i. =ev Fold ■V ^ K 2 7 * V_^ vs. f*-> A f -1 Q . ♦ , Pflt: 4 £0 vLLla trt. 3 koves: 4 S 0 Pot Od^£: : 1 FtiAtfl pot would be:_ Y our &hLL would be % _ of the fUwl pot. Outs: __ 0^u£ty ^ Qdd&: _■ i Profit ;+__ Call =ev Fold Pot: -f &Q VtLLfl ik. s. hoves: 4 &0 Pot Odds.;_: 1 FLkaL would be:_ your Mil would bd % _ of the fiv^ul pot. Outs:_ e^ixuty j a _ Oo trfs:; _; i "Profit : i _ call =ev Fold y t 7 F 1 * K t ) 4 i * . JJ r"-\ A f - A VS. f-s fl y-% J JL # Pot: 4 55 vlLLu Ik *s kcves: 4 40 Ptft Odds:_: 1 Fb%£iL ^pt would be:_ your Mil would bd % _ of the fiKiiL pot. Dw.ts.i_ f g _ Odds: : i Profit : 1_ Call - =ev Fold \ r 4 25- VtLLaLw, .Shoves: 4 20 Put Odd s:_: i Fli/L-fl L pot would be:_ your tflLL would be % of the final p cut¬ outs:_ equity $_ Oriels: : t call Profit ; i. =ev FoLd r -i 6 r -i 10 ♦. r -i 7 , vj r * r f - 1 f -^ Fa 9 JiJ V<S. 6 ^L. 7 A PUt: 4 30 vlLLaln shoves: 4 40 Put Odds:_: ± Final pot would be:_ Your eftLL would be % _ of the final pet. Outs:_ e^u-Lty ^_ Oriels: _ : i Profit : +_ Call “=^v Fold 3 f *»i 5 10 ♦ JL f - 5 A VS. r-1 J f -*i J JPJ 1 ♦ t_/ Pot 4 55 VtLLam- .shoves: 4 45 Pot Odds:_: 1 Flw.PI l pot wonid be- _ yoitr c.nLL would be % of the ftw-ctL pot, Outs:_ ^liLtlj ^ Odds: : i Profit : 1_ call =ev f old A 8 . +. 2 „ *T* , r -i p*- K ±. o vs. 8 p- *■< POt: 4 4C vlLLarn. shoves: 4 40 Pot Odds:_: 1 Flw.uL pot would be- _ Your miLL would be % of tbeft^ciLpcJt. Outs:_ Sanity ^ Odds; ; j, Profit : 1 _ call Fold Decision Versus a Hand Type Shove on the Flop The following problems are the exact ones we did before. Ibe only difference is that now r we are all -in on the flop instead of on the turn. Having two cards to come instead of one improves the draws, basically doubling their equity. This means many of hands that should have be folded on the turn should be called i on the flop. Opta tv^dtr Call Fold .1 i-i-t ■fvpfv. ppt: Pvt: #320 V^LflU". Shoves,: # Zl[00 Pot Odds.: __ i Filrt-ftL pel wewLtf tit: _ yewr cJilL would bt % _ •E>f th; xst. 5 _ Delfts: _ : ± We need the pot odds. YVe hunt around for as many 11 £200” as we can find. There is $200 from the Villains bet. There is S20Q in the pot w r ith S120 extra. What fraction of £200 is SI 20? Cut them in half and it is just like S60 and S100. That is 0.60 more that we were looking for. Add that up and we are getting 2.6: J on our call. The final pat will be S200 phis S200 is (400. Add the original pot of S320 to make S720. Lets call that $700. What percent is S200 of $700? I his 2/7 is an ugly fraction to work with. If we don't know what 2/7 is, we can use the bracketing method by increasing and decreasing the denominator by one. the new r fraction 2/6 is 1/3 is 33%. The other new fraction 2/B is 1/4 is 25%. We know 2/7 must be between 25% and 33%. This is just an approximation, but the average of those is 29%, w r e can just call it 30%. The real number is 29%. Our eight outs times four is 32%. This is basically 66%-33% which is 2:1 odds against. Return from the pot is calculated by 33% of S700. For every three SI 00 s, we get SI(X). The first $600 brings us to $200. The last SI00 gives us another S33. *320 VcLlflurtr Pot odd$\ j£-»t ! 1 wtwUX. m Your cftlL. would Ite % M of tilt i i^al pet. putt:; S* Eqidty ^ 33 RefcKfi^ -from ppt- ^ -1 Op^in, tv^dir x CM Fold We should make this call, but it is very marginal. We are putting in S200 with the expectation that overall w r e will pull out S233. Ibis call will make little money with huge swings, 'lhat is poker. mdkf pot - Q.y-5 VliLfliirt, ShcMfi: 4 1 OQ FLusk draw frt Ortas; - =i Ft^-aC pbt wwaUjI be: O^Q \ J Ypitr eflll wpuLol be % k Ppt- 4120 £l^l£)t vULaiirt. sln(Mt£: 4 ^O PotC-date;__ :i Fi-M-nC- pbt would be; 0 (7 II yr^-r caLl w^juLlH be % oftheflAfiLp&L FOtpt OKttiS Ifefftu riio, pet: 31 Fold qwtes 4 ktttu rw- frfi#*. petr Pp!^&: ;l , 41 DO Pocket fsfltr v[iLfliWi Shp'y'ti: 4 30 bdt^W TF 5, PetC-dcfS; __: 1 pbt WdwiLcI be.; O 1 { 1 ! J Y fiitf efiL£ wpuLri be TS of ttie fLiwL pot- Prti 412.0 Husk draw VLilairt. shau*L: 4 30 Pst PddS]_: 1 FliAfli *at would be; 0.(7 M Ysur ifliL wpicLd be % ^ Ulr of thcfEiwl.prt. Ft>Ld PLiiS: Q ^kh^ftwupfltr ^d£: :i FO"lp( Plit&r ^ Return frptK pu-t; ^ds; 11 42.00 Hush draw vtttaw. SHcvss; 4 60 Pet : 1 FlvuSi upt wouLd b£: f' fl M Your tfl U ^'Pklei be % L ^ IUU (fthtff^aLppt. Bfc Ppt: 4 Pocket pair 3.5 hf.lqw TP Pet Ddste: : i FLiA-flL upt wpwid be.: ^ Ll YD ^«". ,S — hi 1 FOLW Oyks.i J Ri£tw rvL ifr&ito. pet: :1 FDIW Puts: Q E^Lty g. ISjrtUrVt pet: Qdd £r ; 1 mr a&W y Pot- 41 25 ViiLflin, shoves: 4 *)£> Ppt C'drfS: _ i 1 Fifc^L wptt-Ld hi: _ ypKr tflU WpkU?( b' % of t^i fi^L pot. Diets:! S E^uLty £_ + V*+m. pptr_ ■Orf^S-" _: L DpSi/t + Flush drftw CflU. Fold Fpt: 4200 Flush si raw v£iU,i ^ She ' /Ss: 4^0 Pot Od£(£:; __ [ 1 Fi-w-Et pot wowl-d be: y pic t' eflli wpuLrf bg ^_ of tfrie ftwrL pot. Fold DL4t£: ^ E^Lty £_ F^itKrki. fvO*n. potr_ _ii Ppt: 4 ytiLci^ shcve&= 4 Pot Dcltfs:_: i FlivSil Tipt wpie-Lol hi:_ YCKF tflU VJPHle! br! % of th? ft,k^aL ppt. Diets: ^ ?_ Seetw rM. Fj-4+m. pot;_ Pddi; _; i Flush dr&w C-flll Fold Ppt- 4 50 ViiLflirt, ShpVts: -$-Q Fdt Oditl:__ : 1 Fi-yi^C pot ^vOKld be:,_ ypitredLL w^uLd be % _ of tloe ft^L pot. Dl4ts;i+ ^ulty $_ ftietMrM. frfiin.plrt;_Pdd&r _ ; i ■^1 J* V&w + FLwsh draw C-flll Fold Pot; 4lSO t sl^iot VtlLOirt.Shm/te:^ 4 O Pot OrfiEs,: _ :1 Flw 4 ^ t>bt WBwid be; p.H Li Y^wr weald H % 0 f ttae fLMLppt. apt^ Pet: . * 3 ™ r Vu.1 Sin- Shove*: ^125 £lrt,der Pot odds;-:i FLs*fl<, Tidt would be: PQ II ypwi' efllt would be % of tine flwfll pet, Fold Out*: 4 ^i«ky£ _ tej£tu rifl- firfi-iv- f} 0 t: Oddi: :1 Fold out*: 2 ^«£ty ^ Rjftunrt- t^OVu. pot: Oddi: : 1 opm mder Ppt - 4 4 oo 4 VLiUS ■SkiP'/fS: $2 5 " O' Flush draw Po+ 0flWss -— [ 1 Ft*uat fdt would be: rvo M ypLir tfl LI would be % j *fttitflimLprt. ^ , jJ _. . pot: *400 JPDfiteet f>ai,r vllLsiK ,shooes:^ iO£> feLtfW TP Pet oddi- __ : ± Flfifli.. set would be: P.n II Your tflLL 'wf^i-d be % flftheftwfllpet. Fold CM)tS:lS sanity ‘S l^umfirwupct: Oddi: 1 ± Fold outs: ^ tetum ffwu pflt: Oddi: :i opeiA, ' " ■' : " r: ' r VLiUiiut shcvw: 4 2 0 £> ektder potDdds; :i FLwUIl "0171 would be: P,Q [ LL Y'oiptr eoLt w&uld be %■ of the flwaL pot. e^ut shot p et- 4320 4- viiLdiio shove*: 4 ^ Hush draw prtDfi| ^- :i f LvuSL 1 -flt would be: f* fl | Your enU would be % ^ MUU fffttieflwaLpet. fOld Outs: g fteturnfvww pot: Oddi: : l FDlW out*: 13 E^lty £ te_etu.h^ ^Vo#u. pot: Oddi: :i Pat*. 4 y-Q Hush draw vataUshate:# 40 Pot Oddi: _ : 1 HiA^L ’aot wouLd bg.: _ YDKr tflU WOKl-d bi % of t'rtt fLiAtfL poL Outs: ^ £_ Oddi: ; 1 Fc±- 41 DO VLiUflin- ShiOV££: 4 <5 Q Pot Oddi: __„ l i Fiw-acpot would be; your c-a Ld would be $_ #f the ftr-oL pot. OU.t&: IQ. s^ttfty £_ leetK rm, |V*rtt, prt;_ C>ri^S; _: 1 Slut FE> [ i call Fold call □ Fold Return fv^nu. pot; Dvtr cards. cM Fold Return friwvippetr <^ut shot CM Fold Pot-. 4 JQ VilLpitf, ^.IrtpvSS.: 4 40 Pot odds.: _ : 1 Fli^3L li, 7 t would bf: _ Your tali wo Kid bi ^ of ttit fLw*H pot. Duts: & Equity £_ Oddi: ; 1 Pot: 4 4 ^ viiiaiirt, sv.fMti-. 4 20 Pot Oddi: _: i F^l pot would be;_ YPureflLL wouLri b? ^_ of the fiWL pot. Dut.S: 4 RetkKvt frotu pot; Oddi: j i Hand Versus Range After a Flop Shove We are now going to combine flop all-in equities with combo counting. We already did this on the turn and the math is the same. Jr In this example, skipping the derivation of the pro lit and combo counts: f -1 7 f -^ A f -" CL 0 ■ 0 u V5. P } K V jj Top psdr ^5 C^kVL-boS X 50 Profit = t5QQ set 7 nnux X 0 Profit = _ 0 L^L-I V V\« v two Pair f Cfliwbos X 15 Profit — U5 MrftW C/jrtibos X tiO Profit = iOOO noo XCflLL ev Fold Total: We multiply out the number of combos by the expected profit to show how much that line is worth. I he dominated flushes are rare but really do bring in a lot of money for us. At the tables, if we think we are likely to call, we should look at the strongest part of the range. If we can justify' a call versus the strongest part of the range, then the rest of the range will be even more profitable, there is no more need to do calculations. Sets are the strongest part of this range. We see that at worst we break even versus the strongest part of the range. At the tables we would instantly call without doing any more math. in much the same w'ay, if we suspect that we are going to fold) we look to the weakest part of the range, if we must fold to the weakest part of the range, then no need to do the rest of the math. I his weighted average of all the parts of the range is difficult to do. You might w r ant to use you spare chips to keep track of the running sum. For instance, in this case we said that top pair has 45 combos and a S50 profit for about S2500. We could put S25 off to the side to remember the S25O0. We would probably call the set and two pair as break even. We would know the dominated draw r is rare but worth essentially the w r hole poL Add another S10 to remember the SI000. ff we had negative numbers, those would be in a different pile. Which ever pile, negative or positive, is bigger would dictate the call of fold decision. A K VS. f C a JL JL 4 k- ► Pat: 4 3-00 Villa Lrt. QVt &: 4 BO Pet Ddd$: _: i Ft l pot would b£;_ Your onli would be % _ of the. flftfll pot. Oh±£:__ Odds: : ± Profit : i _ GfllL =bv Fold r- 1 7 ♦ J P> << A . ♦, T ♦ L 1 J r-\ ? - 1 F*- \ TT rt 7 7 VS. K a JL Pet: 4 vt Li a LuSli o vts,: 4 SO Pot Ddd$: __: 1 Flia^L pot would be:_ your crII would be % _ of the fLufll pot. Outs;_ ^«sty % . Odds: ■ 1 Profit ; i_ CfllL = ev Fold , \l, .Ijicu 7 k ♦ J A . ♦, ^ a * L 1 J /■ \ M r-\ f -' r -^ rs A a VS. f - ♦ ^ Ql Pot: 4 ±00 vlLLrlw, s h eves: 4 Pet odds,: _ 1 1 Flirty i pot would be:_ your tali wow Id be ^_ of the fli/Lfllpot OwtS:_ equity ^_ Odds; _; 1 Profit : +_ Call =ev Folct r~ -^ 7 ♦ . A T , 4 , { - \ 8 /-1 9 VS. t -“1 K f -^ a ♦ Pot: 4 100 vlLUj s hives: 4 g 0 Ppt odds:_: ± Fin-wl pot would be:_ your *nLL would be % _ of the final pot. Owt£;_ B^ulty ^_ Odds: _: 1 Profit : t _ call =ev Fold IA o X ~c A 6 c. K 6 oj|Q 6 oj| J 6 o 76 c ASoj|K5o| Q:c. J:o |A4c |K4 cJ|Q4qJ|^4o- T4cj P4o| E4oj 74oj|64oj| 54c Tjo 33o 32o 53o E2c ""2c 62c: 152 75s |[ 74s 735 L J 72 s 64s 63s 62s 55 5^5 53s 52s 54c 1 ^4 1 42 s i ■* 43c b- ,-a \ 1 -JJ 32s ___ . " 1 42c h?o iutobcs m picrlcp rang* 0* .'-fl 2L6*i f > 7 , * , A . a l r ^ 9 * * -1 9 ■ vs. t -i K f -“S a Tap pair set X Profit = oomtas X Profit — Two "Pair c^mko*. X Profit — bpkll.Lt'-fltgrf drftw X Profit = call £V FOLd Total V ' IT r ^ T Q A , ♦ , J ,*J ^N K ^ S j VS. a ✓-> 10 L£J *f* Ppt: + ±OD VtLLfl iw* have£: 4 S' 0 Pot DflWs:_: i fmflL pet would be:_ your call wouiL^ be %_ of the fU^al pot. Outs:_ £_ OctHsr _i i Profit : 1__ CflLL =ev Fold \ r T ±j K l*J Pflt: 4 1&Q ve-LLa iv%, *s haves: 4 s 0 Pot O^ris: : l FibuflL p£>t would be: _ your call would be % of the fu^al pot. Okta:_ Equity f ? Ortd.5r : i call Profit : i_ =ev Fold -"l ^ - \ T r — Q < K _ ►J J , * J / - \ A JJ f * K JJ vs. ? - a * f -\ 10 •3* Pot: $ ±00 VtLLsiIn J>hOV£S.: 4 Sc Pot Odds:_: 1 Flnfll pat Would be:_ Your c-hLL would be %_ of tbe final pot. Outs:_ equity y __ Odds: _: i Profit : 1_ call =ev Fold r——"i K fJI [9] ♦ "s_ 4 4 A f "S Q VS. /-^ a r •■* 10 k_ t _d 4 i_ t _d A 4 » POt: -f ±00 VlLla In Sh oves: $ So Pot Odds:_: 1 Final pot would be: _ your toll would be % aft be final pot. OutS;_ equity y Odds: : i Profit : £_ call =ev Fold QJs IQTi Q9i QSi Q s Q6s Q5i Q4s QJs Q T£.| 9S 0 u B) |&fe 15s L 54s | 83s K -J 82s k_ j A~e X'c Q~c Xoi T _ a &■ j &7o S~e' 1 i u lai 175s , i_ 74s _ ll* L . 72s A6o||K6q- iQ6ff Jlfo T6oJ 96c 8fiq||-Ga LJ 65s 64s 63s j • 62s [AfoJ |K5o j [Q5 d j [J5n T5a 85a 1 ' 1 "5a 65 a | 55 | 54s 53s 52s A4oj|K4o[ C-r jJ4o T4a H hi "4a ■ 64a 54a 1 44 i 43s ■-j 42s V |AJo j |iL3 o j |Q 5 o i | J2o T3oj ,95 a Sja T 3a j 62a 53a 43a | "k% JJ 32s [A2oj |K2oJ |Q2 o | j J2o J 1 1 T2o 1152o 11 B2oI "2a 62o tic? 42a 32a >> [9$ tEMubos m pttilap tm§t TO two Pair set Combos x Pair + Flits h dr&w COKINGS X Nut FT CflUlboS X call =sv a 1 10 A ^_ 4 Profit "Profit = "Profit — Profit = Fold TotfilL; V / r \ n *- 1 n t i. td, *T* Pet: 4 iod VL L la Lio. S In O'VtS: 4 SO Pet Odds; : 1 FurtdLpot w>nLd be:_ Yettr toil Would be ^_ of the fmel pot, Outs,: _ %, _ Odd£: _: i Profit : £ _ call =ev FoLd t -* / - f -* f - J 10 vs. a a * >±. ♦ , ± J Pet: 4 1QO villa tkt- & h ovts : 4 SO Pet Odds; _: i Fl v\&L pot would be:_ Yetir Ctflt would be ^_ of the fivuxl pet. Oats: Equity <f F _ Dcids: _: i Profit : £ _ call =w Fold % f f Pot: 4 100 vUifltw. •Shoots,: 4 Pot Od d$: : 1 Fl^L y>$t wuLrt b.£: _ Your tail wowLd b£ % of the fmfll pet. Outs;_ e^nlty *£ Odds; : 1 Profit : *_ call =^v Fold KSilKB* K"s Kit KH KH K:s K2i |Q^jjQaj Q?s Qfoj Q7s Q5s Q4 5 Q3s Q2s A4o| |K4o|[Q-: tel T4o Dio teJ 1 *■ " 1 54o| 44 | -H fel fej J3o T 3 o ^j 93 0 S3o "j0 S® iH 4jo| £2o S2a ^2a fi2o 52o 42o 320 I ciMnbos mpfeibp Jisfe f -* 9 J. A ■■ ™ 3 *■ " j r % 8 + ^_I_* * A VS. f ' a r -> a A, St t combos. x - pr *i lt opejA, e^Uer combos X Profit TWO Pfli-r _ CokvlIjos X Profit C-flLL — EV FOLd TotflL: Hand Versus Hand on the Flop with Implied Odds in these exercises, we are no longer all-in on the flop. Ibis means that we might not be getting the director immediate odds to make the call, but that if stacks are deep enongh we can make up for that loss the times that we hit our card. Earlier we did similar calculations on the turn. I he flop is more complicated. We could call the flop and then get a free card on the turn, doubling our chances to hit. We could call the flop and then be faced with another bet on the turn. 'Ihe flop call and turn call are independent decisions. These decisions must be thought about separately. It is frequently right to call the flop and fold the turn. Because we do not know r ifw r e will get two cards for free when we call the flop bet, we should pessimistically assume there will be another bet on the turn when you miss, but a check when you hit this means we will be using the Rule of Two instead of the Rule of Four, even though you are on the flop. Just like before, the decision to call or fold is not as w r ell covered mathematically because it is unclear if we will get paid off when we hit. Ihe most we can do for sure is say that there is not enough in implied odds to draw against a given hand. We are also ignoring the other options of raising or bluffing since this is a math book, not a strategy book. r /■ \ 7 ' f ^ A vs. ' - ^ 10 fj’ *J F L _* If L T -J Pc±: 4 45" vtLLnbi, bets 4 40 Amount beliL^d 4 120 Pot Odds:_: 1 FlvmI pet wpkLd be;_ Y^nr £ftLL would be %_ erf the ftiA.nL pet. Outs:_ E^utty *£_ Ode Is: _ 1 1 Profit: j_Mflle£L*p4_ Call =ev Fold For the pot adds, 540 is close enough ta S45 to consider this a pat sized bet for 2:1 adds and thus our call is 33% of the final pot of Si 25. We have lots of outs, not because we have an incredible draw, but because we are only trying to beat Ace high. We have eight outs for our straight. One of them is blocked so we are back down to seven outs. Our pair outs are good for six more outs. We have 13 outs total. This is a monster draw, and in a game we would might consider raising instead of calling. For the purposes of this book though we will look at the math of calling. Later in the book we will look at fold equity that might apply here if we were to shove. Ibirteen outs doubled by the Rule of Two is 26% plus 3% bonus percent for every four outs, lhat puts us at 29%, lets call that 30%. We use the Rule of Two because we are pessimistically assuming there will be another bet on the turn. If we were to get a free card on the turn when we miss, our equity is much higher. Those same 13 outs by are multiplied by four to get 32% equity. Because some of the outs are relatively easily beaten, we need to give back about 4% but our back door flush is worth about 4% bonus. We call it 30% equity. Flopzilla puts us at 48% equity. At the tables, we would take the possibility of a free card into our call. The higher the likelihood of getting a check on the turn, the more value this draw has. I he Rule of Four gave us 50% equity. Earlier using the Rule of Two, we came up with 30% equity because we assumed we only get one card for this flop call. We should use the more conservative 30% equity on the turn and just consider ourselves lucky if we get both the turn and river cards after calling this flop bet. With this 30% equity, we want to convert to odds. I be ratio 70%-30% is 2.33; I and that is the odds we were looking for. With our call being 33% of the final pot, and our equity on just the turn being 30% this is a neutral call on the flop in terms of immediate odds. Since there is really no profit or loss immediately on the call, there is no makeup either. With the possibility of implied odds, this neutral call is one we should make. If we get a second free card on the turn, things aie even better. In reality, even though we have this equity, it might be hard to collect on it. For instance, even though the jack of Diamonds is an out for us, we might fold when that card comes if an aggressive player bets into us. These calculations of equity do not account for us having the poker sense to know when w r e hit our out. Doing the calculations w r ith full knowledge of the board w r ill help build our mathematical intuition so w r e can guess more intelligently in the face of uncertainty. Pot'. 4 45" villain bets 4 4 O Awlqvl ut bekLwci 4 £20 Pot £ : ± FivMAl JiCfc would b£; Y&U.K iTl-rLL would tie % of ike ■flt'UiL pot. Outs: ^uity }Q Odds: £33 : 1 FTfrflt ; f Q Mflleeup: 4 0 C-tlU =ev Fold Lets try another one. In this example, we would abandon the math very quickly once we knew what we need to know We will go through the mental math on this one as we would at the table. We will just do the math enough to make our decision. Pot: 4 4 5 villain bets. 4 +5" Awlquv\t t behLwrt 4 3>0 Pot Odds,: 2 _t : ± Flvlftl p.pt WpkLd be:_ your &&ll would be %_ _ of the filial pot. Ou t£l_ Equity ^_ Odds,: _: 1 Pir&fit: J_Mfll?£Hp:4_ Call =ev Fold We have nine outs to the flush plus a gut shot for another three. That is twelve outs, the Rule of Four puts us at 48% equity against a top pair kind of hand if we see the next two cards for this one price. If we see only one card, the Rule of Two would put our twelve outs at 24% plus a 3% bonus for about 27%. it is a small loss compared to putting 33% into the final flop pot. ‘this is fine because there is still money behind to justify the cal L Looking ahead, with only 330 behind, we will always call the turn bet if the Villain shoves the turn. We decide this with a useful shortcut. Notice that we would be asked to call a smaller amount ($30 on turn instead of 345) for a lai^er pot (3165 on the turn instead of $90). The flop call depended on a small amount of implied odds to work, but now with the reward bigger and the risk smaller, this is a clear call. Both of these calculations use the Rule of Two. Another way to think about this is that Villain will always call our shove on the flop or the turn. Ihis means that both sides will end up shipping this 545 bet and the remaining 530 in at some point. We see from the Rule of Four that each side has about 30% equity in the pot on the flop. There was 545 in the pot before the flop. "Ibis money is considered “dead money” and it is what we are fighting for. Because both sides have a huge amount of equity in the pot, both sides will be compelled to fight for it. This happens in Holdem that the dead money in the pot is large enough relative to the stacks that both players are compelled to go broke trying to recover their equity from the poL Neither side is making a mistake, it is just the nature of the game. Here is a final example that is common when we flop top pair, but expect that we are out kicked. 10 IT l -■ ,r “'i 2 ±J / - \ A JLI f > 10 % 'l- ± -- VS. ' - > 9 JL ? - % 10 Ijl Pot 4 2s bets -$■ SO Avuouvd: belied ■$ *)Q POt Odd^: _; 1 Fli^aL pet would bd:_ y our CrflLL weuLd be % _ of the ftwflL pet. Qw±&\ _ tquitij *£_ Odds: ■ 1 Prefit: i _Mateiutp;^:_ CflU =ev F old Lets go through the mental math. If we really think we are behind on the flop, we have three outs versus a better top pain We can also assume that the Villain will ship the remaining amount on the turn. Three outs according to the Rule of Two gives us about 7% on the next card. We want to skip ahead to the part where we calculate our required make up.. Villain is 93% to 7%. Lets call that 90%-10%. We are going to have to pay for nine losses for the one hit on the turn. If we multiply the Villains bet by nine, we get a huge number and the stacks are not that deep. If we think we are very likely dominated, we just can not: come back from that often enough to play on. Good hand reading can let us know when we are in those spots. As we are doing these problems, we are getting to the point that we should be able to take shortcuts like this to plan our hand. Ihe exercises are only a tool to become intimately familiar with the underlying math. Once we have built that intuition, we can start to improvise or just recall similar situations where you have a I read v done the work. i f - \ 7 t \ A VS. f*-1 10 r- 11 j JJ lv, Pet- 4 4-5“ VlLLbI**, bits 4 40 Pot: Odds: _: 1 FLu-ftL pot wptUd be:_ YDkK c-ftLL woulri be %_ of the pot, ou.ts\ _ Equity ^ _ odds: _ _; i Profit: ♦_M^up:!_ Cali Fold 8 9 f -s 81 , . V •;*•__-J Ijl r* - s 7 f 1 1 A VS. f -\ 10 f- *\ J L*J * l -J L*J Pet i -t 4 .tr vLUflti^ bits 4 4 Q Ayfrauvt-t bekwaol 4 3-3.0 Pot Odds: _: 1 Pll^siL pot wouLd bi;_ Your cfiLl would b i % _ pf tbe fLiAj?il pot. C^A.ts: _ ®vfcy x° _ Ode Is: __ : i Profit I 1 _Mflte(U'p:£_ call =ev fold /- s 10 .♦J 3 . vj 6 f -"’H A r \ 10 VS. f-1 7 f-% 8 L±J A L 1 j 4, Pot: 4 45" vLLLfll^ bets 4 4-5 Amount behi-^et 4 30 Pot Odds: : 1 Fli^aL pot would b £'. _ Your oftLL Would be % of the flr^Lpot. Outs:_ e^uL-ty ^ Oc(d£L ; 1 Profit: 1_ CCflLt [>ev Mfl J? (Up 4_ [ ] fold a' ♦ 8 *f* L - 1 J 4 A t_:_ J f - \ A f 1 ^ a vs. /-V 9 f -^ 10 l L±. ¥ ± _> Pot: 4 30 VlUhLi^ bets 4 25 bikini 4 3-QO Pot Odds,: : 1 T-lvual pot would b^i _ Your cfl Li would bt % cf* the fli^l pot. Outs.: ■— Equity ^ Odds* : 1 Profit: ^_Mflkeu.p :4 _ Get LI Fold vs. / \ T7 T 11 *1* L "b J 0 Jt _j Pot. 4 +5 VlUfttA bets 4 35 AALflkkrfc bcsi^rf 4 lie Pot Oddter : 1 Fulfill pot would be: _ Ywr cflll wowid be % of the fmoL pot Dw,ts:_ equity *g C-dds: : i Profit i 4_ CflLL =ev Mfltawprf Fold PCt: 4 35 vUlfttA beta 4 2ft AiHw.pwn,t tehti^d 4 i5e Pot od dfi; : 1 pin-aL pot wo^Lol b£: _ Yomr will would be % of the ft Aft L pot. £>u±£:_ Equity g oddsi. ; ;J_ ProfE-t : 1_ Mfltefup:#_ Call ^ev Fold Pot: 4 §■£> vlUrul bets 4 Aywouut behti/td 4 130 Pot odds:_: 1 pUvtfl -pot would be:_ Y&ur fifltL would be %_ of the fmaLpot. Outs:_ Equity *g_ Odds: _; 1 Profit : ^_ M«teup.:+_ CflLL =ev po Ld r-^ K r -=U ^ _ JL JL vs. -> 9 r - o> ^_ *T* k___J Pot: 4 35" vLiLfli-iA. bets 4 A«^-oui^t behead 4 HO Pot Odds; : 1 FlkoL pot wouLd be: your efllt would be % of the flM-flt pot. outs: _ Equity ^ odds: : 1 Profit : 4_ Mfftoup:±_ call =^v Fold J A VS. Pot: 4 35 bets 4 AmacuvU: beht-nd 4 £30 Pot Qddz: _■ ± FlkvflL y>ct would be: 1 _ Y &uf etfLL would be % _ oftki.fi fmflL pet, Ont£l_ Uejwuty ^_ Odds,: _; i Profit ’ ^_ call =ev fold \ f \ ft r-^ ft r 1 R o + . o o a' r-^ fl VS, to t \ 10 A j jL> p^t 4 so VLlLoit^ bets 4 20 A^vtou-i^t beiiLpLd 4 3.00 Pet Odds; ; 1. FiiA,f?L wouLd bfi::_ your mLL would be %__ oftki.fi ffruaL pet. Dut£;_ p Odds,: _ ; i Profit ; 1 _ Mflfe£kp:£_ call =ev Fold 10 . ♦. / - > A 3 r-\ 7 /-1 8 VS. /■ - % K r 1 4 — * 4 l_ i _ j L Pot; 4 4 O vULffift bets 4 AlW.DLt vit behuaol 4 t- SO Pot Odrfs;_: 1 PLrUlL pot wouLa be: _ Ycur GflU would be % of the pot. OUtM odds: : i Profit : 4_Mflte£wpr+_ call Fold K Tq [K k ¥j JL vs. Pot: 4 3^ vULcili^ bets 4 25 Am-ou^ut befr^d 4 iiD Pot odds; ; 1 fUa&I pot would be: _ your tflil would be % of the -flvml pot. Okt&:_ Equity ^ Qdrfs: :, i Profit : 4_ Mfitte£wp4_ call =ev Fold 8 4 5 4 VS, Pot: 4 55 VlLUii+v bets 4 40 beWi^-rf 4 Pot Odo Is: ^_: 1 Ft-kUiL pet wouLd be;_ Your e-fllL would be % _ of the -fmed pet, Dkts;_ equity ^_ odds: _i Profit : ^_ Mflfeeup:4_ Call =ev Fold R A •f* J A K __ VS. Pot: 4 30 vtUflu* bet£ 4 20 Anu5i«M: beh w*d # l±0 Pet odds: _: 1 Fmeil pot would be:_ Your tall would be %_ of the ftiA^l pot. Outs:_ Equity ^_ odd^ _: ± Profit: 4__ Call =^v Fold f - 8 s * J * -V 404 ^--J p 1 6 , ♦, f -\ 8 f 1 ' 7 VS* f ^ 9 f*-1 10 JJ ^♦J Pot: 4 10 vlLUsLa* beta 4 10 behind 4 iio Pot Odds:_: I FLiAflL -pot WOuLrf fa& _ Your c-rtLL woultf be % _ of the flAtfi, pot- Quts:_ Equity ^_ Oddi: _; 1 Profit: 1__ Makeup#_ Call =ev F old \ r 4 -\ O [to JLl HE* Liu a' t - s Q VS. f -\ A f-*1 2 ♦ ♦ k__J JL l T_, A Pot: 4 40 vLUglia bets 4 0.0 Af'H-OUyLt bdhL^d 4 000 Pot odds: _: 1 Fwa £\l pot would be: _ Your c&Li w&uld be % of the fliAfll pot. Ou ts:_ Equity ^ Ddd& : 1 Profit : 4_ Mfthzfup:4 _ □Call =^v Fold 8’ + J t 1 2 f“ -^ 8 A f -> 8 VS. 9 f - 1 9 ±J jlJ *]* Pot: 4 25" VlLLcui^ bets 4 Awjmtvt bfih^rt 4 Pot _: 1 Fulfil pot would be:__ Your c &.LL would be % _ of 1 the fl^L pert. outs:_ Equity £_ Oddi: _; 1 Profit: 4_M a'fituyA _ Call =^v Void \ f a' p *> A ^-\ 8] V * *f* i_> k' r-1 K VS. e \ 7 6 ' * t_ _j A L±J Pot: 4 vUlaiw, bets 4 S5 7 bfillL-kLi^ 4 !^ 3 Pot Oddi: _: 1 fU^eI pot would be;_ your e-sli wouLd be % __ erf the filial p£>t. puts:_ s^uitij ^_ Odds.: _: ± Profit: 4_Mflteeap:- - nCftU =^v Void r- s t \ R •F V JL vs + Pot; 4 J L 25" vtiltfitf, bets 4 ±5 4 lOO Pot odds: : i FlwM.1 pet WDklo! be;_ Y^itr eetLL would be %__ of the fl*uiL pot. Ou ts;_ E^Lcuty ^_ oddzi _ : i Profit ; 4_ Mflj?CUp:4_ call =ev Fold \ z' *J ♦ J b_ t _/ 9' f - 1 J VS, r \ 8 f 81 ♦ , ¥ J *T* >, - - ^ Jh* Pot; 4 35 Vt-LL^t-kV bets 4 Azw.i)wM,t belied 4 ISO Ppt Odd£: _: 1 Flr^fll pot would bfi;_ your e-all would be % _ erf the pot, Outs:_ e^wttLj ^_ Odds.: ; ± Profit: *_Mafee^ip:^_ □ call =ev Fold f ' K /-^ Q VS. J f - 1 10 •Tv ♦ . . ♦ , Pet: 4 VLUfltn. bets 4 SO behind 4 S5'C Pet oddi: _: 1 fU-uU pot WDitld bfi:_ your e^U wew-Ld b z ^_ erf the fLirt-flt pfft Outs.: _ equity ^_ Odds.: _: ± Pro-fit: ^_Mflfeeup:^_ call =bv Fold X r Pot: 4 55 vlUfl lia. bets 4 ’^5 AW-QU bfilUkL^ 4 zoo T> 0 t Od{(As.: _: i Fua£|(. pot WO\Ad bi:_ your tall would be %_ _ of tine ftn^L pot. Outs: equity %_ Odds; : i Profit: 4 Call Mdteeup: -4 = EV FdW f - A f- 10 V5. f- 9 io A * 1 ♦ , Pet: 4 J-0 villain. bets 4 55 IdfihLvtpi 4 ilC Pot Odds.: _ : ± Fl-^iI pat would be: _ Youv coil Would be oft *it ftn-PiL pat. Qw.t$.: _ equity % _ Odds: : ± Profit : J;_Mflfee^p:^_ call =^v rfold / v. / r-\ 9 i"-> 10 M JL Pot: 4 $5 vLLLacvL bets 4 && Ai'KflvLVl.t bfiMkV^ 4 9 O Fat odds: _: 1 f£miL pot would be:_ your tfl LL wai^Ld be Jo_ of the fli^t pat. Outs: _ E^wiirty Odds: _ : ± T'ro-fi t: ^_ Doall fold Hand Versus Range on Flop with Implied Odds 'lhis section is very Similar in format to the turn math with implied odds. We are estimating the value of each match-up and counting the combos to find out how likely that match-up is. At the tables we would almost never do this math out entirely. We do the math now so that our intuition is trained when we Jr get to the tables. When we are estimating the value of a match-up, like Af vs 78, we guess at the profitability of that match-up. lhis will be very rough. With deep stacks, we will need to make another decision on the turn. For this flop call, we are just deciding, “Will this put us in a profitable spot on the turn?” Let’s go through a problem. Pot: 4 %D villttUfl* bets 4 ■AkVi-PWl'Vt bfilflLI/Crf 4 200 Pot OtfidS:_„: 1 FUtMi pet would be:_ your tall wcwLd be % _ of the fmftL pe?t. QutS^_ Equity ^_ DddZ: _; 1 Prcrflt : t _ Mflfefi u.yA call n=ev Fold How much is this match-up going to be worth to us? the turn pot will be S2Q0 and 20% of the time it will be ours on the turn. We are paying S65 to lock up $40, sa we Lose S25 every time we call. Were we to do this five times, we lose SI25. However, one of those five times we have a shot at getting the nest of his stack. If we get the entire stack of $200, then that one time pay's for the losses and makes us S75. ff we always get the entire stack, over the course of five trials we will make SI 5 on average. If we figure sometimes the Villain properly folds when w r e hit, it will be a bit less than that. An alternate way to do the math here is to look for money to make up for the times we call and lose. We need to call S65 and pay' for four losses waiting for our win. lhat is S260 to pay for. Villain’s bet plus the rest of his stack pays for that. 'Ihe one time we hit, there is S80 in the pot and we will get that 20% of the time, so we can make S16 on average if we always get his stack. It is a different way of doing the math but same essential result. Ihe nest of the worksheet is done as before. It has been started here. TC'p 'pfTL-lf open- en-der Nwt fr» Sit f 9 J '6 „ V, 0 ■ ■ VS L-J L-J ^ Combos ^ Combos X Combes X _Combos X CflU = ev estLWA-CltEfl f^Stwm Esti-MAffted Return EstL-kViatCCl Ritum — Return FoLrf Total: r ^ A fj] Y] L. J A f - \ 3 V3. r-^ 8 P 1 -^ g ^±J dJ Pet: 4 &0 vlllnip, bets 4 -4*5 ApK-a wkvt behind 4 i2£* Pot Dddfii : 1 FCri/Ul L laflt WOuid b£; _ Youtr eftLL Would be % of the -flAflL-prt- Ofld.^L Cuts: Equity ^ : 1 Profit: £_ CflLl Fold Petr 4 && vl-LIpIia, bets 4 4/T Aw~Qu&Jt belied 4 lS'O Pc t odds*: _: i Fi-ia^L pot w&uld be;_ Y^uisr tdLl would bi % __ of the ftn-fll -pot. Ou ts:_ £_ Odds; _: ± Profit ’ 4_M£teeup:4_ □ Cflll =ev Fold r ^ A k vJ r ^ J , J * 1 7 ^-> 7 vj f - \ 7 |r% L ^ " VS. F T 8 t -> 9 ♦ Pot: 4 &Q villa wv bits 4 4*5" A^-om-vt bfiiiL^rf 4 i^C 1 Pot odo Is:_: i FlkUTl pot would be: _ Yow.r octLL wQuid be % of tbe pot. o uts : equity £ Odds: : i K: t-j a Profit::_ Call =^v MflJflSEW.p:£. X r /-\ o r-i Q o ♦ w-_* Pot: 4 ££> vlLUdiA- bets 4 45" beliLi^d 4 ~l-^0 Pot Odds:_: i Fli^L pot would be:_ Youir taU would be of the fli^fli, pot, Outs:_ equity ^__ Odds: _: i Profit: i_M£ifee^p:4_ Call = ^v Fold K7s K& Kis| K4s iGi K2i :■ JL J L_ J . J [ _J I J ,QJs I QTsj QH QSs||Q7 s . QSi Q5s Q4s|iQ3s Q2s ; Pi m J5s J4s J?.* r \ 7& Tte X?5 14s T3s T2s • l! , 95s li 97 s Mi 95s £7.s | 8.6s 85s -■ 94s 93s 92s £45 80 s 82s Ac K7c Q q T 0 ,"'e 9 0 So Ws 63s 62t ‘So 65o 55 54a 53s __J !A4o K4o J4o T4o A3c K3 d Q3o|i JBo T3o - AIo |K2o Q-oilJ2o l|T2o V2v I S2o \72o $2* 52o 42 0 33 32s ^•Ti 4*0 198 "rmhc? tn pisflop rmrs ■i 0 *. 31«- Tcp pair C-cmkoz x Two pair C-owAboz X Combos. X set C-pmbos. X Cf Ut shot call =ev 00 7-1 9 L*l Bj&titttfffcfrsl Return. BsttwLftte.il R£tn.r>v 6stkiv-atecl __ Return Fold Total: 9 ♦ . r i j 6 LL J f ^ A VS. f -\ 7 i*- s 8 A . LL * J L -_- j Pot: 4 vlUfllko. bets 4 && 4 200 Pot Oddi: _i 1 Fmfll pot Wowld b t: _ Y&u-r &#IL would be ^ j?f the flu^l pot, Ow±£:_ E^iut^j ^_ Odd$: _: i Profit : '_ Mfikeup:4_ □Call =ev Fold Q ^^ T f \ R .♦J J o LLI io f -i a VS. f - \ 7 f -* 8 4 I k — ± __j LL LL Pot: 4 %Q vUIaua- bets 4 Amount bfiiiL-i^d 4 200 Pet odd£: _■ 1 Flirtyl pot would be:_ Y^uiir £ fl LL wouLd bfi % of the fEn-fil 'pot, Oyt£: _ equity ^_ Ddd&: : ± Profit: ^_Mflteewp:4_ call =^v F old r - 1 Q r- m T r- -^ 8 ,*J J u i*j f ' A y . Y . v, vs. 7 8 ' ♦ Pot: 4 $0 vLUfllft bets 4 bfilurt-d 4 ^£i9C Pat Odds.: _: 1 Ftk^L pot would b t: _ Yt>u.r tflLi W0U.LM be % of the ■fLu^t pot, Otits:_ equity _ Odds: : i Profit: i _p:i_ □ Call =ev Fold F 1 Q F “1 T r- i ft 4 t—-—1 u V, u M f ^ 6 6' VS. f -\ 7 F ^ 8 4 I La _A P>ot: 4 90 Vi-Uflti/L, bets 4 £5" bgllLkV^I 4 Pot Ddcte:_ r 1 FtkUll pot Would bt: _ Yousr &&li would bt _ of the fii/ual pot, Outs: _ equity °s_ Ddd£; : i PrO^t : ^_MflfeCUp:4_ Call =^v .Fold KJsjjKTs. K$s|jK7s Kfe K5sp4a Os Os QJsljQTy QPs i QgsJ[QTs; | QfiajjQ5x]|Q4aJ[Q3£ Q2s KJo Q 7 q AT* KTe QTo | m A£o l&n Q9aj| JSo J7» J6e J5s J4i J3s J2s T6i TH 74* . _ -> - _ -. _ $6* 0S||$4i 92s ASo jKSoj QSojjJSo lilSo 9 Sej| llfcj Sds j[ S 5 sj[« 4 s II 83 s:.; 823 A“ o K7c Q'o A6o Kfo? Q6e JGo K5c Q5e T5f Me S5o T3& T2s ’7 0 c-"* |75iJ[74s "3 s 72s 7&? HftljSfo 64 j 63 s p62i 54* | 53s, 52s ’4o (54 e? 54o 44 43 s 42 s |A4o K4 o Q4oj|j4a||T4o Wo |B4o lA3o;K3o Q3ei|J3ojjT3o &3o j[S3o| _ 3o fi3«; 53 b 43o 35 32a AjQpj Q2 b j jJ2oj |T2 o,; 92gJ | B2gj 72* ; 62®: 52o 47 c IPS cctriboi in prfflijp ran. _ 0% TiJp pair Opfit'L t\^dtr N Ut FP S£t p 1 Q T f > R u U \ju f' - 1 f 11 9 vs. f -1 7 f " 8 ■ k_J A 1 s_ i LaJ ♦ EsUm-Kted Combos x - Return = 6stim&ktd C&m.b OS, X -- Return EstihUPtfip! Cpfttbos X -* _Cpt«ub^ X - T^tusrw — CftLL =sv Fold rotfli: t -^ t \ A t -\ { -1 *iT A Q vs. A K A ■jL. Pet: 4 $0 vLUaua. bets 4 Amet-ufet bfihbud 4155 Pot Odds,: _: 1 Flv^l pot ^VowLd be:_ Y&w.r t& Li won.Le1 bz _ cf the {l\ajaI pet. Outs: _ B^ultij ^ _ Odds: _: ± Profit: J_Mflfeeup:/--_ □Call =^v Fold \ s Pet: 4 $& Villain bets 4 Atvneiit^i-t bebt-^pt 4 15" 5 Pet odds :_: i FwvflL pot would be:_ Yeu-r tflLL wei dd be %_ of the fivuiLpet. Outs: _ S^UltLA ^_ Odds: _: i Profit: i_, M«ii«eu.p:4._ Call fold r-^ R n r" r? f 4 C * 1 ** l—;—j u •J* *_;_/ f 1 r* f 1 r- f* > I f- 1 f T 5 5 _±_ VS, A A K *T* s_ Pot: 4 90 vlLIeLl'u bets 4 20 behind 4 3-S'-S' Pot Odds:_: 1 firuaL pot would h&: _ your enll »a^£>m.LipI ht % _ of the ftpyal pot. OutS:_ equity ^_ Odds: _: i Profit: *_Mflfeeup;4_ □Call = ev Fold f 1 " T 1 f -> J J VS. A K Pot; 4 VcrLLflliA. bets 4 A*vu?wnt behind 4 iS "S Pot Odds;_: i pot would be;_ your crII would be % _ erf the fiutil pot. Ou is:_ e^^Lty y_ r Odds: _: t Profit: i_Makeup;:!_ □CfllL =^v Fold K7s K6i K5sl K4s K3i K2i J KJo QJe Alb KTp QTc QJi QT* Q9s|[Q8> Q^i CWtjlQSs Q^|lQ3i[[Q2i| , ^jJL -J __J _ 4 ,_ __A_l J7a 11 J6i j l5s J4i |] J3s If J2s T4& T3a T2s A 9 o PVaB 1 ASo KSo Q£o JSo TSc 9Sc A~c K'i'c Q”w J~□ 77~ S”g A6e K6e Q6oj J6o T*o 5>6o, 8fe I A3 o K5o Q5c J5 q lT5c :95cj|j S5e L_L_J1 J l,_J L J L_Jl_ !A4u K4 c Q4g . J-iu 74p 94o B4 g 73 e 93 c 54* 53* 525 ■io IWtfli 54o | U J[43»j|4a*j ■A_5 c ilo Sjo| 73o 63c 53o 43 a 33 32s .Uo K2o Q2# J2o T2 c 92a 82o ITlo 62c iyil Tr W Uj-D 'MB 1£S cantos- ir; preffop rariir? 52c -2o 32 c ™ ■■■■■IV 0*4 lltti ' 5 ' l*. F 1 a . + , z 1 *. 2 L±- f -*i 9 m > -J f 1 "S 9 ■ k J VS. r - A ±> n; EitLHinted TOf fair _combos * - KCtwm. - ot/£>rp3LK Co i/ubcs ^ _ T^etk^i/b E^tL.nw.sted Combos X - Return 6sttiv.il teti _Combos X - Return — C-flU =5V Fold Total: Set Poe feet -pair below tp Fold Equity Our cards have both showdown equity and fold equity. Showdown equity is the value we get when you go to showdown and have a superior five card hand. Fold equity is what makes bluffing and semi-bluffing work because sometimes we will bet and everyone folds. In semi-bluffing, when called we still have appreciable equity. As we have seen through this book, it is often difficult to make money by calling with draws. Playing more aggressively with draws is one way to make up for this and is the hallmark of great players. There are many strategic places where betting with a draw makes sense. Here we will see the math behind that. in a pure bluff, we expect that we wilJ always lose when called. If we have a chance to win when called because our draw might come in, then this is more of a semi-bluff. The showdown value of our hand is our second chance in a semi¬ bluff; the more equity you have when called the better. As an example: A Q 7 R A ♦J vj f ♦ 4 ^___H* ^- J K 9 ; ♦ , Pot: SI20 Two players, we are in position, S90 stacks We put our Villain firmly on an Ace but not two pair. Ibis means we have nine flush outs, two Nines, and three Kings unless Villain has Ace King. We will discount the King out by one. Ibis gives us thirteen discounted outs. Rule of Two says we have 26% + 3% bonus for 29% equity against a variety of Aces. This means that if we were to shove and get called, the pot would be S300. We are entitled to 30% of that pot or S90. Since we are shoving S90 and we expect to get back S9Q when called, shoving costs us nothing, it is like a coin flip except we win less frequently and triple up when we do win. The key part of the above statement is when called, ft is reasonable to believe that sometimes when we shove the Villain will fold. Every time Villain folds, we win the current pot. Every time he calls, we break even. I his is a bet we can never lose, on average. I his is a great bet and we should file in here if we truly believe Villain has a single pair of Aces and sometimes will fold. Ihey are not always such perfect situations. Lets change this board a little bit. A / ^ 10 t ^ 7 f > 5 s ♦ .r, . ♦ , ♦ l j V_ _ J Pot: SI 20 two players, we aie in position, S90 stacks We put Villain on the same exact hand range, except in this scenario we only have flush outs without the trips and two pair outs. Nine outs is 18% plus 2% bonus is 20% against a reasonable range of Aces. Now we are entitled to only 20% of the $300 final pot or $60. this means w r e are putting in S90 and collecting only S60 back when called. ■i We need to know how often the bluff needs to work. Ihe bluff needs to make up our S30 loss when called, there is SJ20 in the pot. If he always folds, we make SI 20. Lets estimate some different fold percentages: 1 . ) If he folds 50% of the time, then there are two things that can happen. Half of the time we make SI 20 on the bluff. iTie other half of the time we lose $30. This is a great situation for us since that nets S90 profit. I he average profit is S45 per time we run out this hand. Since we know we are taking the worst of it when called, we want to bracket die required folding percent by Villain. We just saw that 50% folds is real Iv good for us. Let’s try another easy to calculate number. 2 . ) If Villain folds 33% of the time, we make $120. The 66% of the time that he calls, we lose S30. Since losing S30 is twice as common as winning SI20, we will double it to find the average. This means we lose S60 for every time we win SI 20. That is still S60 won over three trials. That means S20 average profit. We like this, but not as much as when he folds 100% or 50% of the time. 3, } The next easiest number is 25% folds. Again we make SI 20 on that try, but the other 75% of the time we lose $30, Three losses of S30 is S9Q, so 25% folds is still good for us, but now we are only making S30 over four tries. Less than $7,50 profit per time we run it out. At the tables, we could stop here, $7,50 profit on a S90 bet hoping for 25% folds is probably about the limits of math and estimation, the art of poker is being right about the Villains holding an Ace and estimating the chance he will fold, Th is is simply the math to help with those reads, 4, ) The final estimate is 20% folds. Again, we make S J 20 when Villain folds. Four times that often, we lose S30, Multiply that out and we see that we break even. Knowing where the break even point is allows us to decide if it is a good shove. We could have just said our win when he folds is Si20, and our average bluffing loss is S30, We see that one win pays for four losses, a ratio of 4:1, This equates to 8Q%:20% meaning we only need 20% folds to break even. Realistically at the tables, the Villain might hold lots of hands weaker than top pair that he would fold to this bet. The more of these weak holdings, the better this will work Let s do another one of these. We already know how to estimate our equity when called. Lets look at a situation where a Hero flops the Worlds Fair of draws: two overs, gut shot straight draw with a flush draw. On the flop, the Villain bets S60 into the S8Q. Hero considers shipping it in for SI80 on top. Based on the history with the player, we think Villain will call with top pair or better. We think he could show' up with |9+, all the overpairs, and set Nines or better. "I here is a good amount of junk that he will fold, like AK. the first calculation should be equity against the nuts, pocket Jacks. We have nine flush outs, plus three other straight outs. We believe they are essentially always good. 'Ibis gives us a minimum of 12 outs for 48% equity, Ihe set has redraws to a boat, so we need to drop back 30% of our total equity. We need to know 30% of 50%. It is 15%. lb at means we have 35% equity against the nuts. Against top pair type hands, we have the fill I 50% equity from our straight, and flush draws and then about 10% equity from our over cards. Klopzilla puts us at 58% equity. We would have estimated it to about 60% (Against over pairs, we are more like 50% equity.) We could try and count the combos and take a weighted average, but we have bracketed our equity when called to somewhere between 35% and 60%. There are a lot more top pair and overpairs than sets and two pair. We could just call this about 50% equity as a SWAG (Scientific Wild Ass Guess). Flopzilla puts us at 50% equity Bracketing and SWAG works pretty w r ell. Lets rough out the math here so we feel more confident at the tables. Our final pot if called will be S260 + S260 + S80 or S600. When called, we will take half the pot back. That is S300, and we are putting in £260. It is already profitable even if Villain never folds. Villain will fold sometimes, so this is an instant ship, unless w r e think there is an even better move w r e can make. Ihe general procedure for these calculations is: * Figure the final pot when called. * Calculate your percent return when called. - ff the return is more than your stack, consider shipping, it is profitable. * If your equity when called is better than 50%, shipping is always profitable. * If the return is less than your stack, find the average loss. * Figure out how many times you can ship and lose compared to the profit when Villain folds. 1 his ratio gives the amount Villain must fold for the move to be profitable. - Use your poker sense to decide if you will get the required folds. Count combos if you can. 4 5 * v 3 ♦ \/~ Pot; ViLlnL^ bets Lv\,to -|.5'Lj -#150 stacks before you. corn vLLLau^ wlLL c-aLL with JJ ov better Equit's] wSoetA,.called: % L Css whew, cflLLeri: w’Li/v win et/v folded to; KiSqutLred fpLduvg % to breflfe £v£i"v: J ¥ ■* Pet: Villa lia, bets $25 u/vte $30 $±50 states villa Lia, will tall witi^i tc"p "paiK ov better two overs av^d a -flush draw ov better Equity wheKcalled: % _ l ess wbei/v called:_ W'ua, where folded te:_ R.eg wired J aiding ^ te break everc:_ 1010 v___A_ J Doug Hull r 1 j f ^ 10 f % 3 4 * ♦, Vj Pot: .#110 -$5Q stacks vLlLau^ will Gall with top "pair o*' better Loss win tvi called: Wtfrv y</h&trc. folded to; R.eojw.u'Soi s oldiv'j? i % to breafe evew,: Pot: $50 $35 stacks vlLLauv wlLL call with ai/vLj'paCi' Bc]ui tw whew, tailed: ^_ draw Loss wiicw, tailed: wIvl whe^v -folded to: Kieani^ed folduT^ % to b^eate eveuv villauA, will. caLL wLtii cua,ia beat ov better bg\u‘±m whew, called: °fo _ l os-s. whtw*- talLect' w f 'w* wh&v~ folded, to: Required fbLdl^g % tc breate tJtw. / ^ J 10 f > 10 f ■> ♦ 1 t ^ L + *_ > ^ \_^ V' - pot: 4; .#1,50 stacks vlllalvt will call with tat; 'pan- at- better with aw, apew, e^dcd straight draw or AJi with back daar flush Equity whew, called: % _ i ass whii* called: Ww, whew folded to; Required fbldlwg % to break even,: Doug Hull Pot; Villa li/i- bets $30 li/ito $50 $■±2.0 shades befbre won call VillaL ia- wtlL call with AQl+ or qo + lyuLtij w^ieiA call eat: % Loss whin, tailed; Wu'twhetA folded to; ■femnired foldiiA^ % to breale eveiA; Pot: .#. 3 O LiA-to ^■■50 $2_t>Q stacks viLLaivc will call with (H&.+ Akts Boulti] wh fit'V called: % L oss 'avi zia, ca LL. t g\ • win - whevcfoLrfed to: 'R.tauiv'ed folding % to break everv: Folding Nut Flush Draw on the Flop Effective stacks: $200. 7 + vs. -• Si iil E3 L J K Ql f.jlMi K!.:;L1| f *»* u • Q- ! , -'- L | rr» ^jiij 'ii - , 'i Jfii Jiii .?■ [T9*i n« t ; 1 1 '■■ • kJifkJ - r - -j tSiS' Cfcaa-ais ±1^ iitiatesa .±1 .ai «?£! i t'i Efe. K_’i J!-i KJi Ki JJ* Eli _04t Hi 13 A ? C- - ,* ■.■ ” Vir H:s Me Jio Tfc &4o ife "nj -Oa. KJ* Li‘J: J:o T2* :-. U^JLJ ljuJLJ a dU Vi’ K ■ •/• i A5c K3u |QSS*|| r-.A K’o 1 ■§■■19 •J. K.: :■ q;-J Ai#|K In Q-ii -Hi AS*" K]u QIj . M&M tt» <*' 'i M*-- !-!:■ ilh (Jli; 1/Hl Jii r. ,i*i P* - r ^L .Hi ,.t;» ’ll. _ r i Hi i>> iJi II. I! - ■ ai.j, 3fo JS5 l E-i t?i U r.-i Tj 9Ji «i| lit B3t tit 4?n iSSa. !Zl ]ih Ci Eli _ Pi I li as Villain raises to SI2 in MPl. A player calls and we call on the button with weak suited Ace. We know very little about these ranges at this point, so lets go to the flop. Pot: $39 Three players, we are in position, Si90 stacks 'Ihe original miser bets S40 into the pot and the middle player raises it up to $120. 'ihe flop raiser is not the type that would raise on a draw in this spot, so we put them solidly on two pair or better. Most likely we are against a set of Nines or Fours with the occasional King Nine suited. Further, we believe that the flop raiser is never folding. If the flop bettor does not re-open the action, the remaining 570 will be bet on the turn. It is unclear to us what the pre-flop raiser has or if he will come along to the turn, but we think he certainly has a weaker range than the flop raiser. Lets start with pure aggression. Do we have the odds to just ship it right now? We might remember that a flush draw is 25% to win by the river versus a flopped set. if we assume pre-flop raiser has very little equity and is will ing to call, then he will contribute a lot of dead money to the pot. In this rosy situation, we w r ill put essentially 33% of the money In and only collect 25%. 1 he 540 in pre- flop dead money is not enough to justify getting S190 more in right now since our 25% equity in the dead money is only S10. Clearly if all the money goes in now against a set, we are losing lots of money. It gets even worse if the pre-flop raiser does not come along. Can we call the raise? In the best case scenario the flop bettor will call but not raise us. Ibat makes the pot 5120 x 3 for 5360 and the original S40 for S4G0 total with 570 back. We make the nuts on the turn with only eight cards since the Nine of Clubs brings a boat or more to a flopped set. We will make this draw about 18% of the time. Lets call it 20%. Ihis means we are entitled to 580 of the pot, and we are putting 5120 in. Ihis is not good for us either. However, we have 570 in reserve. Let s take the best case scenario where we hit our flush and get called by both Villains. Ihe set still has ten clean outs to a boat or better, that is about 20% equity to our 80%. the final pot would be 5600 again and we get 5480 on average when we hit on the turn. I hat means we only get that 5480 20% of the time. 'Ihat is 596 (think 10% of 5480 and then double it) in the absolutely best case scenario. And our best case scenario has us losing money on average. If making our draw on the turn does not make us money, then calling the inevitable turn shove is going to be ugly for us also, there are seven board pairing turns where we are drawing stone dead. Imagine we get to the turn three ways for S120. the pot will be S360 + S4G for $400. Ifw'e catch a brick that does not pair the board and both players go all in before us, then giving us the best possible odds on our draw there would be $70 + $70 + S400. We would be forced to call getting such a good value on our 20% draw. The final pot would be S600 again so we would be entitled to SI 20 for our S70. Essentially, by calling the flop w r e are setting ourselves up to be pot stuck on the turn. The turn call on a non-pairing brick would be +EV, but the w r hole line would be bad for us since we are losing money even those times when w r e do hit as we saw' in the analysis where we hit on the turn. J All of these analysis w r ere with the very generous assumption that the third player is shoving money in stone dead. In more realistic scenarios we are doing much worse, fust fold the flop, even with this monster draw if you truly believe the Villain has two pair or better. Folding Middle Set on the Flop Effective stacks; £1600 at $2-5. /■-> a t — Q L*J vs. £,4 e Kj« P*| I®; <P i| Q«i Q:i Q*l| QiJ PI i Q 0 - ... ifr o . . icr ■ ■ ” Hu 75. 5:', 3 A 1 K. ■> V ijJVjT’li P’t ;! f frtj LJ " AWbCJo rtvj J;aj£;r- y>r im .‘5l jito | ?h\ JS, :'.Jjifr )Ji!ifi. JH. n* CEt KV JCi> KS. -tJc K.'i O. assist :!P y:-i q:l ji. ; -^i TPa-p 7ll T s 7flt T H ’ 4« 7 rk T7a 4<p|K In l^jj 1 1 n ,-lr U4#|j| bi •UilKJii Qipirild .13* !»«. _ 4 *y;<V> .'■ »'■ J •- -V - V : g»J|Er «.j • lr. >4 \--n 7«1- -1’ 3*,. -1. (■;* JJjj EIj tfSi 7!d t TU ■ ! -i Ifil S3. t=h, Jli 0 > ]Tp !■. B l L 1 11 UtlH | "Is, I'4l ;’lj c±\ 44 M C*= J&7 7\r kj 43. iy 41. j’L. [rw Mf. 'i:e As; lia u 131 :ii| Ki* Qi-. ! In |T4* Vi. 1..! "4r; 5Juj u .■ill j Ci, J .■ KJo Q-=4 m p*i y=i Ira ■'i^j t:u JT-: y 1 22u Aia K.J o ,QJ: Jif, rn# it- t £1 Oj lJ Cfi 14 V Nitty Villain limps in U'J'G, we raise with pocket Queens to S3Q and are called by the Button and the Nit. 4 We know very little about these ranges at this point, so lets go to the flop The Nit checks to us. We have the third nuts. We are only behind top set and a flopped straight. We bet S8Q into the roughly $100 pot. I he Button makes it $160. He makes a minimum raise on this dangerous board. We feel he wants action. They jokingly say that if lack Ten is the nuts on a board, it is out there. We must strongly consider the idea that we are behind right now. A set of Kings does not make sense with the pre-flop action, but it is possible. In Vegas lots of people play trappy with big pocket pairs like this. Jack Ten seems very reasonable given the play. When this hand actually was played out at the Venetian, 1 instantly started doing the math assuming I was on the draw with the third nuts. Lets do that math here. Assuming we are against the straight, we have seven outs on the turn. So we win 14% percent plus a bonus 2% or 16%. We will lose 85% of the turn cards and surely face abet. We will miss 85% to 15% or a. ratio of 5.66 losses for every win on the turn, if the Nit folds, we will be asked to put in S80 to win our original flop bet of S80, his call of S80, his raise of SSO, and the 580 that w r as in pre-flop, plus 520 more that was in pre-flop. We can count 4.25 times our call even if the Nit foJds. Even though w r e are not getting the direct odds that w r e need to make this call immediately, there is enough in the stacks such that taking a slight loss for the opportunity at winning his stack is worth taking. If we happen to be against a set of Kings, w r e are dead to a single out, but a set of Nines has the same problem against us and of the two sets, the Nines seem more likely considering the lack of pre-flop aggression. None of this math we did really mattered because w r ith the pot now holding $340, and effective stacks at $1420, the Nit ships it in. So to recount the flop action: the Nit checks, we bet, Button min-raises and the Nit check-raises all-in for a 4x pot sized bet. We are dearly behind one of these two players, if not both. At this point we are easily drawing nearly dead to a set of Kings and a flopped straight. We only have only one out to the set of Kings. If by some miracle w r e are against two flopped straights, we have seven outs on the turn and additional three again on the river. Roughly speaking w r e can apply the 2% rule to make 17 outs 34% plus 4% bonus for 3R%. (The actual number is 36%, but this is a great estimation that can be done at the table.) In this most optimistic scenario we are essentially breaking even and sometimes we are drawing near dead, 'lhis is an easy fold. At the actual table, the min-raiser on the button called with the expected ) I". Ihe nit tabled bottom set. This is actually a worse scenario for us had we called Jr because the lower set is acting as a blocker to us getting a boat, taking away three outs. Our equity would have dropped to 24% from 36%. 1 w r as very happy with my' easy fold, but then the turn was a King giving the Nit a boat. Sometimes 1 wish I played worse — that would have been a £4S0G pot if 1 called and caught lucky. It is a great exercise to run analysis like this about your equities in different scenarios, it helps to build up your intuition. Looking at enough different scenarios will make it easier to remember or calculate the equities you need at the table. Flop Call on Paired Board Effective stacks: S300 at S I -2 with a UTG straddle to S4. Three limpers and the Button gets friskv r with 62s makes it S20. Solid FAG calls from the Big Blind as does the U FG straddle and a I impel. itH m~>| 3i.Taj3CTij ; ESl X't ££► K3a 3U. QJ* $:■ QJ» <12.1. jT.J *3. j JSi r. It-. Jlk J3l 7U Ij^ i6i • LjfajL, ^ ljl u ‘' W* Q?1 QJ> ®* SSI 13 kJijH :^|Jfo|jj?6ajfc j |Fj|_]L_i ^ p rlj. : <■, : ■ M KEu A :-i USo L- "■ ■■■ Li."' $$6 6 ♦ "V“ 2 v.s. A7a. ¥'p Afci Ltd AI-: K?D A*l t--!.,. qr-# jip t . ■. i-'a ■:=• | AJfcjOD-Qfc: x, ;r?i fejij.Jio : !«e Sij J : Ms i AS? Jtlv J?o *i- ■ • ffci|33l tfil 3:» 5--, S3* Pi -a (H»j[§fc ijUaji Kk A3c Kl:. <?='. 35o 75. G5* 13a ?1. £!a I Uft K'= JQTTb Tb 7': C: l*u ■. ■. . ia> j-. ;oj j - aai kt<- va< •_■ "3a Alb f-Ji LUH ! A^.tlBi Q'- j'u ~:w p?s ji' - j^| 53. n*| A^jj-KJo :j. - : a ;{*2» | «.*;>:3b .n n jjr« psajjiiB ’ 'Up 1 A3&, (C!fl to tit, K* lie 3t - : j3j 21b tJl W rfrt 1 n -»- r jri MMI IA«% We know very little about these ranges at this point, so lets go to the flop. Pot: S80 Four players, Hero is on Button $280 effective. The TAG donks out on this flop for $60 from the Big Blind. From playing with this player all evening this bet represents trip Queens, usually KQs+, AQo+, 77 or the rare AdXd. I his is overwhelmingly going to be trip Queens or better. Ihe next two players fold. Ihe Hero thinks that the TAG will bet again on the turn unless a Diamond comes. The bet on the Turn will be too large to call. Is the Hero right to call for his flush draw here? If Hero is not already drawing dead against the TAG s full house, he has 8 outs. Ihe ninth Diamond will boat up the TAG and Hero will lose the rest of his stack. Jake Hero’s eight outs and double it to 16% while adding 2% bonus and we have 18%. Call it 20% for simplicity. Hero will suffer this $60 loss four times for a total loss of S 240 for every w r in. If Hero gets paid in full every time he binks his flush, there is 8220 in reserve and the current pot of SSQ+S60 for S360. He will make SI20 over five trials for an average w r in of S24, under the rosiest conditions . Ihe above though does not account for TAG s redraws on the river. Instead of getting paid off in full for a profit of S360, we have to account for the fact that TAG will still occasionally beat a flush on the river. I he TAG still has 10 outs to a boat or quads. We do the math again saying that on the turn the clean Diamond out was hit and both players are all in for 8280 for S560 plus the original 880 making a S640 pot. When the Hero hits good on the turn and gets paid off, because of redraws Hero still only w r ins 77% of the pot on average (Not 100% as we assumed above) or 8490, call it 8300. This means that Hero will call the flop and 20% of the time he will walk away with S3 00. 1 his is a profit of $220 from his current stack of $2 SO. Ihe other 80% of the time he will fold for a loss of S60. Four loses of 860 is a total loss of 8240 and this is offset by a single win of S280. Over these five trials Hero is up 840 for an average win of 88, under the rosiest conditions. What does that mean overall? Look at our assumptions: * Hero is against trip Queens, not the boat. * Turn hits the dean outs or a brick, not the poisoned flush out. - Hero gets paid in full when he hits on the turn, but 25% of the time he still loses to redraw. ■ Hero folds on the turn when he misses. After all of this, Hero finds an S8 profit on average through this line under ideal conditions. What about more realistic situations? Sometimes Hero is against a boat already and is drawing stone dead. Worse, he will stack oft" when a flush comes on the turn. When against a full house, the rAG might bet small enough to induce another call on the turn. One card in the deck will quietly make the TAG a boat and Hero w'ill stack off dead to it also. On the rare occasion that TAG has a nut flush draw the lAG will stack Hero when the flush comes in. in this flush draw over flush draw situation, Hero’s pair outs will be very hard to capitalize on since he will not know he is good when he does hit. If the Hero really believes that the TAG has KQs+, AQo+, 77 or the occasional AdXd then this call is at the rosiest a break even call when against a single Queen. Sometimes this hand has massive negative implied odds. I he TAG also might not payoff the flush, making the play even more dubious. This is a high variance, losing play for the Hero under the gentlest of assumptions. Facing a Massive Donk Ship on the Flop Effective stacks; $500 at S2-5. Naive player who I just stacked one hand earlier. He limps in pre-flop and then calls our S35 raise. He could have just about anything here. I he player was terrible and could have anything from the other two Aces to low suited connectors to suited garbage hands. A A * vs. Imijmjp Hi j:-, b >_■ H [7 3 r. gji m* s,j F’l ZH Til - 1 . T3.1 TL. n&e K £ n JQS-. )h ;:i> \%b, tin QJ: gin ::= ■.-i- L J s ~‘: " r -- 351 33a & ^>j o j[T': J'lll’u 7J| ii Mi TS*| Mn Kf,- fife; H 3 *J|KH| AM KJe_ jr« t:t ?5i i-m t :» |^j i« ::i A ’7 K’P Qi- Jin 7«* ’iff! H*i tlu jQ&t B* Til He jQ^bj \ J *ms. m ORuXn Mps&pf- ina cr> Il.i* —* fe We jump right to the flop. -\ 7 / \ J [3~1 L±J •f* ^ j t , k _ 4 Pot: S77 l wo players, we are in position, S465 stacks Ihe Villain clonks bets all-in forS465. What do wedo here? A terrible play r er might do this for a variety of reasons. He was tilty from the prior hand, he does not know how to play a flush draw, or he is afraid of the flush draw, the kinds of hands w r e expect to see here are: * Flush draws * Overpairs ■ Sets How are we doing against each of these? Flush draws: These draws only have eight outs because we have a blocker, there is also a negligible effect where we can over flush if he does turn his flush. Fight outs, twice is the Rule of Four for 32% with two bonus percent for 34% equity. (The actual number is 33% so that is a fine estimation.) If we call, there is a £1000 pot and we are entitled to S666 of it. We make S200 on average when we make this call versus flush draws. Overpairs: Ibis Villain clearly plays erratically and he might have been playing pocket Kings waiting for a safe flop. With the flush draw out there, he might ship it in w r ith Kings or Queens here. If he holds these hands, he has two outs twice and so that is about 8%. That means we are entitled to S920 of the final pot. We make about S460 on average when we make this call versus overpairs. Sets: Sets are the big fear here. If we think he would play an overpair like this, then for the same reasons he would play a set like this also. We are the ones drawing thin. Our backdoor flush draw adds another 4% to our 8% for about 12%. We are entitled to SJ 20 of this pot, so we lose about $340 on average when we call against a set. lime to count the combos. Overpairs: Four Kings times three Kings is twelve pairs, but order does not matter, so it is six possible pairs of Kings. I his makes twelve overpairs of Kings or Queens. Sets: 'Ihere are always nine sets possible on unpaired boards where we don't hold blockers. We can actually stop counting right now'. I he overpairs are more numerous than sets. Overpairs win more than the sets lose. This, means the overpairs alone more than pay for the sets. Mhe flush draws are all massively profitable so this becomes a fist-pump call. Villain showed two Clubs, missed and left the table down $ 1000 in back to backhands against me. Folding Top Pair + Open Ender Effective stacks: 70 big blinds in a tourney, far from the money. We open for three big blinds in late position and are called on the button by a solid player. K ~Y“ vs. ,, Eii E5i K'. .Ui C=. El. IT A Jt J: Jl • Jl, |I. J : ■ i£5 • Lili <2li||tJ6c Q<; Q-i qji Q2I- uuuj jjli ?"■ Jfn j?i i l4i, ill 12* 154 j It ::•! TJa T.’k Tj _ 1 j- JUn: jfJajjjQOt Jin 71( &5r a H IK ■ W i ) b 1 : “ 'a kjl^l * ■ A&a ■Efe Ofe Jk T*= Hr j!to -Mi !-% Ais fcfv Qlz J3« :\s K-. ?:« ’Jt- f jii |^|| :-i 53s .'i K In Q.i Ur. TJ; (Lie II.I twi -j;]y|dli *;■> Kjp Qrs 73it E3l ; l3u 73*j;i-Ss -!. lJ _ HE ijMi: i Bi 'jLtlatt! fifty# ms We get to the flop: J fiol f s 7 f > t T J 4 1 _:_> LVJ -j L-—J Pot: 7 BB Two players, we are out of position, 67BB stacks We tire 4BB in and are called. Off to the turn: r j’ [lb f ^ 7 f s a 4 , V J * k a ♦ ♦ Pot: 15 BB Two players, we are out of position, 63BB stacks We have the new top pair and an open-ender. We fire 12 BB in and the Villain ships in his remaining 51 BB. Regardless of the strategy of the line up until now, what is the best move on the turn when we get shipped on? First question is what do we put him on? 1 his is a solid, conservative player. We do not think he does this as a bluff. 1 here are no combination draws available, and we have the best pair plus draw. What makes sense? * Straights, flopped or double gutter on flop - Burned two pair We are drawing reasonably well versus the two prime candidates. Let’s figure out our target equity. I he pot was 15 BB on the turn, we bet 12 BB and the call of 12 BB makes the pot before the raise 39 BB. Let’s round it to 4QBB. W'e have to call 51 BB so lets round it to 50 BB. 'Ihe final pat would be 140 BE and we would be putting in 50 BE. I.50BB final pot would mean w r e were putting in 33%. Ihe pot is a little smaller than that, so our call is a little bit bigger percent of the smaller pot. Lets say 33% since it is easy to remember. dr Straight: We expect Villain would have 89s for a flopped straight, though King Nine would have made a sneaky double gutter. Either way, the Villain always has one of our Nines so we only have seven outs and we are drawing to a chop against the double gutter. Seven outs is only 16% equity, and sometimes we are chopping, so it is even worse. Two pair: I his is very consistent with the play of the hand if the Villain holds top two pair. Flopped two pair or Sets would have l ikely made their move on the flop. Lets just take the top two for our math here. We have eleven outs for 22% plus about 3% bonus equity for 25%. We can stop the math immediately. Ihe two most likely' hands are nowhere near target 33% equity we are looking for. 5IBB is a good fighting stack, so we fold and go on to the next hand. Nut Flush Draw Against “Same Bet” Effective stacks: 1300 in a S1-S2. The Villain limps and then calls our S12 raise. p"- A 4 ♦ ♦ vs. |;£Bi K/i Eflt K1. ¥Am IGi KZ» 1 ( J Ihi 1 Jla r«- JlA. ]>: Jk. Jla . J?» Lsll T7-i Tk Til- T-ib' LSI TZlj ■ r ■ ■ * ■'! J " * ■" K5o ||«« ■ ;■ «■ sPil, A&j Kid C3: Jib jTH. W* ua iliL.: IHllHii lii.lCb! A '.2 X ] o el Jo j l _ 1 yfryj :» ?4l; !k : T5l Wg'IHfiKw if-; 'k- dip Ej AI-.2 K.2i> JJfl: ‘t-S* B>S; 32c 'Jo: kJ= ' ' A *1 K V A^*; JJn ■■ _ Jb ^ J XM KJb .™y , 13= P>: l& It 1;. „ j J kJ .-A": Kid C'.v- ■ gll jrir ;if<3. *:p !2pj4. The flop comes: V 7 r S IV l V L ^ J t j / ♦ l ^ j \_ ^ K _^ Pot: S27 Two players, we are in position, S290 stacks I he Villain checks, we bet SI 5, and the Villain check raises to $30. the mental dialog here is, “Our opponent is an idiot, this bet serves no purpose/' We might consider a re-raise, but it is unclear we have any fold equity. Lets just follow the calling line. We are almost certain to face a bet on the turn. We already know there is plenty back to chase a flush draw for one card, but let's do the mental math anyway. We are hunting for “SI5s” since we have to call that amount. We see the Villains current raise for one, his call for two, and our original bet for three. I here were two mote in the original pot of S27 for a total of five. Hush draws come in about 20% on the next card, so we aie getting direct odds to call for the flush without implied odds, ihe implied odds only make it clearer. Additionally, our Aces might be outs and some beautiful days the Villain has a worse flush draw. All these add value to the call. -\ r to ^ _ 71 * J Ld L._ j A 4 Pot: S87 Two players, we are in position, S260 stacks Ihe Villain announces same bet and throws in SIS. Ignoring the more aggressive raising line, this is a trivial call. His range has not strengthened, in fact it has actually weakened with this silly bet that gives us 7:1 on our call. Since we made the flop call assuming we would have to call a turn bet and the pot got bigger while the bet stayed the same, we are getting better odds. We know for certain the calling line is profitable. Rounding off the numbers and going to the River: Our Villain checks. For him to have us beat, he would have needed to min raise the flop, min bet his flopped set on a flush draw board, and then check the river with a full house. Players would almost never play a flopped set like this and Quads are just not likely either. We overwhelmingly hive the best hind, and the Viliam likely has a very dubious King. We bet whatever w r e think he would be willing to calk Even though the pot has ballooned to £120, the Villain has essentially put in his half SI 5 at a time. Know your player, and bet what you can. I bet S4f>, and he folded. Ihese ridiculous min-raise and barrel “same bet’' are common and price you in with your draws. I he Villain feels like they milk us for the maximum Si J Jf because usually we miss. As we saw, we had the correct direct odds to call, so Villains tiny bets are a mistake that we are happy to benefit from. Big Draw Versus Turn Check Raise. Effective stacks $300. Villain limps inMPL We raise to SI2 with KQs and get called by the limper. Ibis Villains range is not particularly well defined by limping and calling. We can put him on a range like this: / - *1 IK j* - Q \JL \jl VS. I k lj l p MKhi K’l Ift I !■ I-i Kv. tli ■J V Jl • Jl._|I._J'._J | —. t Uaj- ib J 7 . Ib. Jb lii Q life! Ill I Th i i JJi Vm 12 a ,'ji: e;-,- n® ~n Ate' K!;< t*: Jjo % W» Mi SJs Sis A 7 a Q'= r® LJCiJ " ?t " il Afr^|L&u Qfc .IsojjTf. v ‘jjJ|"k' Ws- x:* n!« cu ?:□ r'n vi e ir® Cc HIHUHHH u Ait K 4 c i;c. .u» Mt wi ]£4 *Jt Hp ■’]. ;ni d.'s ;Hi ::ih 'Hij - 4 is A : i K 1 U i;.= : JJ:, TH* 0 ?-? I'e 'Ir- i’c ) 1 n .AAk'KIo i.-.. ftt ftf'liifl ’is ?:-j :■> jj> =:p| Ci l£ i'. It will be very Villain dependent. Most Villains would have raised with Aces,so they can no longer have them now. Some Villains would limp-reraise if they had Aces or Kings. Some Villains don’t like to raise until they see a favorable flop. I his range is just an example to work with and nothing more. / \ J CD to V, ♦ 1 J Vj Pot: S27 Two players, we are in position, S190 stacks Ihe Villain checks. We expect that to happen most of the time, so we can not make much of a read here. While we only have King high, we have a gutter bail straight draw and a second nut flush draw, two overcards can be north something also. We bet S2Q into a S27 pot leaving S17Q behind. thinking of made hands, overwhelmingly Villain has top pair when he check- calls the flop. I here are lots of slow played overpairs and some sets possible also. Even against top set we are drawing very well with 33% equity. Ibe call instead of a check-raise is also telling. Imagine that you hold a set of Nines on this board. Every Heart possibly brings in a flush. Seven, Eight, Ten, Queen, King can all complete a straight. This check-call indicate that there is an upper limit on the strength of Villains hand. When the time comes, we might discount the sets, flopped two pair, and overpairs from his range. There are a handful of flush draws and straight draws possible on this board, a fe w with a pair to go with them. Considering that we have huge equity against even top set and the fact that Villain will fold often on this flop, w r e are happy with the bet and not upset that w r e got called. The Villains range looks like this: __ jPai-R- i * 9# Iw ft :. : h ]| fib 5 b -h 2b " Ad h. ■ J f—I As b KA & Or: Q* 1* Jd Ji Te Td Ts & 6fl k 8a s. i [ -c flflj ijil 6c fra i fa j Jc vs e* -a -Is 1 ,c hi as M F - J B * J .n J ,s 12253* 1 . 3 . 5 1 * i'2" = ■yi Y Y Rltt pan Y •iH.erpti Y top pp Twlc-w [p middk pi* wrak pair higji □□ rriadr hamd Y Huihiiuvi-- Y OLSD gUCElliM t.L2% ijvetr-irdi- i?j 2crd bckdr fd. |>,E'j tu:Jh*iv.'-ji3ir 13.3'% Oft Oft sm Oft oft Oft fijihii’-nv?',: Y f.'Jihdr ^oejd. r ■ ■ ■_! i ■ 1 - —EUlat Y Mid-pan Y JUtEJlM’pdn ?uc:Vi*-ci'. , ffc. .AB i'i^r -r^>.- Ujiiif We are not terribly concerned about reading the hand too much yet, though it is safe to assume we are behind at this point. T Q n 0 4 j o * u , ; IK ■"-N. fl Pot: S67 fwo players, we are in position, SI70 stacks Ihis is a great card for us. Ihe top pair changed and the Villain mostly had top pain Unfortunately, a straight came in for King Ten and for Eight Ten. We improved our hand against the most expected holding of a Jack. All of this encourages us to bet for value. We bet 5^0 into the pot and the Villain check-raise ships in the lest of his stack for SI20 on top. We now have a math problem. First, the calling odds. Using nice round numbers to keep things simple the analysis looks like this: Our S50 and his call are S100. There was about S70 in the pot on the Turn. He shipped SI 20 in, so we are looking for how many " SI 20" we can find. His bet is one, the pot holds SI 70 before the ship, so that is two more. There is a remaining S50 which is just under half. We have found just under 2.5 times our call amount in the pot if we call. Next u r e want to calculate our needed equity from the calling odds. If we can not convert 2.5:1 into a percentage from memory we can estimate it from easier to calculate ratios. We will bracket the 2.5 in between 2 and 3. 3:1 on our call would be 75%-25% to break even as the lower estimate. Similarly, we figure 2:1 on our call would be 66%-33% to break even. We need somewhere between 25%-33% to break even on this call. A mathematician would correctly say we jr j can not simple average 25% and 33% to get the actual percentage since the math does not work that way. This averaged estimate would put us at about 29% If we call it 30% that is close enough for w r hat we are doing here. By chance, the actual number is that we need 30% equity to break even because we are calling SI20 and the final pot will be S4J0. This means we are putting S I 20/£410 or 30% of the money In the pot and we need to collect at least that percentage back. If I were using this percentage method, I would estimate the percentage of my call Ur is way in my head: S4I0 is close enough to $400. ifw r e halve SI 20 and S4Q0 we get S60 and S200. Halve it again and we have S30 and SI 00. This is 30%. ("the more of these shortcuts you know, the faster you can estimate.} Whatever method you use to arrive at “about 30%'* equity being needed is fine. Next we estimate our needed outs. Thirteen outs times two is 26%, then we get a bonus percent for every four outs. That bumps us up thiee more percent to 29%. Again, this is close enough. ffw r e have thirteen outs, we are break even to call. Next, we need to know what Villain has heie so we can count the outs. Will the Villain ever do this with a draw? At most low stakes games, the answ r er is no. This Villain has a hand, and it is better than ours, is it possible that he picked up a pair with his flush draw? AhQh would be a great combo draw, but he can not hold that hand since the red lady is with us. Ace and Ten of Hearts is the biggest draw possible here. There is only one combination of this hand, and we are ahead of it. We can mostly ignore this hand, and it just builds a safety margin in for us since we beat it anyways. What about big hands that would check-raise shove the turn? The most obvious are the straights, sets, two pair and the occasional over pair that was played strangely. I lie good news is that our best draw, the flush, beats all of these hands. Our second draw to a King high straight is usually good or at least chops against the straight. We assume our flush or straight is always good when we make it without pairing the board. Ibis gives us eight flush outs and three straight outs. These are eleven absolutely dean outs. We are targeting thirteen to just break even. Our quick estimate using only our flush and straight equity says this is a fold. We might find a call with further analysis though. Remember, thirteen outs is our break even point. We don't actually make any money at thirteen, we just have a wild ride where we break even over the long term. Since the short-cut did not give us a clear call, we can go to the individual hands. The straights. We have nine clean flush outs for about 20% equity. Every now and then we are against Eight Jen (without the Ten of Hearts) and have two bonus out to a higher straight. Ibis is just a little bonus equity that will not change our calculation. Sometimes we catch our straight for a chop. We have 20% and need 30% so we are losing about 10% of S400 final pot in this spot or S40. lbe sets. Pairing the board w r ith the Nine of Hearts is a poison out. Since we are calling all-in there are no reverse implied odds where w r e lose more money when w r e hit our hand on th is out. Ibis gives us our normal nine flush outs minus one, for eight flush outs. We can add our three straight outs for eleven outs total. Double the eleven to get 22% plus 1% bonus for every four outs is more like 25%. We are 5% down or S2Q for the sets. Overpairs. Pocket Kings or Aces may have gotten here for some Villains. With these we have nine flush outs, and we also get the tw r o Queens for eleven solid outs. I here are sis conditional outs: three Kings and three Lens against Aces. 3 be three Tens are chop outs against Kings. Of these sis conditional outs, lets discount it to three. Eleven plus three is fourteen outs, so that is 28% I- 4% bonus or about 32%. Some of this is chopping a straight w r ith pocket Kings. We can call that break even against the over pairs since we need about 30%. Two pair. Two pair is either Jack Nine, Queen Jack, or Queen Nine. Jhe w r orst case scenario is two pair w r ith a Queen, and it is also the most consistent w r ith the play of the hand. We will assume the worst case, meaning our Queen outs are no good, but our King outs are good. This gives us nine flush, three straight, and three King outs for fifteen outs 30% +4% bonus for 34%. I bat is J 5% over what we need or S60 profit. Now r w r e know r the outcomes of each likely holding, and w r e must figure out how likely each is. Straights:'I he re are 12 combos of KT and 16 of T8. This is 28 combos Sets: Ihree of each for 12 total combos. Two pair: Nine for J9, six for Q9 and six for QJ. ibis is 21 combos. So now if we play against every possible combi nation, with the more nuance d analysis, here is how we are doing: * 30 Straights losing $40 each for -S1200 * 12 Sets losing S20 for -S240 - Overpairs break even, no need to think about them. * 20 two pair winning S60 for S1200 Ibis call looks more and more dubious. To make this a call, we need to discount the straights and sets from Villains range. Put this into Flopzilla and try different ranges, it is very difficult to justify calling here. vs. 313 vs vs. vs vs vs. vs. vs. vs / \ 3 t -" 9 VS. ^ 4 ' l*J l±J 4* Jl ♦ *_A_£_ 4 vs. SO vs, 20 vs. ' k t ' A VS. K [fll uu A LLI ♦ vs, ffi 33 vs. ff — J f f 10 LL A r—■"* 3 P p 3 L±J ♦ „_ 1 _y vs. r-' 1 J ^^ J L±- A vs. A * y\* 7 v ITI /■—\ 9 vs. f ' K fsl ulI * J V _ t _ J j-J JL vs. ft 30 ft 7^1 vs. 2 ^ % ^ vs. ff 3 fe ?■ 50 VS. vs, *$. 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K - " K ±* Li A Li Li lJi- # outs_ £> ft JLOO vs. ft £ # outs 2 g _ 5 VS. % A 7 [♦- * ^ 8 T . *, /■-i 13 /- - " A V3. —> K / - * K Li Li Li Li (T| 7 fsl ■ 1 7 7 vs. Li 2 + A ♦ \r 2 ♦ -- -^ -^ r- "> A [A 2 1 5 1 ♦ . L HE* . L ^ / ^ A / \ IK vs. f ^ A f ' a A Li li IjL # outs 2 # outs 2 # outs 3 ft ifT vs. ft -5~ ft ,_9s vs. ft -5~ ft .Li vs. ft. r-> A r-> A !♦- r-> J wi. f -' 5 r- A A f-1 7 A V<S, f ' A f-^ 2 L?l # DU-ts. _ 3 3 vs, l fo_y_ A * 7 4 vs. # c^ts 5” *23 vs. XI. # outs Q> g(g> vs. % /■ -V a 171 fsl r -' 15 •f* L±J 4 r -> A \9' vs. -•> K -^ a A * _-_H i * k,_> # OU-tS % 23 vs. foJfJ: 1 ^ 5 *-•* 3 r*-^ 8 fe] fs] r-> 3 J. ♦, JL i ^ ^ JL V3. fy r-^ 3 r i A k' V3. f n, <\ a [ j' + . ♦ , L*. 4 4 ^_i_J # OUtS_ g # Putts 14 iS* vs, % 2*2 % £?£* vs a 3 2 10 4* . 4- . ♦. v . vs. set # outs! T - O f_0 _vs. fo 1 QQ vs. set # outsi T - S’ IS 1 vs. S2 vs. # outsl T - 2 5 ~ vs. % 3s vs. set # outs! T - 15 f 34 vs. 9 ♦ 9 ♦ vs. set A K vs. m set # outs 1 1 - 0 # outs 1 1 - 4 ? 2 vs. fo. 100 fo 3 VS. f. 3± < 20_ vs. % 20 ft 23 vs. f -' K i J + < _ / jk. VS. Nutt Ft> f9l n *\ 9 JJ L ^ i VS. # outs A.y~ - £ # OU.tS v=s. 1A vs. £?<& Nut FH \7-±o VS. Nut Ft> # outs A ^ - 7^ £A vs. 1<& Nut Ft> r ' A H J -> K VS. Nut Ft> l 1 j 12 # outs A ^ - 12 Q 3 2 10 . A . 4* . ♦ VS. overpaid # outs A A ~ 2 5~ vs. %^5 t *\ r ^ k J A, A, vs. overpair # outs A - £> 14 VS. ? 0 _E&_ vs. Overpair # outs AA ~ 2 -^5 vs. fo 5 vs. Overpair 9 ♦ 9 ♦ vs. Overpair VS. overpair # outs A A -13 30 vs. fo_^0_ # outs. A, A. - 2 vs ■ 5 # outs A A - 4 3 vs. ..9l # outs 62. ~T - 2* 12 * vs. r ' K | J VS. TWO Pair A l±J # ow.ts6Z.~r - 2* IS 1 vs. 2*2 r i 9 f-> 9 VS. TWO PGtir L±J r — *i 3 JJ r 3 L ^ , VS, two Pair # OK ? ~9± .ts GIT - -4- VS. f 0 ...9 r A jlI r ■> K liJ vs. Two Pair # outs 62. T~ -13 # owts62-T~ - 2 # outs 62-~r - -4- 30 vs. To vs. \ ¥ ♦ 4 4 VS. straight # outs 45^ 1.0 23 vs. % A A VS ^3 # outs -1 ? 3g VS. % vs. two Pair # £)U.t£^y^" ~ O fo HOP vs. 0 pp. lr VS. + ope^ tv'vdtv Opfin, evi^tcr VS. + FLu^h draw # DUtS Al<^ - 2 $ 102 vs. 0 # puts S’_9 - 2* £2 vs. $_lj? # outs K_9- 14 £>£ vs. 32 ¥ ♦ 4 4 VS. Straight # outs 3t-3 fo 2-0 VS. SO vs. # 0w±£ 7?-14 £S vs. 32 VS. TW£) PftLK # 76^22 -59 vs. fo_SO_ VS. Tcp pftt.r PaLr VS. + ope^. t\A*dtr OpfiJA. eader VS. + Flush draw # Puts AK- ~ ±7 3..9 vs. £1 #£>W±£S7~ S’ # outs kJ> « S2 ♦ fKl fKl vs. |T| (T| JL +j vs. # outs Jt- 2 # OUtS Jr- 3 # outs Jr -1 5 VS. 7o °(o^5 vs. fo SO 3R vs. ft 2 vs. # outs Jr - 22 % 50 vs. fo _5_0 T A T A U . ♦ . A , ^ , J . * . * . 4- , vs. Poctedt pair bdbw tp # _ 2 x -% VS. 7t> S' K \/c: Pocteet pair I ’ bdtawTP # owte 62.62. X 5 vs. ^ 5" Poetedt pair bdbw tp # cwt£6Z.GZ -C> IOC 1 vs. 0 ppatedt -pair bdbw tp # ow.te 6Z.6Z ~ "J~ X 16 vs. ff £4 Patteet pair below tp # DM.te62.62. _ 1.5" $ 34 vs. % 66 f i J /— *\ 10 Pceteetpalr UL 4 ^_ i _J bfibw tp # 0Mte62.6Z. vs. % 5 T A T J. J 4- , ii . 4 . J . * . T . 4 . K| VS. £,U.t shot # outs62,r - O Jo 1 00 vs. 0 K i vs. C)U t shot # oi/±s 62.T ~ 3 v3 vs. vs. <^w.t shot # owtsCZT - 6> % ±00 vs. 0 r /■ ■* fl 4 ^_:_h 4 \ r j vs. CfUt shot # outs 62 - 1 - 5 ^. 5 " % gg vs. vs. shot #onts62.T 5\«fT S'S' vs. vs. qutshot # eutsaT - 4 % J>± 7 Q Q / ¥ , ♦ , ¥ i J , 4* , VS. Fmli- House. # outs 73 -2 % 5_ VS .% 3s_ f-1 F 1 K K 4 L_I_ j .iu tIii at of a teiiA^ # OUtS A - 2 vs , f 3 s r f - 1 K K JJ Liu VS. overpaid # outsi r - 2. % ^5 vs. °(q_5_ K K Jiu VS. Fli^sli drflw VS. 0p£t/v e^der VS. overcards # ou.ts KL6Z ~ ^_2T_ vs. % 20 #0UtsST~ S S’2 vs. j.S # outs AT - 3 ~v3 vs. A' m 7 Q Q f ¥ 57 . 4 , 57 ¥ J , 4- VS. Full House to**?? -7 f> vs. S'! vs. Three ftf a tetiMri # cuts aJ- £ 1*4- vs. ^_£^l VS. OVdrpfllr # OI/Lt£~| P * 1 fo 3% VS. ffi 2 VS. Fiusih dfavv VS. o-petA, ei^der 10 ♦ VS. overewards # outz TT - 7 £M- vs. l.i& # outs ST - S’ fo ST VS. lS # outs AT" - (9 1<99 vs. 9 7 Q Q f ¥ w . ♦ , s7 ¥ V . * . VS. Full Htovi&t # outs, 77-0 fo O vs. % 100 VS. Otffirpflir # £)u.t£"i r ■ 12 vs. % vs. Th \rtt of # OUtS AJ?- g lg vs. g2 vs. FLias>i drpw F ' f - 1 A 10 JL JL VS. VS. Ovsrcarcte # outsf<jj 2 , - i£> g<& VS. # 0 utsgr- g g2 vs. ig # outs AT26 p.5^ 40 vs. <&£> - \ 5 •f* 4* 4 4 vs. set # outs- 4"4 - 2 S vs .% 2s vs. two Pair #outsf^"r^ s? g iff vs. % g2 VS. TopptTLr # outs K662 _ 5^ % S3 vs. ft 11 VS. Qvirp&ir # o ute A A - 22 50 vs. -5 O A * A v vs. opt evader <^at shot VS. + Overca rd # outs 62 _ / ~ (c> fZ S*<& vs. % 1~4- # outs A 62 “- 4 - % -* 1 vs. .-V vs. set #out£ 44- 1 vs. 2 # pwtskLGZ - O 1Q<0 vs. 0 ra m L±- Lhj VS. r^ppflLr # 0 Ut£ A,A "~ 2 % 3s VS. h 5 VS. QVfirpfltr VS, 6 iA,der CfUt shot VS. + DverGflrd # cixts 62. J- g ^ S’2 vs. # puts 62.-J ~ & ^_S2_ vs. lg # owtsA62.-4 A VS. % J> * ♦ 4 # ow.ts4'f - 2* 22 vs. IS* vs. two Pear # ow.tsK,T - 2* 22 vs. 12 r ' r-- a J + -f- k_:_ VS. TcrppaLr # outs k!62, - 2* fo 2*2 vs. % 1 S’ VS. Overpatr # A A * S 1 ^ vs. 14 vs. opei^ et^der shot vs. + overc&ro l # OU t£ &J- 22 ft -52 vs. % 5O #outzA02.-10 23 VS. 70 * 4 vs. set # ou. ts44j^_ 4 % 3 vs. % _vl vs. two Peter # owtsKCT - 22 5 '0 vs. % 52 VS. ToppciLr # outs ki6Z “ 3 5 3 VS. 7o 7 VS. DVfirpatr # onts>A/4 - 2 vs. O'pet^v etA,der shfft VS. + CVC re arcl VS. 7o 5" # OettS tg. J - S’ $ £ J 2 vs. $ jS # outs A62. “ 4 vs. % 9 4 9 ft T . . . 4 . u . 4 . u . * , VS. overpaid # outs 33 - s t IS vs. % S2 VS. Overpaid # outs _.9_9 - 2 s 5 vs ,f Js; VS. DV&rpP.U # outs „5_9 - 2 % 3s VS. TO VS. Overpfllr VS. OVfirpalr 5 4 VS. overpaid # outs - 11 25~ VS. To # D\A.t& 33 ' & ^o_l4_ VS. # out*. 33j^ 14 6S vs. 32 * 4 4 * VS. Nut Ft> # outs AT - (b % 14 vs. % VS. Nut FH # outs AT - 14 &B. vs. % 32 VS. Nut FH # outs AT- 11 VS. o US /—* 8 7 VS. Nut Ft> f - 5 r —n [5 35jl VS. Nut FD L±j # outs AT - IS Jo bb vs. 34 # outs AT - 14 Jo &2. vs. % 32 4 4 - set #ou.tsTT- 1 vs. 2 r ' r—“■ K K vs. two Pmr # putts hi"T * O ^_L00 vs. 0 VS. Ov/fcrpalr # outs A A - 2 ? --^5 VS. Jo VS. T>P + T.K- Opfi*o, eader VS. + F L us,h draw VS. Oft \A* tv^dtr # outs AK - O % ±00 vs. % o # outs J~g ' 13 /O vs. 30 # outs <£.'J - S’ S'2 vs. fo 1 S' f -■> 8 [7] vs. set ^ ^ lij # outsTT - 13 [8] [7] vs. two PflLr 4 i - # outs KIT - 1-4 # outs A A ~ 15” ff 3D vs. fo TO -\ 8 r ^ 7 V3. t.p.t.k.. 4 JL f 32 # outS/AKw ~ 15" vs. fo &Q f> 3-f vs. fo_&£?_ ^ * 8 r ^ 7 VS. -S c*> 4 JL tv^dtr # outs 62. J- 1? 34 vs. ft 6>6> 41 vs. f_53_ Pot LS: 100 vlllatiA, bets: so 3 : ± oiA/ the c-flll Pot Is: 100 vlllcaiA/ bets: y-s 2.33 : i oiA/ the call Pot Is: 100 vIIIr'ua, bets: 20 o : ± oiA/ the cflll Pot Is: 100 vllUuiA/ bets: ioo 2 : i oiA/ the call Pot Is: 40 vttlaliA/ bets: 30 2.33 : i oiA/ the call Pot Is: 5"5" vllUatA/ bets: 3 s 2.5"7^ : 1 oiA/ the Cflll Pot Is: J-0 villain, bets: oo 4.5 : 1 on, the call Pot Is: 66 villain, bets: 41 2.61 :1 on, the call Pot Is: ^ villain, bets: 65 2.32* : i on, the call Pot Is: 12 villain, bets: 12 2 :1 on, the call pot Is: 5 villain, bets: ±o 1.5 : i on, the call Pot Is: 366 villain, bets: 125 3.4 : 1 on, the call Pot Is: 1 00 Pot Is: ±00 VlllaliA, bets: 50 villaI ia, bets: J-S call Is fo 25 of total call Is fo so of total pot Is: ±00 Pot Is: ±00 villain bets: 2.0 villa Iia, bets: ±00 ca ll Is f 14 of tota l Call Is fo 33 of total Pot Is: 4 0 Pot Is: 55 villaI ia, bets: SO villam, bets: 35 ca ll Is f so of total call Is f 22 of total pot is: y~0 Villain bets: 20 call is ig of total Pot is: ^ villain bets: 65" call is Jo 30 of total Pot is: S' villain bets: 10 call is ^ 4 o of total Pot is: £>£> villain bets: 41 call is Jo 2 g of total Pot is: 12 villain bets: 12 call is ^ 33 of total Pot is: 300 villain bets: 125 call is ^ 23 of total r- 1 ■ ■> a y\ t - J M 6 JL r——> 9 t —i A /-- Q VS. t > 10 t - 9 1 l*J L±J # outs 5 fo ±1 VS. fo 23 1 : Z.o3 t i a J f ^ K f i 8 f K f — A K vs. - 1 6 .♦J 4 i_:_ j # outs ±0 f 23 vs. fo J~J- 1 : 3.35 K r- ■ ■% A £ < 1 j t i 4 LL r i K , ♦, f -^ a 4 f > J <—£ VS. f -^ 6 ♦ V_-_- 7 IL # outs 0 f O vs. f> ~LOO 1 . Co r-^ J .♦ J r i 9 ♦ i 1 J f — ~i a r-n K r - 9 /-V 10 vs. f -1 A c -^ a L?l Lfl 4* v_:_, # on ts 3 ? J^3 vs. 7~ 13.2_9 : 1 r-^ 3 4 l 1 j r 8 r- 1 10 ,♦ J f 1 10 c - J r-^ J vs. f-> A f -\ K _J A [±J # ante X4 % vs. 32 2.13 : ± /-- 4 f i [J f i K F p 2 [♦J A f -n K /-\ fl vs. p* ^ 4 p 1 -" 5 Ijl L*J l*- # onts 5" fo^3_ VS. 11 g.O_9 : 1 r 7 J ^ J >J f i 4 Li r i A r-* J /-\ J VS. p*-i 6 /■-\ 9 i L±J A * ^_i_■< # outs IQ % 23 vs. % y~y~ 1 : 3.35 /■ 'i 6 t 6 f * 7 C 1 51 s -> 8 f -'i 9 VS, -\ J ? - J l±J LLI iJ # puts -f g 3 ± vs. g f —* 6 * k._:_i f -\ 10 M 4 Li 2 t ' 10 li f > J Li VS. r 'y 4 JL 4 # outs, O f 0 _0 _vs. fo ±00 Oo ± 0 . ±± : 1 1 # outs. 15 fo 34 vs. 1 : l.J?4 id .♦J t 1 8 r-* 6 ±J f -"s a 1*- /■ % fl A _;_j / - Si J LL vs. f -' A >._^ r - -x a jt. # outs 15 vs. 24- 1 ; 5\25' t k 8 , ♦ J 7 ♦ T\ LiJ f 1 5 r ^ K UL J l±J vs. r* ^ 9 s___/J V #Ol*t£ J 20 vs. < jS_SjQ. 1 : 4 r*-i A /-> 7 r- — 2 t \ 6 M L±. * L- ± -J r A K VS, r 1 10 F* 8 k + , l + J A # OutS -f # outs 7 L f—“’ 6 5 C 1 5 10 a V___ d 4- J .♦j L ♦ L J ~ n A r 10 vs. 5 9 JL ♦ i, __ _^ ■Jl # outs ^ vs. ^ X£> 10.11 : 1 5 '. 25 ' : 1 1 # OU ts 11 fo 2J5 vs. 7^5^ 1 # outs 2 5 vs. J^5~ 1 : ±3 A /*-> 18 f —\ 4 p"-1 4 l + J . ♦ , A r \ J vs. ^1 t 8 L±J JL'l # OUtS 2 fo 3s vs. 5~ iJ r j ^ 8 r -\ 3 ir V- > --\ Q i 4 .___ j 3 j*'-* K /-> ffl vs. Y Z' 10 l*J 4 s_ t _> 4 J \_ i _h # outs, 3 r ^ 10 r-\ [8 - -% 3 1* 1 10 ♦ J k_ z _- l*J l±J r i J f - ^ 8 vs. r'-*i 10 f-* K li l±J * L A ' J L±J # <9K.tS O r -i 7 , ♦ . r-^ 6 4* i 1 J p i 3 ! ♦ _^ 2 j--^ 7 LL f-> 7 *J vs. --V 5 f -- 4 LL # outs ±0 %_RO_ vs. 2.0 vs. g 23 vs. J~J~ 3.35 9 [♦ J f ■ 4 if ^ 6 1 j 3 4 r-\ 6 6 vs. ’a] KI 4 is- * —^ IL 4 ^ 4 ^_ k # outs g # outs ±0 V 4 \___ 4 iy k_/ * i 6 •J* -___> 5 f - A —> 10 vs. r ' 6 r- 9 jL, [ 4* J JL JL # outs 0 X S’S VS. XS 1 1 g 23 vs. %° JJ: i 3.35 %o _0 _vs. X too 1 OC 2 /* - \ 7 1 + J f y 5 f 1 8 /■ - " 6 Lt- /-N 8 vs. 1*-*1 A A ✓ - \ A Ijl # outs ZIQ fo 4 5_ vs. 55_ 1 : 1.22 r—”s 3 J f i 7 k + , r * K ♦ k_^ 4 p > 7 Lil /-> 7 VS. -% A l±J f -i a # outs g £2 vs. lg 4.-5 £ : 1 r i 4 2 Ol 6 t * k _;_> ¥ J r - A -> A vs. " - ^ 7 8 L±- L*J ±, # outs y~ l^? vs. g4 1 : S'. 25" # outs, 13 ft 30 vs. ft 1 ■ 2.33 r ' 10 A r t 8 r j 2 M . * J l*?*. |8' id VS. r ^ A K JL JL # outs g ft_22_ vs. ft XS* 4.5'6> ; 1 t i 7 /■ \ A F 1 fl id l*J L *J y. r- K J VS. -’ 8 f - 9 L±_ ^ 1 j . ♦ „ # DI/±£ g* ft g2 VS. ft lg 4.5'£> : 1 VlLUt l W Shoves: 4 100 Pot Odds: 3.7s ; 1 Fmalpot would be: _ 1.1 Y our oflll would be % gi of the fi-Aftl pot, Owt£:lS^ e^wfcty g 33 Return from pot:_ odrfs: 2.o.‘. : ± Opet^ finder + Flush draw x Cflll [ ] Fold Pocket -pa ir below Tp call x Fold Return- from pot: Pot: 4100 VHLfl la Sh o' V££; 4 30 Pot Dddz: ~' ? : 1 FLAflt pot would be:_ your tall wouLd be % _ of the -flwjjtl pot. Outs: 2 Faulty g -* odds: 24 : i. c^ut shot Pot: 4120 vlLLalAShoves: 4 SO Pot Odds: -:. r : 1 Call x Fold Return from, pot: Flwalpot would be: _ - r: Your call would be % 2 1 of the fi-Afll pot, C>utS: -4 Faulty g 9 odds: 1.0.11 ; i Flush dr^W x C-flll Fold Return from pot: Pot: 4120 villa La sh o' ves: 4 SO Pot DddS: _0_: 1 fLaaL pot would be: 1?_ Your call would be % •' of the ftAfll pot. outs: ^ Faulty g_^ Odds: 4 ; i_ Pot: 42.00 Flush draw vUlal* shoves: 4 <bO Pot odds: 4,33 : l FlaflL pot would bt: ~- :n v your cflLL would be % 1 3 of tke flaiil pot. Pot: 4 55 Pocket -potr vlllnlu Shoves: 4 35 " be Law TP Pot Odds: 25 ? : 1 FlaAL pot would be: r25 OfJ LL your oalL would be % 2 % of the flaill pot. Fold Outs: ^ Equity £ 2q_ Return from, pot: 4 : 1 x Fold puts: 2 equity g 4 R_£tura from, pot: odds: -!4 : 1 Optv\> £dvct£r pct: A±2S -)- vlUniu shoves: 4 ®)0 FLusVi draw pc * odds: 23 9 :1 Fla A L pot wo u L d be; ' H II Your c-^eLL would be % so of the flaiil pot. Pot: 4 Flush draw vtllnlu shoves: 4 &O Pot Odds: : £ FlaflLpot would be: ^ 1 C LL your sail would be % of tk£ flailL pot. Fold owtsis - Equity 33 Retura from, pot: odds\ zloz. : ± 0 Fold Outs: ^ Equity ^ 20 Return from pot: odds' 4 : ± Flush draw Return f YQY& ■pot; Pot: 42.00 villain shoves: 4 50 Pot OddS: 5_ _: 1 Fmfllpot would bt: _2_ Your call, would be % i '• of the fUutl pot. outs: ^ Bqulttf f D _^_ odds: 4 : ± Pair Pct: 4 so -j- villain, Shovts.; $■ 40 Flush draw Pc>t Dsleti: ; 1 Fma L pot would be: _ your call would be % -.._ of the fbud pot. Outs: 14 e^wfcty g 3Q RitLtw. -fyc*™. pot;_ odds'. ,33 : i Pot: 4±gO vUIru*. Sl'io\/es: "40 Pot Odds: 5.5 : 1 FIia^L pet wouLd be: ^ / ~ your eflLL would be %_i . of the flvLflL pot, OutS; *4 Bquity g ? Retu.rw-frenA.pett_^dds: !•:• _i : ± £}ut shot Call x Fold Pet: 4-400 villain shoves: 42 £> 0 Pet odds.: : i Ftw^lpet would be: _ y our call would be % ,3ft ef tke final pet. outs i 5 %_ 33 Return. from, pet:_ odds,: _y__<_ : ± open. tv^dtr + Flw.sln oircrw x call □ Fold open ender call x Fold Return from pet: Pt*: 4300 v'dlaiin. Sloovss: 4^-05 Pet Odds:_: l Flnfllpot would be: ' : " ' ‘ your tall would be % g of tke final pot, Duts: S* Equity g i? odds: 4.S2 : ± Pet: 4-400 VlllflLm ShoVfiS: 4 ~^0D Pet Odds.: _: i Ft m3l pot would be: . _ _ your cgLL would be % i ~ ef tke final pet. outs: 2 Faulty % * Return from pet:_ odds: _: 1 Pocket pair below TP call x Feld ^ „ Pot: 43D0 opeiA, r villain Shoves: 4200 £l\p( g y Pot c>i ^^ : 2 * 2 ^ : 1 FtkvflL -pot would be: ' H D II Your ctf LL would be % so ^ MU ' (jfthefMtpife <^W± shot Pot: 4320 -)- VtliflUs ,SlnO'/£S: 4200 Flush rirctw Pot oddS: X£ ’ 11 Flvsjl l pot would be: 7 " 2r: v nn \ 1 Your call would be % 2 ^ ^ WUV ofthef^tpot. x F0Lp( OutS: S equity g i7 Return from, pot: odds.: 4.22 : l x] Fold outs; 13 equity g 22 Return from, pot: odds: 2.5 Y : 1 Pot: 4 7^0 Flush draw vUtal^ shoves: 4 ^0 Pot Odds: : 1 Fma L pot wo mid be: 1 ^ C Cl LL Y^t<^ call womld be a? of the flmftl pot. Pet: 4 ^0 DVfirCfirrfs villain shoves: 4 4*0 Pot Odd s: 3 . 2 S : 1 Fuvfll pot would be: C Cl LL your oflll would be % 24 of the flvLfll pot. X PoLpl OutS: ^ enmity g 2# Return. from, pot: odds: _4 _: i y - f^OLpl OutS: &> equity g 12 Return from pot; odds: &.&3 : ± Nut x call □ Fold Return from, -pvt; Pot: 4 1 00 viLlain shoots: ^ SO Pot Oddi; 2 : 1 Filial pot would be; ■ Your cat L wpwlpl be % -:f of tke final pot. outs: i 2 ^ulty g ^ Oddi: Zl25 : i Pot: 4 45 Vi. LUt In, 3 h OV£S : 4 20 POt OdplS: - 1 : 1 Ftma L pot would be; _ : _2 _ Your call wpuLd bt % ■ • ■■ of tke final pot. Outs: B qulty % $ Return from pot:_ Oddi; i-un : ± <s}ut skot call x Fold r A f > 2 l*J f > J t > K r ^ A s_i_ / r A C 2 J ♦ VS. < > 3 Pot: 4 1 00 ViIUuia, bets 4 £0 Akviout^t behind 4 ^.00 Pot Odds,: 2.25 : 1 Filial pot would be: 2-&o your coll would be % 31 of the fli/tal pot. Outs: is Faulty 27 Odds: 2.7 : i Profit: ^ 10 Mgtleeup 437 X call =ev Fold 9 /-\ 10 /-\ 4 /-\ 6 •F JL , 4 1 - /-\ K /-- 10 vs. t > J e > a ^4 , ^ 4 „ •F •F Pot: 4 J -5 villain bets 4 J-5 A^uouiA,t behind 4 ^50 Pot Odds: ^ _ : i Filial pot would be: 225 Your call would be % 33 of the -fmfll pot. Outs: 13 equity 30 Odds: 2,33 : 1 Pr0"f!t: x call =^v Fold r-> A UJ t -> A 4 j /-^ 5 [±J f -> 3 .*J f -^ r > -'l t -> A j VS. K a UJ __- M Pot: 4 villain bet^ 4 30 An^OW-i/vt b tklvuA 4 150 Pot Odds: 2,75 : i Filial pot would be: " T 5 Your call would be % 2 7 of the fli^o L pot. Puts: g equity % ig Odds: 4.5 £> : 1 Profit : 7 Mflte,eup: 43-ff x call =ev Fold 4 4 L 1 J . V 7 4 ^ 4 J r ^ A r v Q vs. ✓*- s K f - "i K M l*J j±J L5J Pot: 4 y-5 villain bets 4 4S An 4 . 0 w.iAt behind 4 Pot odds: 2,67 : i Fl^aL pot would be: Your call would be % 2.7 of the fLwaL pot. Puts: 11 equity % 2.5 Odds: 3 _: l Profit: 5 - ! Mflfeewp: ^--*^ scan o=ev nFoid 5 Lr VS. Pet: 4 &Q vlLLati^ bets 4 ^O An^ow.i/vt b tinted 4 300 Pet Odds.: 2_: ± f -" 6 Li- fio Ifio] ♦ JIVJ [9] t - 1 7 ► J 1>J f ^ 8 nri * - J ♦ 1 i Fmal -pot weodd be: m i£Q Your call would be % 33 of the ftiA -0 L pet. Outs: 11 Smutty % 2.5 Odds: _s _: 1 Profit: ^ ‘ ^ Mflleeixpi ^ 4 -- ucuLt n=ev □Fold /"--\/-\ K 10 4 K J M l*J f y K r- n a VS. A t -^ A UL . Vj ♦J M Pet: 4 2-2-0 villain bets 4 Avuou-Wc behind 4 300 Pet Odds,: 2/u 7 : 1 Fi^eLpot would be: 2.50 yeur call would be % 2 g of the filial pet. Outs: 2 Equity 5 Odds: i_9 : 1 Profit : ^ ? Mfl feeup: 1102 Cali =bv \x Fold ■\ f -\ J f-> 31 A ♦ j L*J VS. r S /•“-*\ K 4 v_i_ / -A Pot: 4 20 Villain, bets 4 Awiouut behind 4 Pot Odds: 2.25 : 1 Ft^fll pot would be: Z '- L0 your call would be % si of the fmfllpot. Outs: g Equity ig odds: 4.56 : 1 Profit: +S?Mflfeeup: 4i23 CflLl =ev DFold - N Q f-*i 7 f -^ 7 y M / M / HE* o V ___ J / ^ 7 /*■ \ 8 vs. g t \ 10 L*J JL pot: 4 7^0 Villa tw. bets 4 45 An/u>uwt beklud 4 ^00 Pot odds: 2,5^. : 1 Flrua l pot would be: 1 ^° your call would be % 2g of the fulfil pot. Puts: is Equity % 34 odds: 1._?4 : 1 Profit: 4ia Mateeup:£_J_5 call = 6 V Fold > 0 ( - 9 VS. ( -\ A /-\ 10 ■ s_> ■ s_> , * J •F v_ / Flush draw Combos .straight Pair + £Ju± shat Cam.bas a. 9 7 Commas Caabas K9siK8s K7s K 65 Kfs K4s K3s K2s ^■tQJsJjQTsj Q9s QSs Q7sJ[Qfaj[Q5s Q4s Q3s||Q2i j^J J8> 7J[^J|^J: »*, ^Jl^J |T9s|TSs T7»||T6»I|T5 s| : T 4* T3s|iT2s| 9So |^Jj [ S7sj| S6s 1 1 S5s 84s 83sj|S2s j ?6$ j [ 75s ll 74> 73> ][ 72> j 1 860 [ ; 6o;^^65»] 64s 63sj[62sj 198 combos tn preflop range 0 % 216% /- A f -^ 6 /- 10 f - ^ 2 [4, 4 1 V, ■ j 4 1 J r i 9 r "v 9 vs. f *\ A ( \ K ■ L_-j ■ ,__u ,_. Fuwsti draw Combos Th ree of a tetrtd Co tv. bos. open. en.o(er Combos TWO PCI IK >f Combos *\ 4 L 1 j . ♦ . *?• J 1*, c ^ r ^ /*■ > t i 9 9 vs. K K ■ ^^ ■ _. Full House Combos Three of a temd 4 Combos TWO PCU.K Combos Po&teet -pair below TP 24 C£mb#£ L | KJo| QJo 2o| K2o Q:d Ko AS* _, H •^JH KSi [K7sJ|Ki63| K5s K-d KS ;K2s QSs Q7s| jQfallQg. Q4s Qjs| |Q2s J7s m II J5i J4s 32s TS& |T7ji||T6i||t5j 1_J [ _J1*_I T4j |T3*| T2s 9 >'5 i 9fe 1 95s 94s j 93s j1 92s i87sl \Ms\ S5s S4s 35s S2s 37* u [7fo.j 75 j I 74s 73s I __■ 112. S6o [76oj Ul |&5s &4s j 63 s | |62s 35o “ fc ■65o 55 54 s j53s|(52s 34d ' 4 °i 54o f4o 44 43 s |42s 33e 1 63o | : S3o J3o [ 33 j 32s 32o \!2<f 62o 52o J 2o 32o [22 19S combos m preflop rar§e : 0 *. 21 VS. 4 Combos Combos TWO pair 4g cwnbos IS’ (3Dmt3DS r ^ 4 4 r i 4 *£• ^ 1 J r ^ 10 . *j r ^ 5 *f* r 1 ■ ■ vs. j l±J r 1 j LJ Full House Combos D\Jtr ptfur Combos Tcp pfltr X3 Combos Three of a teLnol combos /-\ J i», t \ 8 t -1 J •J* J * 4 ♦ J / \ ( 1 f % ! ■ -’ 0 0 vs. A j m < _ j ■ - LL UJ Full House 3 combos Dverpair ~j^5 combos FuLL House Three of a \zivid combos combos /-\ 3 K f-\ A /-\ 9 4 v_ i _ > /■-\ A / \ J VS. f \ K /-\ a _L1 A l V, Pot: 4 100 villain shoves: 4 %0 Pot Odds: 2 .2.5 : 1 Filial pot would be: Your call would be % 31 of the ftwfll pot. Outs: 14 equity 32 Odds: 2.13 : l Profit : t 3 xCflll =ev Fold 3 v \ P7 ✓-^ r 3 3 vs. K * . V ! Pot: 4 100 villain shoves: 4 %0 Pot odds: 2.25 : 1 Filial pot would be: 2&0 your call would be % 31 of the fmfllpot. Outs:__g_ equity ig Odds: 4.5£ : 1 Profit : ^ ~ 34 call =ev x Fold / \ t - \ 3 i*— ] -"> E r > A r \ 9 .*J ♦* _ 1*. V-—-—^ A — ] -n E VS. k -> fl •J* 4* L J vj .vj Pot: 4 1 00 vlilaivi shoves: 4 £0 Pot odds: 2.25- : 1 Filial pot would be: z&o Your call would be % of the -fmalpot. Outs: equity % 20 odds: _: 1 Profit : ;t_S^ Call =^v x Fold [AKsj (AQsj | AJs | |ATsj |A9sj[ASsj ^A7sj [A6sj ^A5 sj [ A4sj [A3sj | A2s j K7s |K6»||K5 j| K4s||K3s |K2s jlQTs I Q9s QSs Q7s||Q6s Q5s Q4s Q3s Q2s Jk /v> -A A A A ^ A 198 combos m preflop range HHBDH _ _ or; 21 . 6 % r t to* V-' /-\ K J r A <** s_> /-\ 9 V 1 V -> o -i r 9 vs. " "^\ K r-\ Q 1 ■ <■_> ■ M J?J 4 5 combos X _ 3_ Profit = set 4 Cowibos X Profit two Pair ^ Combos X -2j Profit Cflll - £ v x Fold Total: r— 1 4 r ^ 3 r i 9 f ^ 3 s l + J l±J vj f > A Y VS. a -\ Q ±J 4* V J v 1 d M Pot; 4 ±50 villain 5 h Q\Jt £>: 4 20 Pot Odds.: 2.gg : 1 Ft^alpot would be: 310 your call would be % of the flktflL pot. Oute: 3 a Equity ^3 odds- o/5f : 1 Profit : xC«ll =ev Fold \ / ♦ L V * •F 1 K — K vs. / ^ a /-\ fa U*J JEJ v L J M Pot; 4 ISO vllUtlru shoves: 4 20 Pot odds: ^gg : l Fl^Lpot would be: your call would be % 3& of the fmfll pot. Puts: s equity ^ odds: i_9 : i Profit : Call =sv x f old /-* t -\ 10 10 vs. a a * k V, ♦ 1 Pot: 4 ISO Villain Shoves: 4 Pot odds,: S.gg : 1 ¥i\AMi pot would be: 310 Your call would be % of the fulfil pot. Quits: Equity ^ _Js odds: 0,05 : 1 profit : ^ 214 xjCflll =ev Fold 3 * L 7 *_/ l*J 'k' '9' JJ vs. / s a 4 -_ i _^ / - \ a Pot: 4 15 ^ villflUv Shoves: 4 So Pot Odds: 2,:?F : : 1 FttA^Lpot would be: 31 -° Your call would be % of the filial pot. Quts: 3J? equity 23 odd S: aiQ : 1 Profit : ^ 1 -- 5 ' xC^LL =^v FoLpI K7s K6i K5 s K4s KJs K2s J^QJsjjQTsj Q9s- QSs |Q7sj Q6s jQ5s Q4 s jQ3s |Q2 s 19S combos in preflop range r 4 , . r > 3 , r -> 9 UL r \ 3 M f - 0 • 0 a VS. f ' y Q 4 1 j Y M fLw&Vi dmvj iLS* Combos ^ Profit — ovtYfair weaker cverpair Top pair Combos Combos Combos X X X Profit Profit Profit = - y-so = 114 0 =■2-30-5 x call — &V Total: 4 [♦, 4 4 / \ K / - \ 9 vs. / - \ Q / - \ IQ _LI 4 4 J Pot: 4 ±50 villain shoves: 4 Pot Odds.: 2 .gg : 1 Filial pot would be: 310 Y our call would be % 26 of the filial pot. Outs: 3-9 equity g_9 Odds: gi2 : 1 Profit : £i_2? xCflll =ev Fold 4 8 t \ 10 t s 2 v, 4 HE* > 9 / - \ j VS. / - \ 8 *J 4 * l x ^ 10 Pot: 4 ±J-0 Vlllfltl/u Shoves: 4 120 Pot odds: 2.42 : 1 Filial pot would be: 41 ^ your call would be % ^3 of the filial pot. Outs: 36 B^uuty ^ g2 odds: 0,22 : 1 Profit : 4 21./ xCfllt =ev Fold f > 4 / > 8 10 2 \ 10 -> j vs. /— *\ 8 /-\ 10 M lil 4 4 ^ 1 j Pot: 4 ±J~0 vlll aiui shoves: 4 120 Pot Odds: 2.42 ; ± Filial pot would be: 4io your call would be % 2,9 of the fHiA/fll pot. Outs: 4i equity J 3 Odds: oog : l Profit : xCflll =ev Fold t \ 4 /-\ 8 ^ > 10 r—> 2 4 L- A -J . 4 , f m \ a /■ \ a VS. -\ 8 -\ 10 4 l±J 4 Pot: 4 villain shoves: 4 120 Pot Odds: 2.42 : ± Filial pot would be: 4 10 your call would be % 2-9 of the filial pot. Outs: 2 Equity 5 Odds: jj : ± Profit : * ' 2. s call =ev x Fold r\ m 19 S comboi in pts-flop range _ 0 *. 21 . 6 % opei/u tv^dtr Top p air overpnir set 4 i *J 8 ♦ W.___H- 10 L 2 r-' 0 ■ 0 a VS. s' l + . f > 10 + & C-okviioos ^ Profit = 10 Combos, X- Profit 24 C0I/U.bos X Profit — 2 Cp^ubos X jg Profit x call = 5V Fold Total: r-> O r-^ IrI r -> A Cm U M u U ___ J '6' — A vs. — Q / a 4* L J 4* L ^ J 4* L A j 4 Pot: 4 140 villa uv Shoves: 4 100 Pot Odds,: 2,4 : 1 Flu,aL pot would be: your call would be % 2? of the filial pot. Outs: Q 6^ulty % o odds: oo : i Profit : +_ t£p Call x Fold \ r ^-> 0 '-\ ft [7T r-\ A La 4, u M u [♦J O 4 ~ J ' \ rr / \ « -V A ( - 7 7 vs. Q fl id _ 1 L±J 1 ^ j Pot: 4 140 villain shoves: 4 100 Pot Odds: 2 .* : 1 Flu-aL pot would be: 34-0 Your call would be % 2 of the filial pot. Outs: 42 equity 3s odds: o.Q5~ : 1 Profit : ^ 224 x call =^v Fold \ /■ vs. Q Pot: 4 140 vlllolw.skov/es: 4 loo Pot Odds: 2.4 ; l Flwcil pot would lot: Your coll would be of tke flu-dl pot. Outs: 2 equity 5- odds: ±3 : i Profit : +_i £2 call =ev x Fold r •F i^j l + J 4 l 1 4 -\ A ^ \ T T -\ A / \ A A K VS. Q fl +. Pot: 4 140 VlllflLi/t Shoves: 4 100 Pot Odds: 2.4 : 1 Filial pot would be: ^ 4 £ Youcr coll would be % 2,3 of the fuual pot. Outs: 3g Faulty Odds: 0.16 : 1 Profit : ^ 1 --^ 4 xCall =ev Fold A 19S combos in preflop rang? _ ' o% it .6% Mobster W taker Oxftr^mir overpfar Nixt No Pair (M l- r"-> 6 r-\ 6 oT *f* , _ > 4 1 f - s 0 t -' 0 vs. f ^ a fa] m L j m L •f* 4 1 2 Combos x X.0 Profit = 30 combos X 2_24 Profit - Combos X 'Profit = Combos X l_?4 Profit — x Cflll =ev Fold Total - 2 oo GTO£) -.%? 4 31D4 2640 / V 2 3 ♦ J ♦ J L A 7 — — J J VS. *K ^ * . Pot: 4 55 vtUfltw, bets 4 25 AntouiAt behind 4 3-20 Pot Odds,: 3.2 : i Fit'UiLpot would be: :g5 your call would be % 2-4 of the fl^udpot. Puts: 14 Faulty g 32 odds: 2.13 : 1 Profit : 4S Mflteeupr : ~ x call =ev Fold [81 r- s 2 [31 r -> 7 ■>J ♦ ^—i— 7 L*J ♦ J r \ 9 7 \ 8 vs. r \ A / \ 7 * ^3 Pot: 4 55 VlLUiua, bets 4 25 Ah/lduW t behind 4 ^20 Pot Odds: 3.2 : 1 FtvuaLpot would be: 105 your call would be % of the fl^lpot. outs: 14 ^uity ^ 32 odds: 2.13 : 1 Profit: 4 & Mflteeup: 4 - iy X call — BV fold — 3 / •> 3 . VS. A 7 l*J 1*1 V J L±J LJ ’Pot: 4 55 VLllflLt^ bets 4 zis Amount behlud 4 120 Pot Odds: 3,2 ; i Flt^al pot would be Your coll would be 24 of the filial pot. Puts: g Smutty ig Odds; 4 .S 6 : l Profit : £ Mflfeeup: 4 o/ X Call =ev Fold Sy 1 8 ♦ 2 ♦ 3 ♦ 7 ♦ 7 * vs. A ♦ PDt: 4 5 ^ Villain bets 4 25" AwiouWt behind 4 120 Pot odds: 5.2 : ± Pi\A,al pot would be ■ _ '' your oa IL would be % 24 of the filial pot. Puts: g Fruity ig Odds: 4.5 £■ : 1 Profit: .L _ Makeups'_ xCflll =&v F old 135 :ombos in preflop rane i o% 21 . 6 % Dv/erpfl[.r Top pear set Two Pair 8 V r % 2 f ^ 3 Li_ r 1 7 .♦J r i 9 ■ i' > 9 8 VS. ' \ A ♦ r 7 s ^ J Com-bos X Profit — 4 3 5 b combos X XQ _ Profit - &0_ 4 Combos x 1 5__ Profit = bQ 2 C-otubos X Pro fit = ^0 Call =ev Fold TotfiL: \ / vs. Pot: 4 viii&u a, bets 4 y-s Anvoimt behind 4 y~5 Pot Odds.: 3 , 0 ? : i Ftt^alpot would be: 3 ^o y our call would be % 33 of the pot. Puts: 1 5 Faulty 34 odds: : 1 Pro-fit : 42 Mflteeup: 4 - ^ x call =ev Fold r i 3 r ^ Q r 1 5 r J . tf-J M Y y' \ Q VS. a' k' LJ A V. 7 4 1 V. * 7 L*J Pot: 4 %0 vLLLr'ua. bets 4 Amount beblud 4 y ~5 Pot Odds: 3 dJ- ; i Fl^al pot would be; 33 - your coll would be % 33 of the fmfll pot. outs: 10 Fruity °g 23 odds: 335 : 1 Profit : : Mflfeeup: E" Call x=ev fold to f \ a t > 5 ■> 4 lf ; 4 1 ^ /-\ /s f N /■ \ TT Si J VS. A K L_—_J L*J J*J Pot: 4 *0 Villa tru bets 4 7~5 Amoun t behind 4 y~ 5 Pot Odds,: 4 2 -PJ~ : ± Final pot would be: 230 your call would be % 33 of the -fmal pot. Outs: 11 Equity ^ 2S Ootols: ^3 _ : 1 Profit: 4- 1 £ M«teeup: 454 x C-flll =sv Fold 3 / - \ Q 4 v-±- J ( \ 5 ♦ ^_ i _ 4 J M / - \ TT r \ T T f -\ / \ TT K K vs. A K UJ L*J Pot: 4 £0 Villain bets 4 7^ Avuount behind 4 7^5" Pot odds: ‘Sip? : 1 Final pot would be: 230 your call would be % 33 of the final pot. Outs: 15 equity g 34 Odds: i ._?4 :1 Profit: 4 s Mflteeup: 4~ 4 xCflll D=ev Fold 19S combos m preflop r to t. a 5 J l ♦ , 1 - 4 1 M r •> 0 f -' 0 VS. r- A K a L j m L J 4 4 1 Top pair Combos X 3£t Combos X two Pair 2 C-om.bos X £ _torsos x X call =ev 25" Profit — O Profit — Profit - _25~ Profit — FoLc^ rotnl Pot: 4 0*0 villa u a, bets 4 4P behind 4 120 Pot Odo (S: 233 : 1 Fwualpot would be: - s o y our c&ll would be % so of the flv^al pot. outs: ig Bo\ui ty g 4x Odds: 1.44 : l Profit : Mflk£up: 4~ 2 4 x call =bv Fold ■V /■ t > 6 9 r*-1 r 3 l *J \ _/ l*J — — — — 8 VS. A 7 4* A _± Pot: 4 &o ViLUuu, bets 4 45 “ ArttoM.i^t behind 4 120 Pot Odds: 2.33 ; 1 Filial pot would be: 1S ° your ooLI would be % 30 of the fii/ual pot. Outs: ip Faulty g 23 Pdds: 3 . 35 ' : 1 Profit: ^ ~ 11 Makeup:^'-- x call = ev Fold t \ 6 4 * ^ ^ t \ 9 [♦J * . ni > 5 f y 3 ♦ L - A - J f \ A / > A f -\ 9 9 VS. A 7 M nj i±j Pot: 4 &0 villa iv^ bets 4 45 T Amount behind 4 3.20 Pot Odds,: 2.33 : i Filial pot would be: 150 Y our call would be % so of the filial pot. rr tc\*i t j> Cal KAt Irvwtr ? Cal Odds: Outs: 13 S^uLty 30 2.33 : 1 Profit: Makeup: ^ xCatl =ev Fold r-^ 6 ^ x ^ f - 9 [♦, r-^ 5 r-^ 3 4 TT /-\ A /-> A < > K fl VS. A 7 .♦j l±. ♦ 1 Pot: 4 £0 villain bets 4 4 £T AyvcoujA,t behind 4 3.20 Pot Odds: 2.33 : i Filial pot would be: ±5 ° Your call would be % 30 of the filial pot. Outs: 3g Faulty g£ Odds: a±6 : 1 Profit: 4^4 Mateeup: 4~ 13 xCall =ev Fold y A5s iA4s||A3siiA2sl IlKQs [KJs (KB iK9sj KSs K% 1 L J v J \ L J K6si K5s K4s K3si QTs Q?i Q8i Q7i Q6s Q5s Q4; |Q3s Q2 s LI_ LI_ ) LI_ j LI_J L_I_j LI_LI_J LI_LI_J !9S combos in preflop ranee _ 0% 21 .6% h/" f > 6 Hh k_ * f -■> 9 . ♦ . f - N 5 ♦ , s. _ j /- 3 [♦J •o '-1 9 ■ VS. / - A uu t \ 7 _tJ overpalr 2 Combos ^ iLO Profit — oj~o iStrfli0ht 3 Combos x 20 Profit “ GO set 0? combos x 40 Profit = 24 0 I^Okvut/vfltred draw O combos X 20 Profit ~ Fold Total: 12(9 o>3o X ll = ev ■* ' A Y Y L ♦ f i J Li. r- A Li- /—^ K LiJ VS. ?- 1 a 4 r t 9 4 j ‘s_ t _ s # outs, 5 f 0 83 vs. % l7 4.88 : 1 n- ~ MM ' 7 „ * , * i K Y r 1 * 3 Y f - A l_J r-■% K vs. -■'i 7 liJ i*-1 8 # outs 5 " 82. vs. iLS 1 ■'f . 5 " £? * i. r 1 -> 7 /* "X 7 M f ^ 10 ?-' 7 A -■> 8 LiJ vs. f -*1 8 JL f -\ 9 # outs 2 %Jl 2_ vs. 2g 2 . 5^7 : 1 f-■> 8 i 3 [91 l*J l*. t ♦ A A VS. 8 9 , V, 4 i._—- -* 4 ^_:_ * # OutS g f 2,9 vs. fo JjL i : 2.4 5 Y .♦J 7 7 'j' a 1 vs. [Al k! L_^ 4 ^_ z _ u 4 ^___ j # cuts ±5 f> 4g vs. -5T2 1 ■ 1.02 f — > J t \ 7 »"—i 7 l*. M 7 -\ 8 VS. a' K l ♦ . .♦J 4 %._. . j 4 t,_ Z _^ # outs g g 74 vs. g 26 2 . 25 " : 1 ,/-*v 8 [4, 9 l"-% 2 Ijl /•-\ A UL K _) vs. r-> 7 6' # ou ts :L4 .5~ 1 vs. 4-9 1.04 : 1 /■-> 5 y) r*—™? 10 y. r p 7 J*J r 1 a * 1 1 > -" J VS, 9| * ^_/ f -1 9 # outs £> ^_2^_ vs. y ~4 1 : 2 .£ 5 ~ r-^ 7 f \ 9 5 4, 4 v_£_> s*s f -^ 7 / \ 7 vs. K-" 9 r -" 9 L*J A LtJ # outs 1 \/ # 01 /CtS 2 3'2- vs. S’ r- 2 f % 5 9 JtJ A l_J -1 2 A vs. /-- \ 6 l_ r-1 7 # 0u.ts> ±0 ft £*2 vs. 3S 1 f-- 9 / r -> a ♦ ^—\ A r -\ A A a *t* ^_> vs. f* - ""1 9 f ->. 9 # cuts 4 ft 21 vs. ftJ ^3 ±±.5 ±.6>3 r*-^ K 1*, 7 ^b / * K 1 K VS. p*-? 9 f- 10 ^_:_- L±J jb A # OW*S 14 ft &0 vs. ft ±.S r j " 6 .*J A K A t -% 6 V*b -1 7 jb VS, -1 a k *b r ' J A # outs 1 ft ^t3 vs. ft 5 J~ 1 : 1.33 r* 6 M — A l*J ' ' K .*b p*- 6 jb '- \ 7 vs. f 1 A Jb r*- a jl # outs 14 ft 43 VS. ft 5 J~ OJS , 1 1 i n ■* Q ±u 4* . J . 4 . . * . vs. # ou.ts.3T - 2 fo 3& VS. VS. TWO PfllT # putts 3t- 14 fo_50_ vs. 50 vs. Top pair # 0U.t£ Jr -14 ^3 vs. $ 47 VS. WCfllW Ovcrpfllr A 4 K 4 vs. E>otou i/urted dKflW VS. # outs 62 . 62 , “ 1*4 5~4 vs. 46> # 0 u±s 5 ~ 6 ?~ 6> gQ vs. vs. 3Q i n T Q i. U , 4- . J . 4- . *7 , ♦ . VS. Straight # o uts K16Z- ~ 1 . 7 - Jo _3 5_ vs. &>5 f l J J ♦ 171 (71 L±J LL T>HLr VS. + OpfilA. £|A,^£K # DU.t& gj-g VS. 7o 25 ^ vs. FLusVl drflw # DLitS A 2 -g % fefe. vs. 34 Op£iA, £ader VS. + Hush draw VS. TW£) Pair # outs A62-. "1-4 % &Q vs. 4<9 # ow.ts r^-o VS. pair + £fWt shot .97 vs. % 3 # ontsTkS - 4 g±L vs. 15~ T If J . ♦ . li ♦ . * , vs. FLutSh drflw # outs S’ 3 ~ 3 vs. % 33 # ow.ts6Z.~T % 33 vs. f»_23 VS. t shDt # outs g>2 vs . lg vs. set VS. TWO PUIY # owts5j5_2_2 fo 11 vs. ft S’3 # OW.t£ KJ-13 vs. VS. Tap ^alr # owt&K-6Z. -5" $ S6> vs. ft 20 ■* n i n o . 4 H . ♦ , 1U VS. Top ptfLK # outsK.62. -5 ZL5 VS. 7® vs. two "Pair f —i 10 f -N 9 4 i ^ j # outs 62. T -O t (s_y__ vs. -V3 vs. set # outs 62.62. '0 J VS ■ ft -^3 vs. tv^dtr VS. overcante # 0W.t£ KJ - 13 2? 6? vs. 44 # ou.ts AK.-1 0 ^ ~ vs. ' • 1 VS. OVfirpalr # outsKCK. -5" 0-3 \s T Q A j , * . %y . * . A 4 vs. r.p.r.kL. f 4 5 vs. % 55 r=—- f i A 2 JLI vs. CfUt shot # out<. hCGZ. ~ 3 S '3 vs. 11 vs. ope^ easier # outs'TS’ ~ vs. 20 vs. set A + 2 vs. twc Pair # outs _,9 %o 30 VS. % To # 0U\S jj-i-f 'S'O vs. ft -S'£> Pocket pflLr bfibw TP # outsi r -2 fo J?3 vs. fa y- •««*** Q R . 4 . U VS. overpair # puts <£L6Z- ~ 2 $ -9 vs. _9i VS. Weaker overpair #outs '! I - Q. fo 3o vs. fo 10 m VS. Straight # outs y~% - o fo 3 vs. r ' — J J L±J vs. Lr + ^ut shot VS. overearoU vs. set # outs 3 S’ - _5 # owts/\K. “O vs. % 33 vs. b QJ5 # 0w,ts£>£> - 2 . VS, Q A n n u . 4 , u , 4- , vs. Three of & kivui # ou.tsG 2 .-J ~2 ^ -J VS. VS. Fw.lL House # - 4 % i y~ vs. # g3 vs. weaker werptflr # outs)<.f<L -2 ^ - J 2 vs. % S Pocket pair below TP A $ A ♦ sip pflLr, VS. Np draw, < Aie VS. Nut NO Pair # 0IAt£ J J - 2 # DIAtS k3 -O .-J 2 vs. ^ -Js* vs. ft 2 # outsAhG- _ 2 -Js* vs. % 2 VS. Overpair # OW.t£ a3- ig vs. 3^ VS. Topper 00 fiol 4 h._:_/ l±- # cnxt£ AJ- lg £>3 vs. 3^~ vs. two Polk # ouk&7'3 ~14 -50 vs. % 50 fiol 8 4 \_r_J vs. # outs 33 ~ 14 4C> vs. VS. Nut FP # outs A K- _ 12 40 vs. ^0 vs. t 5 flpwiiA.aterf plrffw # outs 5" 2 - g-5~ vs. % 1A N ■7 i n Q vJ V ±u 4 . 4 vs. # outs <52, J -g °(o&3 vs. 31 VS. Opca filler + Flutsh draw # outs 62.J-1 5" ^_4£_ vs. 5 2 vs. Flush draw # outs A2 “15^ fo_&5— vs. 35 r > 10 r > 9 4 , vs. ovcrpfllr 10 ¥ 9 ¥ vs. set vs. r.p.r.K. # outs JJ-13 1 vs. # outs 33- 4 ^_2i_ vs. ^ # outs AT ~3 vs. 14 A 5 10 v . + 4 VS. Tpp-pfitLr # DU.t£ A J-2 1A vs. VS. <Sjl4t shot # 0l/tts3'‘f - *4 81 vs. ff l.j Pfl Ir VS. + FLusk drflw # 0W.t£ A S’ - 2 S' vs vs. set # outs AS - 2 11 vs. ft %3 VS. Nut Ft> # outs A'*?' - 2 5^ vs. ft. 3s Poe feet pplr bebw tp # outs JJ-2 ft vs. ft S r* ^ u r* -^ K r -\ 6 i*j [♦J 4* V J f - 6 6 VS. r-\ A -\ 9 ^ te 4 1 v ♦ J V*_ t _ Pot: 4 3 O Vullfllw S ki OV£S: 4 SO Pot Odds: 1.6 : 1 Plt-vaL pot would be: 130 your call would be % sg of the flrval pot. Outs: g equity a? Odds: 3 ; 1 Profit : Call = X Fold \ r -' j ( - V 2 /-\ a vj l*J 4 " d j — a vs. f \ A f ^ K +J 4v 4 _±_ j 4 ^_ £—J Pot: 4 SS villa i IA, s h oves. : 4 4 0 Pot odds ,: a.3g : 1 Flt^wLpot would be: ■■ 35 your call wouLd be % 30 of the filial p ot. Outer 11 Faulty 42 Odds: 13 g : l Profit : ^ 16 xCflll =ev Fold f1 2 ♦ J f > 4 l + J f '> 9 ♦ J f \ J ♦ ___ J — J VS. o' •F j / N a l*j Pot: 4 120 villain shoves: 4 130 Pot odds: 1 . ?5 : 1 Flual pot would be: 3S0 Your call would be % 34 of tke filial pot. Outs: 42 Equity % 9 a odds: q.0'5 :1 Profit : £220 xCalL =ev Fold *-\ 4 .♦J ? - 6 -% l y /-V 3 ♦ _£_y f \ /V / \ E? f \ 6 A VS. 5 5 sJ L±j Pot: 4 60 Vlllfllw Skoves: 4 JO Pot Odds: 1.&? : 1 plusl pot would be: Your call wouLd be % 38 of tke ft wa l pot. Outs: Y Equity 23 Odds: 3.3 ,5 : 1 Profit : i_3f’ Call =ev x Fold 6 ♦ 5 ♦ -\ r" / \ n 5 5 vs. 6 7 ♦ Vj * Pot: 4 1 50 vlllaiu, shoves; -f ISO Pot odds,: a : i Filial pot would be: A - 0 Your call would be % 33 of the filial pot. outs: Y % as odds: 3.35 : 1 Profit : £_S~ call =^v x Fold \ /' -> 5 t > J 4 * V J r ■> K U*J K A 4 * VS. -\ 5 vj f \ 5 Pot: 4 25 " vlllalw Shoves; 4 20 Pot Odds: 2,2.5 • 1 Fiwal pot would be: Your call would be ?£ 31 of the flual pot. Outs: 35 Faulty % & 3 OddS: t>,45 : l Profit : $ DS xCfltl =ev Fold 5 2 - l J — 10 -' 10 vs. /* \ A -\ K ♦ J l±J L±J l±J Pot: 4 J-5 vllLatw. shoves: 4 1-00 Pot Odds.: pT5_ : 1 F'uvftl pot would be; 2 ' ?5 ' your call would be % -■& of the fli/uil pot. Puts: ±5 Faulty 5-5 odds: 0.22 : 1 Profit : ^ ^ xCail =^v Fold -\ 10 -* 10 vs. r-\ a -\ J ♦ IjL jeJ 1*. pot: 4 120 villa in* shoves: 4 ^ Pot Odds: 2.5 : 1 Fiyudpot would bt : your call would be % 2 ..? of the fliA^l pot. Puts: 45 Faulty % ^ odds: an : i Profit x call =ev Fold f* -> 5 l + J / V J M r "i 6 ±> — — -\ -\ 7 8 VS. K j V, _j Pot: 4 1 05 villain shoves: 4 O 5 Pot odds,: 2,11 : 1 Filial pot would he: your call would be % 32 of the ftual pot. Outs: 3^ Equity % fe3 odds: QJ5$ ; 1 Profit : ^ x call =zv Fold \ / k f -\ 2 ? w \ 7 ♦J _J JtJ — 7 * - > 8 VS. t - A 'a s_/ ^ , LjlJ ♦ i_z_ A J Pot: 4 GO villaLw, shoves.: 4 So Pot Odds: 1 . 7-5 : 1 PliA^al pot would be: 220 Y^Ltr oall would be % &ftht filial pot. Outs: 13 Odds: : 1 Profit : ^ xCall =ev Fold f -^ 5 s , f -1 8 M r-^ 3 UJ 7 ' 4- 7' v. VS. / ^ A UL -\ a *F ^ 1 j Pot: 4 &0 vitiate Shoves: 4 £>0 Pot odds: 2 _: 1 Flu-al pot would be: JSo Your call would be % 33 o-f the filial pot. Puts: fc equity % odds: a.g^ : 1 Profit : 4 -13 Cali =sv x Fold ^-N 7 . +. '-\ K . ♦ j /-\ 4 L*J r -\ A VI -\ A Um VS. -\ Q r- j ±\ Pot: 4 55 villain. shoves: 4 40 Pot odds: S, 3 g : 1 Fln-al pot would be: ' - ; 5 your call wouLd be % 30 of the flu-al pot. Outs: g Equity 33 odds: 2.03 : 1 Profit : ^ t xCflll =ev Feld f-> 4 , + J * > 2 . ♦ , r-^ a LJ — — ( \ f \ fl a VS, A 3 ♦ 1 1 + v / ♦ ♦ , Pot: 4 25T Villatw, <ShoV£S: 4 2£> Pot odds: u.25 : 1 Filial pot would be: & 5 Your call would be % si of the fual pot. Outs: ii Faulty 33 Odds: 2.03 : 1 Profit xCctll =^ v fold /-> 6 r-^ 10 ♦ , r 7 J?J — r *\ r \ -\ n 8 L+J 9 VS. 6 L±J 7 Pot: 4 30 vLLLai^ shoves: 4 40 Pot Odds: 1- *5 : 1 Fl^fll pot would be: 110 Y our call would be %_s& of the flktfll pot. outs: 4 Smutty % ig Odds: 4,5 £> : 1 Profit : ^ ‘ 20 Call =^v x Fold /"-S/-S/-\ 3 5 10 J V x 7 1*. ' 5 ' A VS. / \ J f ^ J JL 1 * Pot: 4 5" 5" villfliw Shoves: 4 45 " Pot odds,: 2.22 ; l Plu-al pot would be: 145 your call would be % 31 of the fVal pot. Outs: 3 i? Equity % ?4 Odds: q>. 35 ~ : l Profit : 4 62 xCc^lL =ev Fold f y A r- 8 p- *1 2 l + J ♦ , _J f \ K ^ -J a" . v. VS. f > 8 J r \ 7 4 . , y Pot: 4 40 villa iu shoves: 4 40 Pot odds: 2 _ : 1 Plu.al pot would be: 12c your call would be % 33 of the fli/u?L pot. Outs: 13 equity 44 odds: 1.2? : l Profit : ^ *3 xCflLL =ev Fold ** 27^ villalv* s hosts', 4 100 Pot Odds: -' 1 5 : 1 Fl&'vfllpot would be: * — J your calL would be 2, of the final pot. Outs If? Equity % &c Return from, pot:_ odds, 1 . o.frT ; ± o pe^ e^der + Flixs-h draw x CflLL [ I Fold Pot: 4100 villain shoves: 4 3 0 Pot Odds: V r - r -' : i Flafll pot would be: 1 ■'• Your call would be %..j__ of the fUuil pot. Outs: 2 Equity g £ Return from, pot:_ Odds: : !■-■ : 1 Pocket pflt-r beLow tp* □ call x Fold Pet: 4120 villain shoves: 4 So Pot Odds: : 1 Fulfil pot would be: -" youb call would be % 2. of the final pot. OutS: -4 Equity % i£- Odds: 5.25 ■ 1 Pot: 4120 Flush draw villaIn shoves: 4 30 Pot Odds: 5 _: l Final pot would be: ^ your call would be % t of the final pot. □ F old Outs: ^ Equity Return from pot:_ Odds: l, j^g ; 1 Ojut shot call x Fold Return from, pot: FLusk draw 4 Q_DD VlLUttrt,£lno\/££; 4 &0 Pot Odds- ^33 : 1 FtmAlpotWDuLd.be; Your cflLl wouLd be % ± ' : of the final pot. Pocket -pair below tp Fot: 4 55 villa In s h oves ; 4 3 Pot Odds: 2.5 ? : I Flna L pot would be: 125 Your calL wouLd be % of the final pot. x call call ■ | . Fold Outs: ^ x Fold Outs: 2 Texture from pot: Uqyltft f_ s&_ odds,: ±y>£ : i Hietum. from pot: odds : Equity % ±1.5 : l Oftv^ tv^dtr + Flxsb draw x call Fold Return from pot: ^125^ villain shoves: # Pot Odds: 2.3 ft : ± Final pot would be: l ' your call would be % >- of the filial pot. outsit equity % gtf odds: €>£>? : ± Flu&k draw x C-fllL Fold Return from pot: Pot: 4 vlllalnShoves: 4 &0 Pot Odds: -V g : i Fima L pot would be: ^ your call would be % >• of the filial pot. Outs: ^ Equity % Odds: i..Fg : i Pot: 4 2.00 villa'll*. Shoves: 4 50 ■ppt Odds,: -b_ _ : 1 Fmfllpot Would b£: _____ Your call, wpuLd be % i " v of t\n.t fln.otL pot. Outs.: ^ Bqultij % 3& Return frovw pot;_ odds: __ ; 1 Ftusk draw X call Fold pair prt: 4 50 -f- Villa'll*. ShoVCS: 4 “40 Hush draw vot od ^- 05 '■ 1 Fulfil pot Would bft: _____ Your cqLI would be % of tint flvud pet. Outs: 14 Equity % s& Return from, pot:_ odds: 3 ■_ 1 x call _j Fold Pot: 4±SO Villain Slip's: ^ 4 0 Pot odds: 5.5 : 1 Ftfc-val pot would be: 1 : ' Your tall would be % 1 5 of the flvual pot. Outs: ^ Equity % ±& Return from, pot;_ jg-gT : 1 <S|ut shot x Oft LI Fold O'pekv e^der + Flush rirCiw x CflLL Fold Return from, pot: Pot: 4-^00 villain shoves: ^25" 0 Pot odds: g.* : 1 Fi^flLpot would be: „ Your call would be fa :. : : of the flwfll pot. outs 1 5 Faulty g .s,o odds: q,& 7 ~ : ± 4300 villa ifr'Shovts: 4i 2 5 Pot Odds: ■=■■ ± : 1 Ftufl L pot would be: __J_ Your efllL would be % of the flVLRl pot. Outs: £ equity % Return frDru pot:_odds: - .it : 1 opeu euder x Cci LI Fold Pet: 44 DO villain shoots: $ iLQO Pot Odds: ''■ : 1 FluoLpot would be: Your OflLL wouLd be % i ' of the final pot. Outs: 2 Equity g g Return- from, pot:_ odds: ±u. ; ± Pocleet pair below tp Call x Fold ~ „ Pot: 43 DO Opt\As 1 vlLLam shoves: $ 3.00 t t-'W/i tY ^ Odds.-. Afe : 1 Fuval pot would be: v H n\\ Your oflll would be % 22 oftkefUaipot. tit shot P£ * : 4320 -j- vlllAlu, Shoe's: 4 20£) Flush draw p ot odds,-. z& : ± Ft ia^a L pot would be: r -' v 0 Cl LL Y^wr call would be % 2% of the fulfil pot. FOLpl Outs: {? equity % sa R£tum from 'pot: odds: 2..±3 :1 Fold OwtS:±3 equity g 52 f^gturu, from pot: odds: ojfcz : 1 Pot; 4 y-o Flush draw vUi«U shoves: 4 40 Pot Odds: ; i FUvfllpot would be: : ‘ ■ H D ! ! Your &AlL would be % 2? U4dUV of the pot. Pot; 3 ^0 CV£FO$ villain Shoots: $ ^0 Pot Odds: - : 25 : 1 Flu. A L pot wo u L d be: 1 r ■' Z" 1 F 31 1 Your call would be % 24 LslAM ^tkefUfllpot. PoLpt OutS: ^ equity g 3£, from, pot: odds: i/S ■ 1 x OutS: G? Equity g 24 f^tum. from pot: odds: 31 Y :± Nutt FP Pot: i OO v'MaiiA shoves: 4 50 Pat O&dli 3_ : i x call Fold Return f YOYUL pot: Flvutlfotwould bt: _ . Your mil would be % y. r - &f the final ■pat. QUtSrl2 equity ffi 4g odds,: ijQg ; i Pat: 4 45 villain shoves 4 20 “Pat odds: s,35 :1 Fmalpot wowld be: . _ Ycutr call would be % of the fUud ■pat. Puts; Scpuk y g 16 Return ’from. pat;_odds; ^ ^ ft * i. <^w.t shat Call x Fold 7 ♦ J A l ♦. Q ♦, ___ ^ a' Y VS. f \ K f \ Q tJ , ♦ - PDt; 4 IDO vLLL auA, s> ho\/es: 4 S' 0 PDt Odds: 2.25 : 1 Fmalpot would be: 2 £q your call would be % 21 of the flkUiL pot. outs: _9 Equity <g 44 odds: 1,27 : 1 Profit : ^ X call =^v Fold \ t f -\/-N/-\ 7 ♦ . A w " - Q _ i _* — f 7 *J 7 A vs. -s ♦ J r ♦ £: Pot; 4 ±oo vllLnLw. shoves: 4 So PDt Odds: 2.25 ; 1 Fl^alpot would be: your call would be % 31 of the fmal pot. Puts: 3 Equity % 31 odds: 2.23 : 1 Profit : -t 0 Call x=ev Fold 4 / \ A /-\ Q VS. f \ K /-\ a 4* 4- .♦J Pot: 4 ±00 villain shoves: 4 %0 Pot Odds: 2 , 2.5 : 1 Filial pot would be: 260 your call would be % 31 of the filial pot. Outs: 12 4 ■ 1 - Equity 3 s Odds: i.26 : 1 Profit : * 10 xCflll =ev Fold 1 7 ♦ , ^ \ A .♦J /- \ a 4 > -\ A - \ TT /- 8 9 vs. K 0 UL Pot: 4 100 villain shoves: 4 20 Pot Odds: 2.25 : 1 Filial pot would be: Your call would be % 31 of the -fmal pot. Outs: 44 4 ■ ■ ii Equity ,3? odds: 0.03 :1 Profit : ^ 1 ' xCflll =ev Fold K miu . V A AJs J |ATs] |A9sj j ASsj ^Vsj [A6sj [A5 s j ^ A4s J ^A3 sj ^A2sj Ik3s iK:s lelaliaiH k?s K6s K5s Q9s Q8s Q7s Q6s Q5s Q4s Q3s Q2s . /L .A-A- ) 19S combos tn preflop range — 0 % 21 . 6 % Top pfllr set two "Pair D0kW,LIA,Glt£Ct draw 7 l ♦ . A . Q 4 r ' 0 ■ L 0 ■ vs. K _ 1 Q ♦ „ Combos ^ Profit = Combos X — Cl — Profit — 3 Combos, X Profit = 4 Combos, X o-flt = C-flU = EV Fold TotflL: f \ v f 1 -\ r /-\ Q J\ 0 1 i > 4 v_ i _ > /-\ K ✓- J > vs. fol /-\ 10 l*. l*J Hh 4 v ^ Pot: 4 1 00 villain, shoves: 4 Pot Ootots: 2.2.5 : 1 PLiA/fll pot would be: Your call would be % 31 of the -fmfll pot. Outs: 40 Faulty f 0 _i2_ odds: 0.22 : l Profit : i_i 33 xCflll =ev Fold ^ * K /-\ J ♦ V- ± —J /-\ 9 ♦ v 1 ^ ✓ > K /" N K VS. /-\ Q / -\ 10 M 4 * L. x u 4 * ^ 1 -i Pot: 4 100 vlllalw sbo\/es: 4 £0 Pot Odds: 2,25 : 1 Flwal pot would be: Your call would be % 31 of the flwal pot. Outs: 2^ Faulty g2 Odds: 0.22 : l Profit : ^ 133 xCflll =ev Fold < > ir < > T r-\ Q j\ A > ♦ v . ✓ > A < \ K VS. ✓ \ fl /-\ 10 JL •F •F ^ 1 ^ Pot: 4 1-00 villain. Shoves: 4 20 Pot Odds: 2.2.5 ; l Flwal pot would be: your call would be % 3 i of the flrval pot. Outs: 35 Equity g.Q Odds: o.&7 : l Profit : ^ J '' xCflll =ev Fold ir / - \ T ( -A Q j\ A s7 ♦ »- 1 -/ < > A / -> fl VS. /-\ a - A 10 _L ♦ s. A -J •F ^ •F Pot: 4 100 villain, shoves: 4 20 Pot Ddd£: 2 . 25 ~ : l Filial pot would be: 26 Q your call would be % 31 of the filial pot. Outs: 32 Faulty Odds: a/5 - : i Profit : •* xCflll =ev Fold 19S combos in preflop rang? _ 0 * . $ 216 % r-' K 1 . /- J C 1 - ✓-^ 9 l*J r-> 0 m L J r-> 0 ■ l j VS. ( - s Q io Two Pair Combos X 133 Profit set ^ Combos X 133 Profit pair + Flush draw 3 Combos X 5 Profit ±0 Combos x ^2_ Pro f Lt Nut =6>Z0 X CM =EV F aid rotfll:3033 f 1 9 r-1 3 r-\ 8 4* l*. 9 ] f -\ 9 vs. — Q / \ Cl 4 s_ ± _> . . .♦J ^ J Pot: 4 100 villain shoves: 4 20 Pot odds: 2 .2.5 : 1 Flu-al pot would be: 2& 2 your call would be % 31 of the fIwfll pot. Outs: 2 equity % 10 odds-. j? ; 1 Profit : ^ ~ 5 f □ Call = ^v X Fold f > 9 r- - 1 3 r -^ 8 4* V V [♦J l_L J1 fid VS. / \ ft -\ a 4 1 _ _j 4 L A j _ _ _ 4* , v J Pot: 4 ^£0 villain shoves: 4 go Pot Odds: 2,25' : 1 FtywaL pot would be: your call would be % 31 of the fLi/vol pot. Outs: 3^ equity % odds: o^f : 1 x call Profit = BV 4 10 J Fold Pot: 4 1 00 VU.Uav'v. shoves: 4 20 Pot Odds: 3S15 : 1 Filial pot would be: your call would be % 31 of the filial pot. Outs: 13 Equity 27 Odds: 2.7 :1 Profit ; 4 -IQ call =^v x Fold 198 combos in preflop ranee V//AVMBBnM 0 * . * 21 . 6 % /■ > 9 „ + /-' 3 l*J f > 8 l*J 0 ■ - 0 ■ L j VS. 'ft' l±J f y a set & C,Qm,bo£> X. _ 5 '_ 5 ' Pr&fit g Combos X XQ3_ Profit ~ 2^3, evader TWO pair 2 combos x ~ 10 Profit = ~ ZIP x oa LI — 5v Pold Total:^ 2.2 8 r 1 9 8 M \f VS. - s 10 — J Pot: 4 AS Villain bets 4 Amlom iwit behind 4 ^20 Pot Odds: 2,13 : l Flt^ftlpot would be: -2.5 your coll would be % 32 of the flktfll pot. Puts: 13 equity a_9 odds: 2.45 : 1 Profit: Makeup: 4io SCall -tv Fold \ / -> 8 , ( -\ 9 [♦J ^- 1 8 M - y 7 f \ A VS. id — j 4 1 Pot: 4 45T vlLLflUv bets 4 40 Awouwt behind 4 3-20 Pot Odds: 2.13 : i Filial pot would be: 1ZiS your call would be % 32 of the fu/valpot. Outs: 13 Faulty 2_9 odds: 2 A 5 : 1 Profit: ^ ^ Makeups_ x Call D=ev SFoLd r x ~y 10 r i 3 O) L ♦ l V, /■ V A id vs. 7 8 1 A V J l *F M M Pot: 4 45" vLllatiA, bets 4 45T Am.oujn,t behind 4 30 Pot odds: SJ3 : l pot would b£: Your &cjLL would be % 32 of the fuA>^l pot. Outs: 13 equity p 27 odds: 2.7 : 1 Profit : 4~ £> Mflfe£up: 4l^- xCalL D=ev Fold \ / -\ /-\ r -\ Q 8 .4. 4 4L — A — Q vs. V ioi + J •F 1 ^ 4 LJ t — < s_ Pot: 4 so Villain, bets -4 25 An^ouut behind 4 3-00 Pot odds: : ± Hvvzl pot would be: your sail would be % si of the fln-otl pot. Puts: 3 Faulty p 7 odds: is,2_9 1 Profit: 4 - 1 Mflte&up: 4^53 C&LI □-0poLc?t ■fl ■1 Q /- \ 10 4 t Q > < \ J vs. f y K t > J > / ♦ J ^ x ^ A 4 Pot: 4 4 5 villain bets 4 35 " Aw.oui'ut behlud 4 1 - 1-0 Pot Odds: ?Sl3 : ± Filial pot would be: 115 your call would be % so of the fii/v,alpot. Outs:__g_ Faulty ±g Odds: 4.56 : l Profit: 14 Makeup:4^4_ xCflll E=ev Fold * \ 7 / - \ A VS. / > 8 / \ 9 . + , Pot: 4 35" villain bets 4 20 A^uoui^t behind 4 1-50 Pot Odds: 2.^5 : l F'u^al pot would be: ^ 5 your call would be % 27 of the filial pot. . acjflLKSt Lower f CdL Odds: Outs: ii Equity 24 3.1? : l Profit : 2 Makeup: ^ xCflll =ev Fold ^ ■> n f s T r"- y Q u •F J ♦ , ,*j ffll — K vs. f \ A -> K ♦ s___ 4 •F •F L- 1 Pot: 4 viliaUfr bets 4 &0 AkueuiAt behind 4 3~30 Pot odds.: 5.33 : 1 Fi^fllpot would be: ^oo Your oo LI would b t % so of the final pot. O'UtS: ~y~ Faulty p i5 Odds: 5 : 1 Profit: ^ Mflleeupi -f 1 ^ 0 call =ev X Fold \ / Pot: 4 35^ Villain bets 4 30 behind 4 3-1D Pot Odds: 5.y-5~ : 1 FuwLpot would be: your ooLl would be % s 7 ~ of the fmalpot. Outs: 2 Faulty 4 odds: 24 : l Profit: Mflteeupi ^r C-otLL =ev x Fold 8 r / - ^ 2 J l*J /' > J ' a1 vs. / - \ 9 / s 10 •F V. 7 ❖ J v ^ ^ l*J Pot: 4 villa m bets 4 20 Aw-oniA,t behind 4 ^20 Pot odds: 2.25~ : ± HmL pot would be: Your call would be % si of the flutfrl pot. Puts: 1 5 Equity 33 Odds: a.P3 : 1 Profit: 4i Mate;&up: 4~ 0 x call =ev Fold O r ^ P O * O l vj u _) A a vs. -\ 9 — 10 Jfj •F ^ 1 V •f* V 7 Pot: 4 3 0 ViLLflli/v bets 4 20 Aw-ouwt behind 4 2 00 Pot Odds: 2.S : ± Pmal pot would be: ^ your corLL would be %_ _2_9 o-f the ftivaL "pot. Puts: 10 22 odds: 3.5 5 : 1 Profit : 4~ -5 Mntegnp: 4l£ x call =ev Fold 10 A 3 4 4 JU V* \ 7 8 VS. f *\ K K l*J 4 1 J 4 t 1 J JU Pot: 4 40 v'dlaivi. bets 4 35" Amount behind 4 1-50 Pot Odds: 2.14 : l PtiA.nl pot would, be: j j 2 Y our tall would be % 35 of the flu-oil pot. Outs: 7 Equity 16 Ootots: 5125 : 1 Profit: * m nkaeup:4.?5 x call =ev Fold K , 4 , 10 .vj K M — A K VS. f 'N 7 f \ 8 l±_ L±J lil l*J Pot: 4 35 vtLLflm, bets 4 25" Ai'uouwt behind 4 POt Odds; 2.4 : 1 pLi/ual pot would be: ?.f Your call would be %_ 2.3 of the flu-ol pot. Puts: g Smutty ig Odds: 4.56 : 1 Profit: v x call =ev Mctteeup: 45; □ Fold f - y r -\ Q f -\ R j\ O v- ± -J O 4 1 j — A _1 ^ \ K (±J vs. f \ 6 l*J — 7 liJ Pot; 4 55 vlLUtm bets 4 -40 behind 4 12 0 Pot Odds: 2 . 3 g : 1 Fl^al -pot would be; 135 Your call would be % 30 of the flu-al 'pot. Puts: g Faulty ig Odds: 4.56:1 Profit : ^ ~ Mflte&up: ^ 71 s x call =^v Fold \ /* 3 ♦ 1 S f -*< A O •F J A ,V, — K VS. l 4 , Pot: 4 30 villain, bets 4 2D Am-ouut behind 4 HO Pot Odds: 2,5~ : 1 Fl^fllpot would be; your tall would be % 2 .3 of the fw*al pot, outs: y- 6qmty Yo 16 odds: 5\25 : 1 Profit: ___ Mateeup::. SCR LI C=ev □ Fold \ / f \ 9 f > 10 IVI Pot; 4 10 ViLlaivi bets 4 10 Amount bthivui 4 HO Pot odds: 2.5~ : ± pot would bt\ your tall would be %_ *2.3 of the fu^uiL pot. Puts: 3 Equity 20 odds: 4 : 1 Profit : 4 £ Makeup: 4^4 x call D=ev n Fold t 1 ^ 4 ,*J r ■> Q ^- *1 3 A r n Q l±J -- Q , * v * -/ VS. f V A UL 2 l±J Pot: 4 4 0 villa ua, bets 4 2D AfttouvU: behind 4 2DD Pot Odds: --A : ± Fl^al pot would be; 4o your Gall would be % ^4 of the flwal pot. Outs: 11 , equity 24 Odds: s.iT 1 : 1 Profit: ...l_ Makeup;: xCdlL =ev Fold f -"1 8 , + J f -> 2 M *- 8 ._ — — — A 8 VS. 9 9 Pot: 4 2 5 villa Lia, bets 4 20 Avuou:vit b&hli^d 4 3-10 Pot Odds: 2.25 :1 Fl^aL pot would be: £- 5 ~ y our c &LI would be % si of the fmalpot. Puts: 2 Equity g 4 Odds: 24 : l Profit: $ t- Mflte£up:4432 Call D~ ev 0 Fold /—— A L± r L± Pot: 4 OO vlllaliA, bets 4 35" Amount behind 4 85 Pot odd S: 2.^1 : 1 Flwfll pot would b£; lzCl Y ou.Y tali would be % 2 Y of the flwfllpot. outs: g equity % 18 odds: +.56 : 1 K Profit: Mflte£up: 4^-5 xCall =ev fold /" N 4 l*. t > 5 4» r 6 / > T -\ T -> '-\ A J J VS. 6 8 l*J LU .♦j liJ Pot: 4 2 5 villain, bets 4 15- Amount behind 4 1-00 Pot Odds.: 2,67 : l Filial pot would be: 55 Your call would be % 27 of the pot. Outs: 7 Equity 2s Odds: 4 : 1 Profit: 4 Makeup : 4 i£ xCflLL =^v Fold r \ 2 r i 4 JJ /-\ 9 ♦ ^ x ^ -\ 9 LL /-\ J VS. /■ > 8 f \ 8 ♦ ^- —V Pot: 4 3 S' villa Iia, bets 4 2S Awiouia, t behlud 4 1-50 Pot Odds: 2.75 : ± Filial pot would be: " 5 your call would be % 27 of the flkunl pot. Outs: 2 Equity 4 Odds: 24 : l Profit : ^ " 1 r Makeup ; +AO£ □ Call [ =ev x Fold t -^ K r \ a r-\ 4 L±J L±J l*j -\ K f \ a vs. r v j -s 10 L * LiJ _1 Pot: 4 d& villain bets 4 AmouWt bekm-d 4 *3-50 Pot Odds: 2.13 : 1 Ft^otl pot would be: --.so your mil would be % 32 of-the filial pot. Puts: g Faulty ig Odds: 45Q> : 1 Profit : 3.5 M.Cfte£wp;4l^S x Call H=ev [ Fold Pot: 4 55 villain bets * 45" Amouut beklud 4 300 Pot Odds: 2.22 ; i Fiw.fll pot would be: 145 your ogtLI would be % 3J of the l pot. puts: 14 Faulty si Odds: 2,23 : 1 Profit : _Makeup_ x call =ev Fold v / vs. pot; 4 y-o vlllnliA. bets 4 55 Awuw-t beklw-d 4 HO Pot odds: 2.2Y : 1 Ftw,al -pot would bo: lg ° Your call would be % 31 of the ftw.nl pot. Outs: & equity 13 odds: : 1 Profit: ^ 3 -^ Mnteettp: ^3i4 xCfllt =ev Fold [ 10 ] f 1 8 r 1 2 A ♦ <,_:_ \ A f * 10 VS. [9' — 10 ♦ J l*. JL M Pot; 4 SS villain bets 4 Amount behind 4 Pot Odds: 2.42 : 1 Flt^al pot would be; your call would be % of the fiv^ul pot. QD5 2.9 OutS: 3 equity ^ T odds: 13.2.?' 1 Profit M«leeup:4& -9s OotLL =ev x Fold \ r a' vj - > J ♦ J r -■> 7 3J a' — 3 V 3 . — 8 ^ \ 9 JL Pot: 4 £>0 vILUuia, bets 4 40 An^ouvit behind 4 3.2*0 Pot Odds,: 2.33 : l Fl^alpot would be: - 5 ° y our coll would be % so of tbe fmfllpot. Puts: 4 equity g 3 odds: 10.11 : 1 Profit : 4- 32 Makeup: 4324 CrLI x Fold f^ A M f -> J l *■) r-■> 7 l*J A — J k. .J V 3 . — 8 ^ *4 9 Pot: 4 &0 villain bets 4 4£T Av^ou.v ^t behind 4 3.2*0 Pot Odds.: 2.33 : i Fit^olpot would be Your coll would be % so of the fiMl pot. OutS: 4 Squ&Lj f 0 _3_ odds: mil: 1 Profit: 4 - 32- Mfl tee up; 43 2 4 PotLL — 6v x Fold Pot: 4 villa Lia. bets 4 45T Aw-oww-t beluw-d 4 18Q Pot Odds: 2,33 : X pl^flL pot would be your Gflll would be %■ so of the pot. outs: 4 equity .3 odds: mil : x Profit : 4 ~ 3l Makeup : 4324 Co, LL = ev x Fold ^-1 A r - - i J r - > 7 ,vj ♦ w-J k ’a' vs. 8 V ♦ _ / * >, ♦J _ / Pot: 4 &O villa Lur bets 45" Aw.ou.vvt behind 4 ^§*0 Pot odds: 2.33 : x rt^cd pot would be: 150 Your aft LI would be % so of the fmal pot* QutS: & equity g _9 Odds: lp.ll : X Profit: 4- 3 :? Makeup: 43X4 Qull —bv x Fold I_j x [AQj au^jNfc QSi Q_i Qf; q: - q?s q;s T4s T3s iT2s 198 combos in preflop ranee 0% 21 . 6 % r ^ A .*J f -> J 1 ♦ J L J r* 'l 7 r i 0 ■ r 1 0 ■ VS. -> 8 ^L> -> g \G? combos X j 4-U.. Return TWO pair 11 Cototbps X Estimated Return 9 Cotubos X Estimated RftRHA, = nwt ^kot on - uln e£t ^ fltec( _~± 0.00 C 1 UZ snD1: 30 c-tmbos X -lLO Return - -- call =tv X Pold Total: -1 2Q.0 t > 9 * k- ± -/ t y J l *J r—-■> 6 .vj y 4- J A jt. VS. V V Pot: 4 &0 villain bets 4 beiiLw.pl 4 200 Pot odds: 2 . 2 s : i FuuaLpot would be: 210 your coll would be % si of the fivtitl pot. Puts: g t£\uX ty ig odds: A 5 & : i Profit: ^~ 2 / Mflhseup. 4i23 Call x=ev Fold r "• Q r ^ 1 T r -'i A J7 4 J u ,vj fio f > a VS. — 7 f 81 1 4 V * J liJ 4 1 v A J Pot: 4 %0 villa li/u bets 4 ^5" Amount behind 4 200 pot Odds: 2.23 : ± Fi\A,ttl pot would be; 2io Your call would be % si of the filial pot. Outs: io equity 22 odds; 3.55 : 1 Profit : ; _ . _ Mflteeup:4^_ C$11 Cbev BFoLd z' \ Q /-\ T r i ft 4 L- ± - J J U t s A < \ K VS. /-\ 7 ✓ \ 8 M M l*J . ♦ J Pot: 4 £0 villain bets 4 05 Av^ouWc behind 4 200 Pot Odds,: 223 : ± Filial pot would be: 210 your call would be % 31 of the filial pot. Outs: ip equity 22 ootols: 3.55 : 1 Profit: •$' 1 ^ Mflteeup: 4 £ * call i =bv x Fold /-\ 9 ♦ v_ i _/ Pot: 4 %0 villain bets 4 Awiouut behlud 4 200 Pot odds: 223 : 1 Flv^al pot would be: 210 your call would be % si of the fl^l pot. OutS:^_g_ Equity ig Odds: 4 .5<b : 1 J 6 *J > 6 VS. f > 7 / - \ 8 ♦ J l*J 4 V x V Profit: $ ~ - " Mflteeup: 4i23 xCall =ev Fold A4o K 4 o A3o K3o 54s ! 53s 52 s 43s -3 e 33 1 32s A2o K2o Q2o J2o T2c £oj[S2o 72o ■62 o 52o 42o 19S combos m pfdlop ranEe _ /-\ Q r-' T ( -\ R J7 4 V_i_ d J l*J U l*J f s 9 /-> 9 VS. -\ 7 /** 8 ■ a s_ Top pair 21 Combos ^ 15" open ender V" Centos X 2iO Nut Fr> Com, bos X 20 Combos X set Return Estimated Return, Estimated R^twriA, x call — &V Fold Total: 315 -140 - lgQ 135" 130 f 'I 5 t G ■> r"- > 2 .*J •f* . ? V A [o > VS. — A r* > K ♦ , a l. -j Pot: 4 d& Villain bets 4 Bo Am,ouat behii/vd ^^LSS Pot Ooids: 2.13 : 1 Fulfil pot would be . your call would be % 32 of ttie filial pot. Outs: 12 Faulty 2.7 odds: 2,7 : 1 Profit : 4- 13 Mfltemp: 43^ xi call n=ev nFoid f 1 5 p i Q r i 2 ,vj *f* J [k! f -\ K VS. — A f -\ K ID _J l±J JU Pot: 4 ViLLawa, bets 4 BO Ai'vtouut behind 4 ^55 pot odds: 2 j 3 : ± Ft^Lpot would bt\ ^ 50 your call would be % 32 of the fmal pot. Outs: 12 Fruity p 27 Odds: 2.7 : i Profit: 4- 13 Makeup: 435 x call =ev Fold r-> 5 y. -> a 2 ' ±. f > '-' 5 5 VS. A K _±j a Pat: 4 JO villa Iia, bets 4 so Avuouw ,t behind 4 155 Pot Odds: 2.13 : ± Flt^al pat waulal be: 25 o Your call would be % 32 of the filial pat. Outs: g Faulty ig oalats: 4.S& : 1 Profit: ^ 3S Makeup call x=ev Fold ' > / > T J J VS. A K y. Pat: 4 Jo villain bets 4 22 Awiauut behind 4 155 Pot Ddds>: 2.13 : 1 Filial pat waulal be: 250 Y our call waulal be % 32 of the filial pat. Outs: 15 _ ,, 31 Odds: 2.23 : l Profit: 3 Maleeup 4 r x Cftll =bv Fold KTsJjK95| KSs K 7 s K 6 s IK 5 s E 4 s k J|Q' T& J[Q J jl^J |Q 3s j [Q?*| [Qfaj [Q 5 sj |Q 4 sj |Q 3 sj [Q 2 s J 5 s J 4 s J 3 s J2s I.B TSs ITS L -J T 6 s -—J 15 s T 4 s V J T 3 s T 2 s y, 19 So i“il 97 s 96 s v J 95 s 94 s H 92 s ^J[S 7 sj S 6 s S 5 s V - j S 4 s|| S 3 s 82 s p. ; 55 54 s L 54 o 44 43 s U 2 , S 3 c 7 3 o 63 o 53 o 52 o 43 o 42 o 33 | 32 s 32 o T 1 193 combos m pteflop range ■■Hi rwi f -\ 5 l*J /-\ a . . /- 2 r ^ O- i> r 1 > 0 m ^ y VS. /-\ A l±J r i K .. ^ Top pair 24 Combos Estimated Return = 4£0 r k. overpaid Cow,bos Estimated Return = 120 r set C-cmbos Estimated Return, Pocteet pair below tp Com-bos Estimated ReturiA, x Call =ev Fold Totfll : &&&_ f \ 9 \ -> 2 ✓-\ 3 -\ l*J LLI l*J LU ^- j Pot: vtLLaliA. bets $30 tnto $50 $±50 staetes before ijou call viLain will call with jj or better Equity wbien called: ^_ IS Loss when called: °)0 “ wlvi when foIded to:_ so Required foldlnq % to create even: 53 io id _ j * 9 J SK ¥ 8 ✓V. Pot: villa m bets 4^5 l\A.to$30 $■±50 stacks Vllalw. will ooill with top pair or better, two overs awd a flu.sh draw or better Equity whew. called: ^_ 35 _ Loss whew, called: 35 Wiw, whew, folded to ,5,5 RLec[ wired foldlw .0 % to breaks evew.:_ 3°} J 10 f A 3 r "v 4 L*J 4 1 J l vj UJ i ^ j' id . . P£)t: 4 ±±0 4 50 Stfl&tes ViUfiin, will call with top pair or bitter Bc^u Ituj win£ in. called: ^_ Sc5_ Loss whin called o witn. whew, folded to: ±±c> Required foldltn ,0 % to break, evew,: A w J 10 y\. 3 * Pot: 4‘50 435" Stacfe Vilaiw will call with awu pair aww draw Equity whew called: ^_ £>.5 _ Loss whew called C- vviw whew folded to:_ 50 _ T^e^wired foIdLwg ^ to breath evew:_ o_ \r ■\/" -V 8 /- \c 6 *J ♦ V__A \ / r ' J r K ♦ i_ - _ J ♦ ^_ - _j Pot: $±00 $°>o stacfes Villa Lia, will catl with Qia-^ boat or better Equity whew called: ^5_ ±0 Loss whew called: too win whew folded to: _±oo Reyu.lred foldiwo) % to breate evew:_ sg A J - •> 10 /■ 10 <* \ ♦ l*J / * - a r i a A Pot: 4f-5 $150 stacks Villain will call with top pair or better or with an open ended straight draw or A ki with bacte door flush Equity when called: ^_ 4 7" _ Loss when called: o Win when folded to:_ iso Retired folding % to breafe even:_ o ■\ f - \r - \r '-'I A K "Pot: Villa Lw ioStS 4*30 twto dtec 4 ^12C stacks before you. call viLLaiw will c.£?LL with AG Z.+ or + Equity whew- called: _ 5± Loss whew, called: 0 vvlw whew folded to: sc Required foldlwg % to break evew:_ c ■\ r - \f - \r \s -\ s\ s\ j /v j' r-> J Pot: +30 il/uto +.50 +200 staetes Villa Iw will call with C2CZ.+ awd Akls Equity whew called: Loss whet a- sailed: 50 vvlw whew folded to:_ so Required foldlwg % to breate evew:_ 52 Combinatorics You Can Use at the Table. This is a reprint from the appendix of Poker Plays You Can Use When I make a big call or laydown at the table, I will make note of it and then do the math at home. It can take a while using Flopzilla to figure out if you did the right thing. How can you do the same kind of analysis at the time when the information is the most valuable? First, as you run these analyses away from the table, you will build up intuition and pattern recognition. It will be much like how you no longer need to run a simulation to know that AK vs. QQ is about 50/50. This is an approximation but a useful one. The system outlined here is also an approximation, but it is something that can be done at the table. That is worth something. This system is meant for use on the river when bluff catching. When Villain bets into you, the critical decision is how often that bet is a value bet and how often it is a bluff You need to approximate the amount of combinations in each category. Here is a classification of the final boards that we can have: The grey regions do nol rely on combinatorics at the table as much and are less common. We will be focusing on unpaired and single paired boards from rainbow to a possible flush. On unpaired boards, we are most likely to want to count combinations of plausible holdings by Villain where he hit or was drawing to: • Flushes (missed or hit) • Straights (missed or hit) • Sets • Two pairs • Top pair with a range of kickers What follows are estimates that can be done at the table quickly and are easily memorized. A quick reference is at the end of them all. There are other factors you can bring in to refine them such as unsuited connectors like QJo are played more often than 56o and holding blockers. You can make refinements at your discretion later. For instance, you might believe there are any suited cards in Villains range and need to modify that count. Two card flush counts: The flushes are the hardest to count and are why this system was invented. Here are typical boards by the river where you might want to count flushes or missed flush draws. All of this depends on how many suited cards are in Villains range. These charts are reasonable for your average low stakes live player. f \ A '9 U1 L*J y. yj or f n A 9 y< y J Villain might hold Ace Villain might hold King Villain might hold suited connectors All (3 flush) 9 9 -7 (depends on board) Simplified 7 n 3 3 Modify the above for each condition: • -2 for every other high board flush card (9-Q) • +2 for every low board flush card (2-5) • +2 if they play one-gappers • +2 if they play suited garbage • +2 again if they really play any suited garbage • +2 on two-flush boards • -2 for each flush card in your hand except A and K • +2 if AK are both not with Villain (just a correction) What do you do with these charts? Look at the board and your hand. If you cannot see the Ace of flush, Villain might have it That means there are nine Ax hands he can have* In the final row, we give our lessened estimate of how many are in his range because not all of them are played all the time* The same with King high flush draws* This one is lessened even more because thev are not as attractive as Ax* Suited connectors will vary widely based on the board having blockers. This was also simplified for expediency. Count these if you think Villain can play suited connectors. Add up the values from the bottom row that apply to this Villain and board. Next, we need to modify this base value based on the situation to get the final count. Look at each case and make the modification to your count. Note that if you can see both the Ace and King, then we need to add two to their count, mostly as a correction. Let uslookat three seemingly similar boards to see that these approximations make sense. A 8 l±J 4* 1 Jtj Against a villain who does not play suited gappers, this system gives five combos • 3 for Suited connectors • 2 to compensate for AK on board A different three-flush board. 8 f -■> 2 [5] + - This system gives 17 combos • 7 for suited Aces • 3 for suited Kings • 3 for suited connectors • 4 because low cards do not block many flushes A final board where Lhe flush draw never got there. This system gives 14 combos • 7 for suited Aces • 3 for suited connectors • 2 for low card 2 for missed flush Two card straights counts: A 8 id isJ ♦ Sc- - r-J L_ J Suited only 'a' ♦ , 8 A 10 : * l_ j k_ Blocker in hand 1-2 6 Unblocked 2-3 9 Simplified 2 per pair 7 per pair Suited or unsuited (unsuited are played less) Here, you can have blockers in hand. Villain can play the specific two ranks either suited or unsuited. The simplified counts reflect the fact that unsuited cards get played less often. The higher the two ranks, the less this is true. You can modify a bit as needed. Sets- count per rank: Unblocked Blocked All 3 i Simplified 3 i Sets are easy to count. Two pair- count per pair of ranks: Y t — i 8 - ^ 10 4 i *■ ^ Suited only r— A f - s 8 . *, A r--,, p 10 4 V 1 J Blocker in hand 1-2 6 Unblocked 2-3 9 Simplified 2 per pair 7 per pair Suited or un suited Very similar to two card straight counts. Single board pair- count by kicker ranks: K - 8 c -' 5 Suited only r ^ f - 1 9 ji Y ♦ ^ — 'a' Pair blocker in hand 2 8-9 Unblocked 3 12 Simplified 2 per rank 10 per rank Suited or unsuited Ihere are a lot more of these to count if you are concerned about them. Even wilh this simplified counting scheme, this can be hard to keep in your head. Thankfully, you have a whole bunch of chips in front of you. Use them as counters. Make a pile of “bluffs” and start putting chips in there as you count them. Do the same for value hands. Depending on how many chips you have, you could consider them all the same value and compare the heights of the piles. This makes reducing the fraction much easier. A pile of 12 chips versus 4 chips can quickly be halved twice to become 3 to 1. Even if you had 13 chips to 4 chips, this is close enough to work at the tables. Let us try this system on some boards: y A R Q t \ O IV ! 4* J Jl , * , ¥ ♦ -- From the betting, we think Villain has • Bluff: missed club flush • Bluff missed 67s or 78s • Value: two pair- 45s • Value: Sets- 44, 55, 99 o Clubs: 14 combos • 7 combos for ihe Ace • 3 combos for suited connectors • 2 combos for the low flush card • 2 combos because flush missed o Straights: 6 combos • (4-1) combos for 67s (flushes already counted) • (4-1) combos for 78s (flushes already counted) o Two pair: 2 combos • 2 combos of 45s o Sets: 9 combos • 3 combos each for (4,5,9) This yields 20 bluffs versus 11 value Think about a board where we hold the Ace of flush and King of spades. Do we believe Villain is bluffing the flush or flopped a straight? Villain is in the Big Blind defending against our Button raise so he will play one-gappers, a wide range of suited garbage, and 75o. o \ ft A “ \ y - \ o o ♦ u * liJ l*J Lt 4 S o Diamonds: 12 combos • 3 for the King • 3 for suited connectors • 2 for 1-gappers • 2 for the low card • 2 for flush missing • 2 for suited garbage • 2 for real suited garbage o Straight: 10 combos • 10 combos for the 57 While these are simply approximations, they are easy to remember and calculate. On paired boards, all the estimates above are fine if you remember the board pair does not count towards two pair since estimates are for using both cards to pair. With paired boards you will also want to count open trips and full houses. For counting full houses there are two kinds on single paired boards: o Pocket pairs o Unpaired hole cards matching the board pair and one other Full house- count by type and rank: -' A r i 10 10 F 1 9 fjl A + -__J L£ JL Paired oi f 9 ][ 9' UJliJ llv U2P 10 airec V . ♦ , Simplified 3 pc r rank 6 per rank Open Trips- count by kicker rank: '9' r-' J l*. 10 fl •f* Simplified 8 per rank The value of this system is that it is easy to do in your head or by counting out chips at the table. When you are counting these out, contemplating your action, it just looks like you are playing with your chips. Simplified Combinatorics for % NEEDING TWO CARDS Flushes: 7-3-3 (Ace, King, connectors) • -2 for every board flush card (9-Q) • +2 for every (2-5) • +2 if they play one-gappers • +2 if they play suited garbage • +2 again if they really play any suited garbage • +2 on two-flush boards • -2 for each flush card in your hand except A and K • +2 if AK are both not with Villain (just a correction) Straights: 4-10 (Suited, either) Sets: 3-1 (Unblocked, blocked) Two pair: Single pair per kicker: Full houses: 2-7 (Suited, either) 2- 10 (Suited, either) 3- 6 (pocket pairs, unpaired holding) 8 per rank of kicker Open Trips: Computer Tools The answer key for this book was created with a calculator, pen and paper and a few computer tools: Flopziila This excellent software is available from Flopzilla.com, This is excellent for counting combos, just press tab to go from percentage mode to combo mode. Flopziila is not really made for hand on hand analysis, you need to make the range just one combo and put the other hand in as the “dead cards” for that analysis. Flopziila is not able to do range on range calculations either. You can also get the equities on just the flop or turn instead of all the way to the river. The hotness visualization makes it easy to count outs. Equilab This software from PokerStrategy.com shines for hand on hand analysis and range on range analysis. It does not count combos or outs as well. It is easier for solving many of the problems in this book when you are doing them very quickly, but does not have as much information for study. Fold Equity Calculator This is a web page that works on mobile or PC: http://RedChipPoker.com/fold-equity-calculator/ It is a simple fold equity calculator and that is all it does. It was developed by us at Red Chip Poker, so if you have improvements, let us know. These tools are all essentials. It is not a matter of either/or, but both. There are also similar poker calculators for mobile. The author uses Poker Cruncher on iPhone but there are lots of great alternatives. Obligatory Silly Painting Final thank you to Laura for being a huge grammar geek. About the Author After the great success of his first book. Poker Plays You Can Use, in the spring of 2015 Doug quit his 9-to-5 engineering job to do this kind of stuff full¬ time in Las Vegas, He runs Red Chip Poker along with James Sweeney, Ed Miller and Christian Soto. Doug does poker coaching by the hour and in three day boot camp style engagements. Say hello any time you see him at the tables or give him a call to tune up your game: Hull@RedChipPoker.com Text or call: 508.904.9626