Practical Poker Math

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$Poker Math That Matters$

3. Odds in Texas Hold’em WILLNOTs (1,248) : WILLs (78) 1,248 : 78 Reduce 1,248 / 78 : 78 / 78 16 : 1 The likelihood of any Pair in the hole expressed as a probability is WILLs * 100 = Probability as % Total Possibilities 78 1,326 * 100 = 5.9% On average you will be dealt a Pocket Pair once in 17 hands or roughly 6% of the time. Pocket JJ or Better For JJ through AA there are 24 (6 * 4) possible pair combinations from 1,326 total possible 2-card combinations: Possible Pairs JJ or Better (WILLs) = 24 Total Possibilities = 1,326 – WILLs = 24 WILLNOTs = 1,302 WILLNOTs (1,302) : WILLs (24) 1,302 : 24 Reduce 1,302 / 24 : 24 / 24 54.25 : 1 56
The probability of a pair of Jacks or better in the hole is WILLs * 100 = Probability as % Total Possibilities 24 * 100 = 1.8% 1,326 On average you will be dealt Pocket Jacks or better once in 55.25 hands or roughly 2% of the time. Pocket 22 through TT For 22 through TT there are 54 (9 * 6) possible pair combinations from 1,326 total possible 2-card combinations. Possible Pairs 22 through TT (WILLs) = 54 Total Possibilities = 1,326 – WILLs = 54 WILLNOTs = 1,272 WILLNOTs (1,272) : WILLs (54) 1,272 : 54 Reduce 1,272 / 54 : 54 / 54 23.6 : 1 The likelihood of pocket 22 through TT, expressed as a probability, is shown below — first as a percentage calculation then as a combination of probabilities. Percentage calculation: WILLs * 100 = Probability as % Total Possibilities 57 Starting Hands
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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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1. Introduction to Game Theory in P
Page 24 and 25: 1. Introduction to Game Theory in P
Page 26 and 27: 1. Introduction to Game Theory in P
Page 28 and 29: 2. The Basic Calculations Total Pos
Page 30 and 31: 2. The Basic Calculations Another w
Page 32 and 33: 2. The Basic Calculations Combinati
Page 34 and 35: 2. The Basic Calculations This can
Page 36 and 37: 2. The Basic Calculations 52 * 51 =
Page 38 and 39: 2. The Basic Calculations pot odds
Page 40 and 41: 2. The Basic Calculations Total Odd
Page 42 and 43: 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 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 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
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3. Odds in Texas Hold’em Odds of
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3. Odds in Texas Hold’em Open Str
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3. Odds in Texas Hold’em (10 * 9)
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3. Odds in Texas Hold’em 172 + 2
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3. Odds in Texas Hold’em Runner -
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3. Odds in Texas Hold’em 1 Pair >
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3. Odds in Texas Hold’em For each
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3. Odds in Texas Hold’em With onl
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3. Odds in Texas Hold’em 2 Unpair
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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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