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140 pages

English

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Description

What makes Practical Poker Math so useful is how it relates poker odds and strategy to game theory. Using an original concept called Total Odds, the guide presents a complete work-up for both Texas Hold 'Em and the high and low hands of Omaha. The principles are accessible to any poker player at any level and the calculations are colour-coded for ease of use.

Sujets

Póquer

Poker

Informations

Publié par	Ecw Press
Date de parution	15 décembre 2010
Nombre de lectures	16
EAN13	9781554903269
Langue	English
Poids de l'ouvrage	2 Mo

Informations légales : prix de location à la page 0,0574€. Cette information est donnée uniquement à titre indicatif conformément à la législation en vigueur.

Extrait

Practical Poker Math
By Pat Dittmar
Copyright Martin M. Dittmar, 2008
Published by ECW Press
2120 Queen Street East, Suite 200
Toronto, Ontario, Canada M 4 E 1E 2
416.694.3348 / info@ecwpress.com
All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form by any process - electronic, mechanical, photocopying, recording, or otherwise - without the prior written permission of the copyright owner and ECW Press.
BICYCLE , BEE and all related brand elements and designs are registered trademarks of the United States Playing Card Company, used here with permission.
LIBRARY AND ARCHIVES CANADA CATALOGUING IN PUBLICATION
Dittmar, Pat
Practical poker math / Pat Dittmar.
ISBN 978-1-55490-326-9 Also issued as: 978-1-55022-833-5 (PBK)
1. Poker. 2. Game theory. I. Title.
GV1251.D48 2008 795.41201 51 C2008-900792- 1
Cover Design: Tania Craan
Cover image: BICYCLE , BEE
Text Design: Peggy Payne
Typesetting: Gail Nina
Thanks to some Friends for their labors and for what they have taught me
Constantin Dinca Learned Mathematician and Programming Wizard
Peggy Payne For Bringing Order to the Chaos
Alice Jue Lady of Art, Letters and Vodka Martinis
Bernadette Castello For Everything
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.
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.
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.
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.
1. Introduction to Game Theory in Poker
Game Theory - A Historical Perspective
Some believe that the study of Game Theory began with the works of Daniel Bernoulli. A mathematician born in 1700, Bernoulli is probably best known for his work with the properties and relationships of pressure, density, velocity and fluid flow. Known as Bernoulli s Principle, this work forms the basis of jet engine production and operation today. Pressured by his father to enter the world of commerce, he is also credited with introducing the concepts of expected utility and diminishing returns. This work in particular can be of use when pricing bets or bluffs in no-limit poker.
Others believe the first real mathematical tool to become available to game theorists was Bayes Theorem, published posthumously in England in the 18th century. Thomas Bayes was born in 1702 and was an ordained minister. His work involved using probabilities as a basis for logical inference. (The author has developed and used artificially intelligent systems based on Bayes Theorem to trade derivatives in today s financial markets.)
Yet still others believe that the study of Game Theory began with the publication of Antoine Augustin Cournot s The Recherches in the early 1800s. The work dealt with the optimization of output as a best dynamic response.
mile Borel was probably the first to formally define important concepts in the use of strategy in games. Born in 1871 in Saint-Affrique, France, he demonstrated an early penchant for mathematics. In 1909 the Sorbonne created a special chair of Theory of Functions which Borel held through 1940. During the years 1921-27 he published several papers on Game Theory and several papers on poker. Important to poker players are his discussions on the concepts of imperfect information, mixed strategies and credibility.
In 1944 Princeton University Press published Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern. While not the first work to define certain concepts of strategy in games, it is widely recognized as one that has fostered Game Theory as we know it today.
Also important to poker players is the work of Julia Bowman Robinson. Born in 1919, she discovered her passion for mathematics after a bout with scarlet fever and was the first woman admitted to the Academy of Sciences. For poker players her most important work was An Iterative Method of Solving a Game .
Credited by many as being a primary shepherd of modern Game Theory is John Forbes Nash, Jr. Diagnosed as a paranoid schizophrenic, Nash was long troubled by delusions. This condition, now in remission, became the subject of a popular film. His work earned him 1/3 of the 1994 Nobel Prize in Economic Sciences. Born in the Appalachian town of Bluefield, West Virginia in 1928, Nash became well known for a 28-page work he did at age 21 which defined his Nash Equilibrium concerning strategic behavior in non-cooperative games. Poker players are most drawn to the story that while he was in a bar near Princeton and being goaded into approaching an attractive blond-haired lady, he suddenly shouted and then ran off to complete his work on The Mathematics of Competition which is one basis of Game Theory today.
Game Theory and Poker
More than the study and application of a set of principles, Game Theory in poker is primarily about two goals:
1. The study and understanding of the opposition
2. The development of an efficient strategy to dominate the competition.
To be of maximum value, this study and understanding must be translated into effective action, and these actions must be the antithesis of everything a poker opponent thinks or does.
The difference between an antithesis and a correct response defines the utility of Game Theory in poker. An opponent makes an obvious bluff. You are certain that your hand will not even beat the bluff. A correct response in poker is to fold your hand when you know you are beat. The antithesis is to raise or re-raise and make your opponent fold his.
This is an example of