Practical Poker Math

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5. Odds in Omaha Hi-Lo 70 * 2 = 140 This calculation includes the possibility of flopping an AA to produce QUADS. There are 3,840 + 140 = 3,980 possible 3-card Flops that will make a nut Low hand or Aces Full or better to this hand. The odds of this Flop are Total Possibilities = 17,296 – WILLs = 3,980 WILLNOTs = 13,316 Odds of Flopping a Nut Low or Aces Full WILLNOTs : WILLs 13,316 : 3,980 Reduce 13,316 / 3,980 : 3,980 / 3,980 3.3 : 1 AA2X – Single Suited >>> Ace High Flush or Nut Low or Aces Full There are 3,980 3-card Flops that will make either a nut Low hand or Aces Full. To complete this calculation we must also find the number of 3-card Flops all of the same suit as the suited Ace — Comb(11, 3): (11 * 10 * 9) = 165 (1 * 2 * 3) There are 3,980 + 165 = 4,145 3-card Flops that will make an Ace High Flush, a nut Low or Aces Full to this hand. The odds against one of these flops are: Total Possibilities = 17,296 – WILLs = 4,145 WILLNOTs = 13,151 182
Odds of Flopping an Ace High Flush or Nut Low or Aces Full WILLNOTs : WILLs 13,151 : 4,145 Reduce 13,151 / 4,145 : 4,145 / 4,145 3.2 : 1 A23X >>> Nut Low Draw To flop a nut Low draw with this hand, the Flop needs to contain 2 unpaired cards below the rank of 9 with 1 and only 1 that may pair the A, 2 or 3 in the hole. This calculation includes the possibility of flopping a made nut Low. There are Comb(20, 2) 2-card combinations from the ranks 4 through 8 and 30 pairs: (20 * 19) = 190 (1 * 2) 190 – 30 = 160 is the number of 2-card combinations that will flop a nut Low draw to this hand. This is multiplied by all of the remaining cards minus the 6 that might counterfeit one of the Flop cards, 40: 160 * 40 = 6,400 With 6,400 3-card combinations that will flop the nut Low draw to this hand, the odds are: Total Possibilities = 17,296 – WILLs = 6,400 WILLNOTs = 10,896 183 Before the Flop
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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 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 2 Pair >
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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 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: Total Possibilities = 17,296 - WILL
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 :
Page 233 and 234: Runner — Runner Remember — runn
Page 235 and 236: 830 / 160 : 160 / 160 5.2 : 1 Back
Page 237 and 238: For each of these 3 sets there are
Page 239 and 240: Odds of a Runner-Runner 2 Pair or S
Page 241 and 242: Before the Last Card After the Turn
Page 243 and 244: The Calculations With one card to c
Page 245 and 246: 2 Pair >>> Full House Reduce 23 / 2
Page 247 and 248: Open Ended Straight Draw & Flush Dr
Page 249: The River Bet All the cards are out
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Practical Poker Math

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