Practical Poker Math

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3. Odds in Texas Hold’em 2 Unpaired Hole Cards >>> Runner-Runner 2 Pair With 2 unpaired cards in the hole there are 6 cards among the remaining 47 that will pair either card. For this calculation we will multiply the probability that the first card will pair either card by the probability that the second card will pair the remaining unpaired card. That probability expressed as a decimal ratio to 1 is: WILLs = Probability as decimal ratio to 1 Total Possibilities With 6 cards of a total of 47 that will pair either hole card, the probability that the first card will pair either hole card is: 6 47 With the first card paired there are 3 of the remaining 46 cards that will pair the remaining unpaired hole card. The probability that the second card will make the second Pair is 3 46 The probability of runner-runner pairing both unpaired hole cards is 6 * 3 = 18 47 46 2,162 18 = .0083 2,162 122
The probability of runner-runner pairing both hole cards is .0083 or .83% — less than 1%. To convert this decimal ratio to odds, subtract the WILLs (.0083) from the total possibility (1.0) to find the WILLNOTs = .9917. By approximation we know that if the probability is just under 1%, then the odds should be just over 100 to 1: Total Possibilities = 1 – WILLs = .0083 WILLNOTs = .9917 Odds of RR to Pair Both Unpaired Hole Cards WILLNOTs : WILLs .9917 : .0083 Reduce .9917 / .0083 : .0083 / .0083 119.5 : 1 Open Backdoor 3-Straight Flush >>> Runner- Runner Straight Flush With 3 suited and connected cards above 2 and below K in rank, there are 3 2-card combinations that will make a Straight Flush: 123 After the Flop
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Practical Poker Math By Pat Dittmar
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Thanks to some Friends for their la
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Table of Contents Preface . . . . .
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Odds with 2 Cards to Come . . . . .
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This is not perfect knowledge. It i
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Practical Poker Math The first aim
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1. Introduction to Game Theory in P
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2. The Basic Calculations Total Pos
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2. The Basic Calculations Another w
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2. The Basic Calculations Combinati
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2. The Basic Calculations This can
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2. The Basic Calculations 52 * 51 =
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2. The Basic Calculations pot odds
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2. The Basic Calculations Total Odd
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2. The Basic Calculations Odds in T
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2. The Basic Calculations number of
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2. The Basic Calculations sible fro
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2. The Basic Calculations Open Ende
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2. The Basic Calculations Odds of a
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2. The Basic Calculations After the
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2. The Basic Calculations The odds
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2. The Basic Calculations (48 * 47
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2. The Basic Calculations After the
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2. The Basic Calculations Therefore
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2. The Basic Calculations Before th
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3. Odds in Texas Hold’em ♦ The
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3. Odds in Texas Hold’em the arti
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3. Odds in Texas Hold’em In a ful
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3. Odds in Texas Hold’em The tabl
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3. Odds in Texas Hold’em Pocket A
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3. Odds in Texas Hold’em WILLNOTs
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3. Odds in Texas Hold’em 54 1,326
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3. Odds in Texas Hold’em Axs Comb
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3. Odds in Texas Hold’em 2 Big Ca
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3. Odds in Texas Hold’em Among th
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3. Odds in Texas Hold’em consider
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3. Odds in Texas Hold’em Before t
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3. Odds in Texas Hold’em 1 * 100
Page 90 and 91: 3. Odds in Texas Hold’em Starting
Page 92 and 93: 3. Odds in Texas Hold’em the pock
Page 94 and 95: 3. Odds in Texas Hold’em Odds of
Page 96 and 97: 3. Odds in Texas Hold’em rank, th
Page 98 and 99: 3. Odds in Texas Hold’em 39 * 55
Page 100 and 101: 3. Odds in Texas Hold’em After yo
Page 102 and 103: 3. Odds in Texas Hold’em Suited C
Page 104 and 105: 3. Odds in Texas Hold’em Total Po
Page 106 and 107: 3. Odds in Texas Hold’em 2 Big Ca
Page 108 and 109: 3. Odds in Texas Hold’em with AJ
Page 110 and 111: 3. Odds in Texas Hold’em 2 Unpair
Page 112 and 113: 3. Odds in Texas Hold’em ♦ Like
Page 114 and 115: 3. Odds in Texas Hold’em must hav
Page 116 and 117: 3. Odds in Texas Hold’em Pair >>>
Page 118 and 119: 3. Odds in Texas Hold’em Open Str
Page 120 and 121: 3. Odds in Texas Hold’em Set >>>
Page 122 and 123: 3. Odds in Texas Hold’em After th
Page 126 and 127: 3. Odds in Texas Hold’em Open Str
Page 128 and 129: 3. Odds in Texas Hold’em (10 * 9)
Page 130 and 131: 3. Odds in Texas Hold’em 172 + 2
Page 132 and 133: 3. Odds in Texas Hold’em Runner -
Page 134 and 135: 3. Odds in Texas Hold’em 1 Pair >
Page 136 and 137: 3. Odds in Texas Hold’em For each
Page 138 and 139: 3. Odds in Texas Hold’em With onl
Page 142 and 143: 3. Odds in Texas Hold’em Thus of
Page 146 and 147: 3. Odds in Texas Hold’em 2 Pair >
Page 148 and 149: 3. Odds in Texas Hold’em still 9
Page 150 and 151: 3. Odds in Texas Hold’em Open End
Page 152 and 153: 3. Odds in Texas Hold’em 2. The g
Page 154 and 155: 4. Consolidated Odds Tables Texas H
Page 156 and 157: 4. Consolidated Odds Tables After t
Page 158 and 159: 4. Consolidated Odds Tables After T
Page 160 and 161: 4. Consolidated Odds Tables Startin
Page 162 and 163: 4. Consolidated Odds Tables Hand Af
Page 165 and 166: 5. Odds in Omaha Hi-Lo In a 10-hand
Page 167 and 168: Starting Hands Your first chance to
Page 169 and 170: As demonstrated in Chapter 1, The B
Page 171 and 172: The odds of exactly one pair of Ace
Page 173 and 174: A2/AK Single Suited to the Ace For
Page 175 and 176: The number of 3-card combinations t
Page 177 and 178: The probability of A23 with the Ace
Page 179 and 180: AA2X Single Suited to A For the Flu
Page 181 and 182: There are 6 2-card combinations tha
Page 183 and 184: WILLNOTs (270,629) : WILLs (96) 270
Page 185 and 186: There are only 2 2-card combination
Page 187 and 188: Probably Not Playable With the thre
Page 189 and 190: Before the Flop In both Omaha High
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The Calculations These calculations
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Low hand (2), minus the 6 cards tha
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AA23 >>> Wheel or Aces Full To flop
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From the calculations above, we kno
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Total Possibilities = 17,296 - WILL
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Odds of Flopping an Ace High Flush
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Reduce 13,936 / 3,360 : 3,360/ 3,36
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(24 * 23) = 276 (1 * 2) 276 - 36 =
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(48 * 47) * 6 = 6,768 (1 * 2) Total
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After the Flop Nut Hand or Nut Draw
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1. Whether or not there will be a p
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The Calculations With the Turn card
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21 * 100 = 46.7% 45 Wheel (A2345) D
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Total Possibilities = 45 - WILLs =
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Odds of Turning a Boat or Quads WIL
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The Calculations After the Flop and
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Low Draw with Backup Low Card in th
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164 + 6 = 170 possible 2-card combi
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Flush Draw & Low Draw >>> Flush or
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296 + 28 = 324 possible 2-card comb
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Reduce 812 / 178 : 178 / 178 4.6 :
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Runner — Runner Remember — runn
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830 / 160 : 160 / 160 5.2 : 1 Back
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For each of these 3 sets there are
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Odds of a Runner-Runner 2 Pair or S
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Before the Last Card After the Turn
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The Calculations With one card to c
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2 Pair >>> Full House Reduce 23 / 2
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Open Ended Straight Draw & Flush Dr
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The River Bet All the cards are out
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Practical Poker Math

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