Practical Poker Math

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3. Odds in Texas Hold’em 54 1,326 * 100 = 4.1% Combination of Probabilities: There are 36 cards in the deck with a rank of 2 through T, but there are only 4 cards of each rank from which your Pair can be dealt. The probability of the first card is 36/52 and the probability of the second card is 3/51: 36 * 3 = .0407 52 51 It is very easy to calculate odds and probabilities using these methods. On average you will be dealt pocket 22 through TT once in 24.6 hands or roughly 4.1% of the time. Suited Cards Given enough action, suited cards — especially suited connectors — can make great drawing hands. The table below reflects the likelihood that any given player will hold any two suited cards, suited connectors or a suited Ace (Ax). Hand Probability Odds Suited Connectors 2.10% 46.4 : 1 Suited Ace 3.62% 26.6 : 1 Any 2 Suited 23.53% 3.25 : 1 *Note — Suited connectors calculated are 45 through TJ. 58
Suited Connectors These are the connectors that will make a Straight when combined with 3 cards in either or both directions. There are 7 ranks and 4 suits so 7 * 4 = 28 possible suited connectors 45 through TJ from 1,326 total possible 2-card combinations: Suited Connectors 45 through TJ (WILLs) = 28 Total Possibilities = 1,326 – WILLs = 28 WILLNOTs = 1,298 WILLNOTs (1,298) : WILLs (28) 1,298 : 28 Reduce 1,298 / 28 : 28 / 28 46.4 : 1 The probability of suited 45 through TJ in the hole is WILLs * 100 = Probability as % Total Possibilities 28 * 100 = 2.1% 1,326 On average you will be dealt one of these sets of suited connectors once in 47.4 hands or roughly 2.1% of the time. Any Suited Ace — Axs There are 12 Ax combinations for each of the 4 suits, resulting in 48 possible Ax suited combinations: 59 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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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 74 and 75: 3. Odds in Texas Hold’em WILLNOTs
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
Page 124 and 125: 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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Practical Poker Math

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