Poker Math That Matters

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$Practical Poker Math$

Let's look at the four As. We’ll start with the A♣. It can be paired one time with the other three As. Then the A♦ can be paired with the A♥ and the A♠. It’s already been paired with the A♣, so we can’t count that one again. Now this leaves the A♥ being paired with the A♠. And the A♠ has already been paired with each of the others. So, this gives us six different unique combinations for pairing the As. There are six combinations of a paired hand per rank. One way to do this, without physically combining the cards, is to take the total number of cards in the group and then add together all the remaining numbers down to zero. 6 We have four cards in the group of As. 3 + 2 + 1 = 6 Let’s look at the impact of removing a card. Let’s say the flop has come down KA3. How many combinations of 33 can our opponent have for a set of 3s? Remember we said there are six combinations of pairs, but this isn’t correct now. One of the 3s is shown, so there are only three more possible for him to hold. How many unique, two-card combinations can be created from three cards? 2 + 1 = 3 There are three different combinations for him to hold a pair of 3s when one of the 3s is exposed. 73 Let’s look at unpaired hands. We'll combine both the suited and unsuited combinations of these holdings. Let’s find out how many combinations there are of our opponent having an unpaired hand like AK (See Figure 7). 6 Using the “combin” function in a spreadsheet software like Microsoft Excel will give you these answers quickly. For example, if, in a cell, you type “=combin(4,2)”, the result will be 6. Entering “=combin(52,2)” will produce 1,326. This is the number of unique hold’em starting hands.
74 Figure 7. Two groups containing four cards each can create 16 unique combinations. We have four As and 4 Ks in the deck. The K♣ can pair with each A for four combinations. The K♥ does the same for four combinations as does the K♠ and the K♦. This gives us four combinations for each K, and we have four Ks. This is a total of 16 combinations for an unpaired hand. With unpaired hands, you can simply multiply the two numbers together. We have four As and four Ks. 4 x 4 = 16
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Poker Math That Matters Simplifying
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Table of Contents Acknowledgements
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Set-Mining ........................
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Acknowledgements One of the most va
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xi poker fits my family's lifestyle
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2 Throughout this book, you will se
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4 Let’s talk a bit about how to d
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6 want to just play, play, and play
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Measurements Your Surroundings Ther
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Another measurement to understand i
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those sections. For a beginning pla
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Thinking About Bets in No-Limit Hol
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Here's why this works. If we were t
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playing at a 6-max table, he’ll p
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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 and 52: 40 TT88A. Your opponent’s best ha
Page 53 and 54: 42 Gutshot straight draw (aka Gutte
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: 72 When we look at the hand range s
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
Page 107 and 108: 96 make that bet. Looking at the EV
Page 109 and 110: 98 2. Hero: 5♠4♠ Villain: Fold
Page 111 and 112: 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
Page 119 and 120: 108 Value-Betting Value-betting is
Page 121 and 122: 110 and we’ll give him a $500 sta
Page 123 and 124: 112 only the hands that beat us. Ou
Page 125 and 126: 114 2. Hero: K♥Q♥ Villain: Call
Page 127 and 128: 116 7. Hero is out of position: K
Page 129 and 130: 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
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124 all sorts of As, Js and Ts in h
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126 Quiz (Answers on pg. 198) 1. Wh
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128 First of all, the above calcula
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130 past hands may cause you to twe
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132 would want to get the money in
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134 he can call profitably, if we h
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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
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146
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148 Congratulations on making your
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150 Comparing these two bet sizes,
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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
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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
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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♦
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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,
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186 Bluffing Quiz Answers 1. Hero:
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188 Answer: A 1/3 pot bet must work
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190 $24 - $14 = $10 We’re risking
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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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