Poker Math That Matters

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$Practical Poker Math$

Hero: A♠2♥ Villain: A♣7♦ Board: A♥Q♦6♣3♠ You’re behind since his 7 kicker plays. How many outs do you have? Well, you certainly have the three 2s left to give you two pair. So, that’s three outs to a win. However, what happens if the river is a 3? At that point you have AA33Q, and so does your opponent! You tie and will chop the pot. So, you have three outs to a chop with the 3s. The same is true if the river is a 6. You will have AA66Q, and so will he. This is another chop. You have now have a total of six outs to a chop. What if the river is a Q? Think carefully. At this point, you’ll have AAQQ6; however, your opponent has AAQQ7, so he wins. His 7 now plays, and he has you outkicked. So, in this hand you have three outs to a win, and six outs to a chop. When you have the worst hand and are trying to hit an out, it’s called drawing. You’re on a draw. Table 4 shows common draws and the number of outs to a better hand than you currently hold. Table 4. Common draws. Draw Outs Gutshot (aka Gutter or Belly Buster) 4 Pair (not pocket pair) 5 Open-Ended Straight Draw (OESD) 8 Double Gutter (aka Double Belly Buster) 8 Four-flush (aka Flush Draw) 9 Open-Ended Straight Flush Draw (OESFD) 15 41
42 Gutshot straight draw (aka Gutter or Belly Buster) – You need to fill in one card to make a straight. Here we need a 4 to complete a straight. Hero: 6♠7♠ Villain: A♣K♦ Board: K♥5♦3♣ Pair – You have two different hole cards, and one of them paired a card on the board. This is different than a wired pair which is when you have a pair as your hole cards. Here we need either a 7 or a 6 to improve to two pair or trips. 3 Hero: 6♠7♠ Villain: A♣K♦ Board: K♥5♦6♣ Open-ended straight draw (aka Outside Straight draw, and abbreviated as OESD) – You have four cards in a row and can catch a straight on either side of them. Here we need either a 3 or a 8 to complete our straight. We have eight outs to the straight. Hero: 6♠7♠ Villain: A♣K♦ Board: K♥5♦4♣ 3 Three of a kind is often called trips or a set; however, these are different and vary greatly in value. Trips is when one of your hole cards matches a pair on the board. A set is when a card on the board matches the pair you have as your hole cards.
Page 2 and 3: Poker Math That Matters Simplifying
Page 4 and 5: Table of Contents Acknowledgements
Page 6 and 7: Set-Mining ........................
Page 8: Acknowledgements One of the most va
Page 11 and 12: xi poker fits my family's lifestyle
Page 13 and 14: 2 Throughout this book, you will se
Page 15 and 16: 4 Let’s talk a bit about how to d
Page 17 and 18: 6 want to just play, play, and play
Page 20 and 21: Measurements Your Surroundings Ther
Page 22 and 23: Another measurement to understand i
Page 24 and 25: those sections. For a beginning pla
Page 26 and 27: Thinking About Bets in No-Limit Hol
Page 28 and 29: Here's why this works. If we were t
Page 30 and 31: playing at a 6-max table, he’ll p
Page 32 and 33: money for a while and not even be c
Page 34 and 35: Getting Started with Numbers Workin
Page 36 and 37: The last topic to cover in this sec
Page 38 and 39: doesn’t happen to complete our ra
Page 40 and 41: Expectation Value You’re walking
Page 42 and 43: 0.5 * (-$10) = (-$5) Now let’s do
Page 44: Quiz (Answers on pg. 158) 1. Someon
Page 47 and 48: 36 left to come on the river. What
Page 49 and 50: 38 Hero: 6♠7♠ Villain: A♣K♦
Page 51: 40 TT88A. Your opponent’s best ha
Page 55 and 56: 44 you’ll need to add these toget
Page 57 and 58: 46 9. Hero: Q♦K♥ Villain: A♠J
Page 59 and 60: 48 19. Hero: A♠Q♣ Villain: 5♣
Page 61 and 62: 50 The 4/2 Rule I hope you’ve tak
Page 63 and 64: 52 pretty simple, right? But, of co
Page 65 and 66: 54 Let’s try one more. Hero: J♥
Page 67 and 68: 56 We can multiply these fractions
Page 69 and 70: 58 4. Hero: 9♦6♦ Villain: J♦J
Page 71 and 72: 60 So, the equation looks like this
Page 73 and 74: 62 We have a flush draw. The pot is
Page 75 and 76: 64 Quiz (Answers on pg. 174) For th
Page 77 and 78: 66 Implied Odds In this section, we
Page 79 and 80: 68 Table 6. Multiplication factor t
Page 81 and 82: 70 3. Hero: A♣Q♦ Villain: J♦J
Page 83 and 84: 72 When we look at the hand range s
Page 85 and 86: 74 Figure 7. Two groups containing
Page 87 and 88: 76 the probability distribution of
Page 89 and 90: 78 the suited A holdings villain co
Page 91 and 92: 80 8. Hero: 5♥6♥ Villain: 99, Q
Page 93 and 94: 82 section. As usual, we’ll talk
Page 95 and 96: 84 Now, obviously we’re going to
Page 97 and 98: 86 AA: 3 combinations- 12% KK: 3 co
Page 99 and 100: 88 2. Hero: J♠A♠ Villain: QQ, K
Page 101 and 102: 90 So, we lost $360 in Sklansky-buc
Page 103 and 104:
92 Quiz (Answers on pg. 184) Calcul
Page 105 and 106:
94 Take a second and think about th
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96 make that bet. Looking at the EV
Page 109 and 110:
98 2. Hero: 5♠4♠ Villain: Fold
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100 Let's do a quick exercise to es
Page 113 and 114:
102 39x - 7.56 + 7.56x > 0 46.56x >
Page 115 and 116:
104 $81(0.24) = $19.44 2. Our shove
Page 117 and 118:
106 Quiz (Answers on pg. 188) Assum
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108 Value-Betting Value-betting is
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110 and we’ll give him a $500 sta
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112 only the hands that beat us. Ou
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114 2. Hero: K♥Q♥ Villain: Call
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116 7. Hero is out of position: K
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118 and then consider your pot odds
Page 131 and 132:
120 Quiz (Answers on pg. 197) 1. Ho
Page 133 and 134:
122 Seems like a small thing, right
Page 135 and 136:
124 all sorts of As, Js and Ts in h
Page 137 and 138:
126 Quiz (Answers on pg. 198) 1. Wh
Page 139 and 140:
128 First of all, the above calcula
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130 past hands may cause you to twe
Page 143 and 144:
132 would want to get the money in
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134 he can call profitably, if we h
Page 147 and 148:
136 It's obviously a mistake for hi
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138 4. Hero: Q♣Q♦ Villain: 8♣
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140 decision may be a totally diffe
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142 adjustment. So, in order to avo
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144 balanced poker every day of the
Page 157 and 158:
146
Page 159 and 160:
148 Congratulations on making your
Page 161 and 162:
150 Comparing these two bet sizes,
Page 163 and 164:
152 So, we're still better of betti
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154 Your Surroundings Quiz Answers
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156 2. If you played 10,000 hands b
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158 Answer: Probability is 2 6 odds
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160 4. Someone holds out a deck of
Page 173 and 174:
162 4. Hero: 5♣7♣ Villain: K♦
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164 9. Hero: Q♦K♥ Villain: A♠
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166 14. Hero: 7♠8♠ Villain: 9
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168 18. Hero: A♠5♠ Villain: A
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170 22. Hero: 4♠5♠ Villain: A
Page 183 and 184:
172 The 4/2 Rule Quiz Answers 1. He
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174 6. Hero: Q♦Q♥ Villain: A♥
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176 4. Hero: 9♦6♦ Villain: J♦
Page 189 and 190:
178 Combinations Quiz Answers 1. He
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180 7. Hero: 6♥7♠ Villain: QQ,
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182 2. Hero: J♠A♠ Villain: QQ,
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184 outs for 6% equity. Against 66,
Page 197 and 198:
186 Bluffing Quiz Answers 1. Hero:
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188 Answer: A 1/3 pot bet must work
Page 201 and 202:
190 $24 - $14 = $10 We’re risking
Page 203 and 204:
192 0.57($20) + 0.43(-$20) = EV 11.
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194 4. Hero: A♦J♦ Villain has $
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196 6. Hero is out of position: K
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198 2. How often will you flop an o
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200 2. What are some of the factors
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202 5. When might we allow some dra
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204
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206 Chopping Outs: Cards to come th
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208 Offsuit: Hole cards that do not
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Owen Gaines also wrote Hole Card Co
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Poker Math That Matters

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