Practical Poker Math

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3. Odds in Texas Hold’em Odds of Flopping Quads with a Pocket Pair WILLNOTs : WILLs 19,552 : 48 Reduce 19,552 / 48 : 48 / 48 407.3 : 1 Pocket Pair >>> Set or Better Given all of the above calculations, finding the odds of flopping a Set, a Full House or Quads when holding a Pocket Pair is simply a matter of combining the WILLs. Number of Flops that make a Set 2,112 Number of Flops that make a Boat 192 Number of Flops that make Quads 48 Flops that WILL make a Set or better 2,352 We now have all the numbers needed to calculate the odds of flopping a Set or better with a Pair in the hole: Total Possibilities = 19,600 – WILLs = 2,352 WILLNOTs = 17,248 Odds of Flopping Set or Boat w/Pocket Pair WILLNOTs : WILLs 17,248 : 2,352 Reduce 17,248 / 2,352 : 2,352 / 2,352 7.3 : 1 76
Pocket Pair >>> 2 Pair To flop 2 Pair with a Pair in the hole, the Flop must contain a Pair and a third card that doesn’t match the Pocket Pair or the other cards on the board. Without the rank of the Pocket Pair, there are 72 Pairs among the remaining 50 unseen cards. To find the number of Flops that will make 2 Pair with a Pair in the pocket, multiply the number of possible Pairs (72) by the number of remaining unseen cards that will not match either the Pair in the hole or the Pair on the board, and that will not be the pair on the board (50 – 2 – 2 – 2 = 44): 72 * 44 = 3,168 We now have all the numbers needed to calculate the odds of flopping 2 Pair with a Pair in the hole: Total Possibilities = 19,600 – WILLs = 3,168 WILLNOTs = 16,432 Odds of Flopping 2 Pair w/Pocket Pair WILLNOTs : WILLs 16,432 : 3,168 Reduce 16,432 / 3,168 : 3,168 / 3,168 5.19 : 1 Suited Cards While any 2 suited cards can make a Flush, the most valuable suited cards are the suited connectors, and the higher the 77 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
Page 44 and 45: 2. The Basic Calculations number of
Page 46 and 47: 2. The Basic Calculations sible fro
Page 48 and 49: 2. The Basic Calculations Open Ende
Page 50 and 51: 2. The Basic Calculations Odds of a
Page 52 and 53: 2. The Basic Calculations After the
Page 54 and 55: 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 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 124 and 125: 3. Odds in Texas Hold’em Odds of
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
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3. Odds in Texas Hold’em Odds of
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3. Odds in Texas Hold’em 2 Pair >
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3. Odds in Texas Hold’em still 9
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3. Odds in Texas Hold’em Open End
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3. Odds in Texas Hold’em 2. The g
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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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