The Mathematics of Poker

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In the late 1970s and early 1980s, the bond an option markets were dominated by traders who had learned their craft by experience. They believed that there experience and intuition for trading were a renewable edge; this is, that they could make money just as they always had by continuing to trade as they always had. By the mid-1990s, a revolution in trading had occurred; the old school grizzled traders had been replaced by a new breed of quantitative analysts, applying mathematics to the "art" of trading and making of it a science.

Similarly in poker, for decades, the highest level of pokers have been dominated by players who have learned the game by playing it, "road gamblers" who have cultivated intuition for the game and are adept at reading other players' hands from betting patterns and physical tells.

Over the last five to ten years, a whole new breed has risen to prominence within the poker community. Applying the tools of computer science and mathematics to poker and sharing the information across the Internet, these players have challenged many of the assumptions that underlie traditional approaches to the game. One of the most important features of this new approach is a reliance on quantitative analysis and the application of mathematics to the game.

The intent of this book is to provide an introduction to quantitative techniques as applied to poker and to a branch of mathematics that is particularly applicable to poker, game theory. There are mathematical techniques that can be applied for poker that are difficult and complex. But most of the mathematics of poker is really not terribly difficult, and the authors have sought to make seemingly difficult topics accessible to players without a very strong mathematical background.

Product Details

ISBN-13: 9781886070257

Media Type: Paperback

Publisher: ConJelCo - LLC

Publication Date: 11-30-2006

Pages: 382

Product Dimensions: 6.10(w) x 9.10(h) x 0.90(d)

About the Author

Bill Chen was born in Williamsburg, Virginia in 1970 and grew up in Alabama. He received a PhD in Mathematics from the University of California at Berkeley in 1999. He started thinking about poker while a grad student when he augmented his National Science Foundation grant with poker winnings from local clubs. Bill represented PokerStars from 2002 to 2011 and has participated in High Stakes Poker and Poker After Dark. Bill currently lives near Philadelphia. Bill won two World Series of Poker bracelets in 2006. Jerrod Ankenman grew up in Orange County, California. He received a BS in Business Management from Pepperdine in 2004 and an MS in Applied Mathematics from Columbia in 2010. Jerrod picked up poker as a hobby from reading rec.gambling.poker, and as a career from collaborating on poker with Bill (and others). Jerrod won a World Series of Poker bracelet in 2009.

Table of Contents

Table of Contents


Acknowledgments vii
Foreword ix
Introduction 1
Basics
Decisions Under Risk: Probability and Expectation 13
Predicting the Future: Variance and Sample Outcomes 22
Using All the Information: Estimating Parameters and Bayes' Theorem 32
Exploitive Play
Playing the Odds: Pot Odds and Implied Odds 47
Scientific Tarot: Reading Hands and Strategies 59
The Tells are in die Data: Topics in Online Poker 70
Playing Accurately, Part I: Cards Exposed Situations 74
Playing Accurately, Part II: Hand vs. Distribution 85
Adaptive Play: Distribution vs. Distribution 94
Optimal Play
Facing The Nemesis: Game Theory 101
One Side of the Street: Half-Street Games 111
Headsup With High Blinds: The Jam-or-Fold Game 123
Poker Made Simple: The AKQGame 140
You Don't Have To Guess: No-Limit Bet Sizing 148
Player X Strikes Back: Full-Street Games 158
Appendix to Chapter 15 The No-Limit AKQ Game 171
Small Bets, Big Pots: No-Fold [0,1] Games 178
Appendix to Chapter 16 Solving the Difference Equations 195
Mixing in Bluffs: Finite Pot [0,1] Games 198
Lessons and Values: The [0,1] Game Redux 216
The Road to Poker: Static Multi-Street Games 234
Drawing Out: Non-Static Multi-Street Games 249
A Case Study: Using Game Theory 265
Risk
Staying in Action: Risk of Ruin 281
Adding Uncertainty: Risk of Ruin with Uncertain Win Rates 295
Growing Bankrolls: The Kelly Criterion and Rational Game Selection 304
Poker Finance: Portfolio Theory and Backing Agreements 310
Other Topics
Doubling Up: Tournaments, Part I 321
Chips Aren't Cash: Tournaments, Part II 333
Poker's Still Poker: Tournaments, Part III 347
Three's a Crowd: Multiplayer Games 359
Putting It All Together: Using Math to Improve Play 370
Recommended Reading 376
About the Authors 381
About the Publisher 382

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