Practical Poker Math

More documents

Recommendations

Info

$Poker Math That Matters$

About the Author Today Pat Dittmar is head of trading and technical development at TradePointTechnologies.com. At Trade Point Technologies a small group of poker players use their poker skills and state of the art, proprietary technology to play in the one true Big Game: The World Financial Markets. The author’s math expertise comes from years in the financial community, where he held positions including partner in a registered brokerage firm, derivatives trader, big block trader, arbitrageur and Compliance Registered Options Principal. As a longtime resident and habitué of Las Vegas, Pat has played professional poker on and off for more than 2 decades and has worked as a paid consultant to a major online poker site. After a bad beat in the bond market, he went back to sea. Operating under his license as a U.S. Merchant Marine Master Mariner, Pat served as the Captain of small freighters. Much of this work took place along the trading routes off the west coast of Africa. For many years, in special, protected rooms in Pointe Noire — Old Congo, Port Gentil — Gabon, and Abidjan — Cote d’Ivoire a colorful assortment of ships’ Captains, mercenaries, black marketeers, spies and Angolan diamond smugglers gathered to play poker, and on occasion, so did Pat.
Table of Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi 1. Introduction to Game Theory in <strong>Poker</strong> . . . . . . . . . . . . . . . . 1 Game Theory — A Historical Perspective. . . . . . . . . . . . . . . . 1 Game Theory and <strong>Poker</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2. The Basic Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Odds & Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Combinations, Permutations & Factorials . . . . . . . . . . . . . . 14 Money Odds & Expectation . . . . . . . . . . . . . . . . . . . . . . . . . 19 Total Odds & Real Expectation. . . . . . . . . . . . . . . . . . . . . . . 22 Odds in Texas Hold’em . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Odds in Omaha Hi-Lo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3. Odds in Texas Hold’em . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Starting Hands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Odds & Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 The Calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Pocket Pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Suited Cards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2 Big Cards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Rags . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Before the Flop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 The Calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Pocket Pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Suited Cards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 2 Suited in the Hole. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 2 Big Cards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 After the Flop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Odds of Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Money Odds, Overlays & Expectation . . . . . . . . . . . . . . . . . 93 From a Game Theory Perspective . . . . . . . . . . . . . . . . . . . . 95 v
Page 2 and 3: Get $150 Dollars Bankroll For Free
Page 4 and 5: CLICK HERE TO DOWNLOAD POKEROFFICE
Page 7 and 8: Practical Poker Math By Pat Dittmar
Page 9: Thanks to some Friends for their la
Page 13: Odds with 2 Cards to Come . . . . .
Page 16 and 17: This is not perfect knowledge. It i
Page 18 and 19: 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 70 and 71:
3. Odds in Texas Hold’em The tabl
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
Page 120 and 121:
3. Odds in Texas Hold’em Set >>>
Page 122 and 123:
3. Odds in Texas Hold’em After th
Page 124 and 125:
Page 126 and 127:
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:
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 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
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
show all

Practical Poker Math

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?