Practical Poker Math

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5. Odds in Omaha Hi-Lo Any AA23/AA2K 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 AA. There are 4 * 4 = 16 2-card combinations that contain 23. The number of 4-card combinations that can contain AA23 is the number of possible 2-card combinations that contain 2 Aces (6), multiplied by the number of possible 2-card combinations that contain 23 (16): 6 * 16 = 96 The probability of AA23 in the pocket expressed as a percentage is: WILLs * 100 = Probability as % Total Possibilities 96 * 100 = .035% 270,725 The odds of A23 in the pocket are: Total Possibilities = 270,725 – WILLs = 96 WILLNOTs = 270,629 164
WILLNOTs (270,629) : WILLs (96) 270,629 : 96 Reduce 270,629 / 96 : 96 / 96 2,819.1 : 1 AA23/AA2K Single Suited We will calculate the odds of having an AA23 single suited to either Ace in the hole. 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 AA23 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, one Trey and with either the 2 or the 3 suited to one of the Aces (2 * 4 = 8). The number of 4card combinations that can contain AA23 single suited is 6 * 8 = 48 The probability of AA23 single suited in the hole expressed as a percentage is 165 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
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3. Odds in Texas Hold’em (10 * 9)
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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 and 178: The probability of A23 with the Ace
Page 179 and 180: AA2X Single Suited to A For the Flu
Page 181: There are 6 2-card combinations tha
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
Page 229 and 230: 296 + 28 = 324 possible 2-card comb
Page 231 and 232: 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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