Practical Poker Math

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$Poker Math That Matters$

3. Odds in Texas Hold’em The table below displays both the odds and the probability that any given player will receive certain hands as his first two cards. The calculations to determine these odds and probabilities are demonstrated below the table. Starting Hands — Odds/Probabilities *Note — Suited connectors calculated are 45 through TJ. 2 Big Cards refers to any 2 unpaired cards J or higher. The Calculations Hand Probability Odds Any Pair 5.9% 16 : 1 Any Specific Pair (AA) .452% 220 : 1 Pair of Jacks or Better 1.8% 54.25 : 1 22 through TT 4.10% 23.6 : 1 Suited Connectors 2.10% 46.4 : 1 Suited Ace 3.62% 26.6 : 1 Any 2 Suited 23.53% 3.25 : 1 Any AK 1.2% 81.9 : 1 AKs .30% 330.5 : 1 2 Unpaired Big Cards 7.2% 12.8 : 1 Any Ace 14.50% 5.9 : 1 Rags 81% .23 : 1 These odds and probabilities can be calculated at least two ways: 1. Combinations — Knowing the total number of possible 2-card combinations (1,326) and the number 52
of combinations that will make the starting hand, the odds are easily calculated as demonstrated below. 2. Probabilities — The probability of any starting hand can easily be determined by multiplying the probability of the first card by the probability of the second. As demonstrated in Chapter 1 — Basic Calculations — and throughout this book, any odds are easily converted into probabilities and vice versa. Pocket Pairs For each rank — cards 2 through A, there are 6 possible pair combinations — Comb(4, 2): (4 * 3) = 6 (1 * 2) With 13 ranks of 6 possible pair combinations there are 78 pair combinations possible from a standard 52-card deck. The odds and probability that any given player will receive the Pairs listed below as his hole cards are: 53 Starting Hands Hand Probability Odds Any Pair 5.9% 16 : 1 Any Specific Pair (AA) .452% 220 : 1 Pair of Jacks or Better 1.8% 54.25 : 1 22 through TT 4.10% 23.6 : 1
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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
Page 20 and 21: 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 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 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
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3. Odds in Texas Hold’em Set >>>
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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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Practical Poker Math

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