Practical Poker Math

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5. Odds in Omaha Hi-Lo Odds of a Low with 2 Cards to Come WILLNOTs : WILLs 303 : 687 Reduce 303 / 687 : 687 / 687 .4 : 1 WILLs * 100 = Probability as % Total Possibilities 687 * 100 = 69% 990 Wheel Draw >>> Wheel with 2 Cards to Come With a Wheel draw, only 4 of the unseen 45 cards will make the Wheel. As long as this last card to the Wheel is one of the 2 final board cards, it will not affect the value of the hand if 1 of the 2 last cards counterfeits either a board card or a hole card. Of the 45 unseen cards, 4 will make the Wheel and the remaining 41 can combine with one of these 4 to make the Wheel. 4 * 41 = 164 is the number of 2-card combinations, one card of which will make the Wheel. Comb(4, 2) is the number of 2-card combinations that contain 2 cards that will make the Low, including pairs: (4 * 3) = 6 (1 * 2) 6 2-card combinations will contain 2 Wheel cards and still complete the Low regardless of counterfeiting either of the low cards in the hole. 206
164 + 6 = 170 possible 2-card combinations WILL make the Wheel: Total Possibilities = 990 – WILLs = 170 WILLNOTs = 820 Odds of a Wheel with 2 Cards to Come WILLNOTs : WILLs 820 : 170 Reduce 820 / 170 : 170 / 170 4.8 : 1 Low Draw >>> Counterfeit One or More Low Cards in the Hole with 2 Cards to Come With a Low draw there are 6 cards that can counterfeit either or both low cards in the hole. 6 of the unseen 45 cards will counterfeit the Low and 39 will not. 6 * 39 = 234 is the number of 2-card combinations, one card of which will counterfeit one of the low cards in the hole. Comb(6, 2) is the number of 2-card combinations in which both cards match one or both of the low cards in the hole: (6 * 5) = 15 (1 * 2) 234 + 15 = 249 possible 2-card combinations WILL counterfeit at least one of the 2 low cards in the hole: Total Possibilities = 990 – WILLs = 249 WILLNOTs = 741 207 After 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
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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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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 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: Low Draw with Backup Low Card in th
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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