Preface

Without a clear understanding — or at least a great natural instinct for odds, probabilities and the ratios of risk and reward — success at poker is unlikely.

However, with enough knowledge of these odds and ratios to recognize situations of positive expectation, and the discipline to operate only in an environment of positive expectation, long-term poker success is virtually assured.

To get the maximum possible value from every hand, a player need only have perfect knowledge of

1.The cards yet to come

2.The cards held by opponents

3.The future actions and reactions of opponents.

While such perfect knowledge is never available, an understanding of odds, probabilities and basic game theory can go a long way toward telling

♦How likely it is that certain cards will appear or not appear in any given situation

♦How probable it is that certain opponents might hold certain powerful hands

♦How opponents are likely to act or react when examined through a Game Theory lens.

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This is not perfect knowledge. It is, however, very powerful poker decision support information.

Traditionally, pot or implied odds have been compared to a player’s odds of improving his hand to calculate expectation. In this book we introduce the concept of a player’s Total Odds of winning the pot. Total Odds includes not only the odds that his hand is or will improve to the best hand, but also the likelihood that the right move at the right time will cause his opponents to fold and give up the pot.

In any given poker situation, a player with a positive expectation may raise the action, and his opponent(s) will have only 2 choices:

1.Continue to play at a disadvantage and for higher stakes

2.Refuse the raise and forfeit the pot.

This book presents a practical way to combine the application of traditional poker odds and probabilities with basic game theory to give players at every level of skill and experience a crystal with prisms that will allow them to see the best and the worst of their possibilities, their opponents’ strengths and their own best courses of action.

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Introduction

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.

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Practical Poker Math

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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