Practical Poker Math

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$Poker Math That Matters$

3. Odds in Texas Hold’em 2 Big Cards Odds of Flopping a Royal Flush WILLNOTs : WILLs 19,599 : 1 Reduce 19,599 / 1 : 1 / 1 19,599 : 1 Big Cards are any 2 cards Jack or higher. If the cards are paired then their odds of improvement are noted above. The same holds true if the 2 cards are either connected or suited. Below are the calculations that the Flop will pair one particular card in the hole, will pair either card in the hole, will pair both cards in the hole, or will make a Set to either hole card. Starting Hand Hand to Flop Odds 2 Unpaired Cards Pair a Certain Hole Card 5 : 1 2 Unpaired Cards Pair Either Hole Card 2.45 : 1 2 Unpaired Cards Pair Both Hole Cards 48.49 : 1 2 Unpaired Cards A Set of Either Hole Cards 73.24 : 1 2 Unpaired Hole Cards >>> Pair a Specific Hole Card To find the odds of flopping at least a pair of Aces with AJ in the hole, find the number of 2-card combinations that do not 88
contain an Ace, and multiply that number by the number of remaining unseen Aces, resulting in the total number of possible 3-card combinations that will contain at least an Ace. Subtract the 2 cards in the hole and the 3 remaining Aces, leaving 47 unseen cards none of which are Aces, then use Comb(47, 2): (47 * 46) = 1,081 (1 * 2) With 1,081 possible 2-card combinations that contain no Aces and 3 remaining Aces unseen, the number of possible 3-card Flops that WILL flop at least a pair of Aces is 3 * 1,081 = 3,243 We now have all the numbers needed to calculate the odds of flopping at least a pair of Aces with AJ in the hole: Total Possibilities = 19,600 – WILLs = 3,243 WILLNOTs = 16,357 Odds of Flopping at Least AA WILLNOTs : WILLs 16,357 : 3,243 Reduce 16,357 / 3,243 : 3,243 / 3,243 5 : 1 2 Unpaired Hole Cards >>> Pair Either Hole Card To find the odds of flopping at least a Pair of either hole card 89 Before 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
Page 56 and 57: 2. The Basic Calculations (48 * 47
Page 58 and 59: 2. The Basic Calculations After the
Page 60 and 61: 2. The Basic Calculations Therefore
Page 62 and 63: 2. The Basic Calculations Before th
Page 64 and 65: 3. Odds in Texas Hold’em ♦ The
Page 66 and 67: 3. Odds in Texas Hold’em the arti
Page 68 and 69: 3. Odds in Texas Hold’em In a ful
Page 70 and 71: 3. Odds in Texas Hold’em The tabl
Page 72 and 73: 3. Odds in Texas Hold’em Pocket A
Page 74 and 75: 3. Odds in Texas Hold’em WILLNOTs
Page 76 and 77: 3. Odds in Texas Hold’em 54 1,326
Page 78 and 79: 3. Odds in Texas Hold’em Axs Comb
Page 80 and 81: 3. Odds in Texas Hold’em 2 Big Ca
Page 82 and 83: 3. Odds in Texas Hold’em Among th
Page 84 and 85: 3. Odds in Texas Hold’em consider
Page 86 and 87: 3. Odds in Texas Hold’em Before t
Page 88 and 89: 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 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 140 and 141: 3. Odds in Texas Hold’em 2 Unpair
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
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4. Consolidated Odds Tables After t
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4. Consolidated Odds Tables After T
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4. Consolidated Odds Tables Startin
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4. Consolidated Odds Tables Hand Af
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5. Odds in Omaha Hi-Lo In a 10-hand
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Starting Hands Your first chance to
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As demonstrated in Chapter 1, The B
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The odds of exactly one pair of Ace
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A2/AK Single Suited to the Ace For
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The number of 3-card combinations t
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The probability of A23 with the Ace
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AA2X Single Suited to A For the Flu
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There are 6 2-card combinations tha
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WILLNOTs (270,629) : WILLs (96) 270
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There are only 2 2-card combination
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Probably Not Playable With the thre
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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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