Practical Poker Math

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5. Odds in Omaha Hi-Lo The total number of 4-card combinations possible from a 52-card deck is 270,725. There are 6 2-card combinations that can contain a pair of Aces. To find the number of 4-card combinations that can contain AA2x, multiply the number of possible pairs of Aces (6) by the number of 2-card combinations that can contain at least one Deuce and no Aces (4 * 47 = 188). The number of 4card combinations that can contain one pair of Aces and one or more Deuces is: 6 * 188 = 1,128 The probability of AA2x in the hole expressed as a percentage is WILLs * 100 = Probability as % Total Possibilities 1.128 * 100 = .42% 270,725 To find the odds of AA2x in the hole: Total Possibilities = 270,725 – WILLs = 1,128 WILLNOTs = 269,597 WILLNOTs (269,597) : WILLs (1,128) 269,597 : 1,128 Reduce 269,597 / 1,128 : 1,128/ 1,128 239 : 1 160
AA2X Single Suited to A For the Flush possibilities it doesn’t matter whether the Deuce or the fourth card is suited to one of the Aces. It only matters that one of those cards is suited to one of the Aces. In this example we will calculate the odds of having an AA2 with one of the Aces suited to either the Deuce or the fourth card in the hole. This includes the possibility that more than one of the hole cards will be suited to either Ace. The total number of 4-card combinations possible from a 52-card deck is 270,725. There are 6 2-card combinations that can contain a pair of Aces. To find the number of 4-card combinations that can contain AA2x single suited, multiply the number of possible pairs of Aces (6), by the number of 2-card combinations that can contain at least one Deuce and one of the 24 remaining cards of the same suit as either Ace (4 * 24 = 96). The number of 4-card combinations that can contain one pair of Aces, one or more Deuces and one card suited to either of the Aces is: 6 * 96 = 576 161 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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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
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2. The Basic Calculations (48 * 47
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2. The Basic Calculations After the
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2. The Basic Calculations Therefore
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2. The Basic Calculations Before th
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3. Odds in Texas Hold’em ♦ The
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3. Odds in Texas Hold’em the arti
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3. Odds in Texas Hold’em In a ful
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3. Odds in Texas Hold’em The tabl
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3. Odds in Texas Hold’em Pocket A
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3. Odds in Texas Hold’em WILLNOTs
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3. Odds in Texas Hold’em 54 1,326
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3. Odds in Texas Hold’em Axs Comb
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3. Odds in Texas Hold’em 2 Big Ca
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3. Odds in Texas Hold’em Among th
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3. Odds in Texas Hold’em consider
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3. Odds in Texas Hold’em Before t
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3. Odds in Texas Hold’em 1 * 100
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3. Odds in Texas Hold’em Starting
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3. Odds in Texas Hold’em the pock
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3. Odds in Texas Hold’em Odds of
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3. Odds in Texas Hold’em rank, th
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3. Odds in Texas Hold’em 39 * 55
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3. Odds in Texas Hold’em After yo
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3. Odds in Texas Hold’em Suited C
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3. Odds in Texas Hold’em Total Po
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3. Odds in Texas Hold’em 2 Big Ca
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3. Odds in Texas Hold’em with AJ
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3. Odds in Texas Hold’em 2 Unpair
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3. Odds in Texas Hold’em ♦ Like
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3. Odds in Texas Hold’em must hav
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3. Odds in Texas Hold’em Pair >>>
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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
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 144 and 145: 3. Odds in Texas Hold’em Odds 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
Page 156 and 157: 4. Consolidated Odds Tables After t
Page 158 and 159: 4. Consolidated Odds Tables After T
Page 160 and 161: 4. Consolidated Odds Tables Startin
Page 162 and 163: 4. Consolidated Odds Tables Hand Af
Page 165 and 166: 5. Odds in Omaha Hi-Lo In a 10-hand
Page 167 and 168: Starting Hands Your first chance to
Page 169 and 170: As demonstrated in Chapter 1, The B
Page 171 and 172: The odds of exactly one pair of Ace
Page 173 and 174: A2/AK Single Suited to the Ace For
Page 175 and 176: The number of 3-card combinations t
Page 177: The probability of A23 with the Ace
Page 181 and 182: There are 6 2-card combinations tha
Page 183 and 184: WILLNOTs (270,629) : WILLs (96) 270
Page 185 and 186: There are only 2 2-card combination
Page 187 and 188: Probably Not Playable With the thre
Page 189 and 190: Before the Flop In both Omaha High
Page 191 and 192: The Calculations These calculations
Page 193 and 194: Low hand (2), minus the 6 cards tha
Page 195 and 196: AA23 >>> Wheel or Aces Full To flop
Page 197 and 198: From the calculations above, we kno
Page 199 and 200: Total Possibilities = 17,296 - WILL
Page 201 and 202: Odds of Flopping an Ace High Flush
Page 203 and 204: Reduce 13,936 / 3,360 : 3,360/ 3,36
Page 205 and 206: (24 * 23) = 276 (1 * 2) 276 - 36 =
Page 207 and 208: (48 * 47) * 6 = 6,768 (1 * 2) Total
Page 209 and 210: After the Flop Nut Hand or Nut Draw
Page 211 and 212: 1. Whether or not there will be a p
Page 213 and 214: The Calculations With the Turn card
Page 215 and 216: 21 * 100 = 46.7% 45 Wheel (A2345) D
Page 217 and 218: Total Possibilities = 45 - WILLs =
Page 219 and 220: Odds of Turning a Boat or Quads WIL
Page 221 and 222: The Calculations After the Flop and
Page 223 and 224: Low Draw with Backup Low Card in th
Page 225 and 226: 164 + 6 = 170 possible 2-card combi
Page 227 and 228: 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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