Practical Poker Math: Basic Odds & Probabilities for Hold'Em and Omaha

Overview


What are the odds of winning at poker if you don’t know the odds in poker? Practical Poker Math provides a complete and easy-to-understand explanation of the basic odds, probabilities and expectations in Hold’Em and Omaha. All the formulations are completely open and are demonstrated via easy-to-follow, colour-coded calculations. Pat Dittmar has aimed this book at beginning through semi-pro players who want to improve their results and who know that there is not much chance of improvement without a fundamental ...
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Overview


What are the odds of winning at poker if you don’t know the odds in poker? Practical Poker Math provides a complete and easy-to-understand explanation of the basic odds, probabilities and expectations in Hold’Em and Omaha. All the formulations are completely open and are demonstrated via easy-to-follow, colour-coded calculations. Pat Dittmar has aimed this book at beginning through semi-pro players who want to improve their results and who know that there is not much chance of improvement without a fundamental understanding of poker odds, probabilities, and expectations. Pat Dittmar is head of trading and development at TradePointTechnologies.com, an organization that develops and deploys state-of-the-art proprietary trading technologies. Pat feels that successful poker players possess the skills required to play in the one true fast action, around the world, around the clock “Big Game” – the world financials markets, and TradePointTechnologies recruits its traders exclusively from the poker world.
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Editorial Reviews

From the Publisher

"Dittmar answers many questions and fills in a lot of gaps about poker mathematics. . . . His book is for the thinking player who wants to incorporate some mathematics and an understanding of odds into his or her mode of play."  —Poker Player Magazine

"Take advantage of the brilliance offered here."  —Barbara Rogers

Poker Player Magazine
Dittmar answers many questions and fills in a lot of gaps about poker mathematics. . . . His book is for the thinking player who wants to incorporate some mathematics and an understanding of odds into his or her mode of play.
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Product Details

  • ISBN-13: 9781550228335
  • Publisher: ECW Press
  • Publication date: 9/1/2008
  • Pages: 256
  • Sales rank: 980,498
  • Product dimensions: 6.00 (w) x 8.90 (h) x 0.60 (d)

Meet the Author


Pat Dittmar has played professional poker for more than 20 years and has worked as a consultant for a major online poker site. He lives in Las Vegas.
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Read an Excerpt


Certain practitioners can predict, with perfect accuracy, such natural phenomena as the day, the night, the tides and even celestial events that will occur a thousand years from now.

In poker, any player can predict with that same astonishing accuracy the likelihood of any card appearing at any time. He can predict the likely holdings of his opponents and, based on his own hand, he can predict the long–term profitability of any call, bet or raise.

In astrophysics and the navigation of spacecraft, the requirement for accuracy is absolute. In poker a close approximation is all you need.

The outcome of any hand of poker is determined by either or both of the fall of the cards and the actions of the players. If the cards fall so that you have the best hand and you don’t fold, you will win the pot. If you employ a betting strategy that compels your opponent(s) to fold, your cards could be blank and you will still win the pot.

Knowledge of odds and probabilities can turn seemingly random events, such as the fall of the cards, into eminently predictable occurrences. An understanding of positive or negative expectation will tell the long–term profitability of any given play and a grasp of basic Game Theory can tell much about the likely responses of opponents.

The first aim of this book is simplicity and clarity so that any player will be able to access the power of odds, probability and game theory information in support of each poker decision.

To facilitate access, the information in Practical Poker Math is organized into layers. For both Texas Hold’em and Omaha Hi–Lo it is presented sequentially, based on the round of betting. For each round there is a brief discussion of applicability, followed by a table of the odds for that round, followed by an expansion and explanation of the calculation of each of the odds found in the table. In the center of the book is a consolidation of all of the odds tables from both games.

The result of this organization is that the player who is only interested in referencing certain odds may easily do so in the chapter that contains the consolidated odds tables — without having to wade through hundreds of odds calculations. The player more interested in the principles may read each section’s text and refer to the attendant table. Any player who would like to explore the calculation of a certain set of odds can find the expansion and explanation of that calculation in a logical location by the round of betting. And, finally, for the student who wants to learn it all — it is all there.

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Table of Contents


Preface     ix
Introduction     xi
Introduction to Game Theory in Poker     1
Game Theory - A Historical Perspective     1
Game Theory and Poker     3
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
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
Odds the Turn Card Will     97
Odds with 2 Cards to Come     103
Odds of Hitting on Either or Both Turn & River     103
Runner - Runner     114
The Calculations     115
Before the Last Card     125
Odds of Improvement     126
The Calculations     126
The River Bet - Last Chance to Earn     133
Consolidated Odds Tables     135
Texas Hold'em Odds Tables     136
Starting Hands     136
Before the Flop     136
After the Flop     138
Last Card (The River)     140
Omaha Hi-Lo Odds Tables     141
Starting Hands     141
Before the Flop     141
Odds of Improvement with the Turn Card     143
Odds of Improvement with 2 Cards to Come     143
Odds of Making Certain Runner-Runner Draws     144
Odds of Improvement with Only the River Card to Come     145
Odds in Omaha Hi-Lo     147
Starting Hands     149
Odds & Probabilities     149
The Calculations     150
Before the Flop     171
Omaha Hi-Lo - Before the Flop     172
The Calculations     173
After the Flop      191
Nut Hand or Nut Draw     191
Money & Expectation After the Flop     191
Odds of Improvement     193
Odds the Turn Card Will     194
The Calculations     195
Odds with 2 Cards to Come     201
The Calculations     203
Runner - Runner     215
The Calculations     215
Before the Last Card     223
The Calculations     225
The River Bet     231
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