The Mathematics of Poker
Thirty years ago the bond and option markets were dominated by traders who had learned their craft by experience. By the mid-1990s the old school grizzled traders had been replaced by a new breed of quantitative analysts, applying mathematics to the "art" of trading and making of it a science. A similar phenomenon is happening in poker. The grizzled "road gamblers" are being replaced by a new generation of players who have challenged many of die assumptions that underlie traditional...
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Thirty years ago the bond and option markets were dominated by traders who had learned their craft by experience. By the mid-1990s the old school grizzled traders had been replaced by a new breed of quantitative analysts, applying mathematics to the "art" of trading and making of it a science. A similar phenomenon is happening in poker. The grizzled "road gamblers" are being replaced by a new generation of players who have challenged many of die 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. This book provides an introduction to quantitative techniques as applied to poker and to a branch of mathematics that is particularly applicable to poker, game theory, in a manner that makes seemingly difficult topics accessible to players without a strong mathematical background.
Acknowledgments viiForeword ixIntroduction 1BasicsDecisions Under Risk: Probability and Expectation 13Predicting the Future: Variance and Sample Outcomes 22Using All the Information: Estimating Parameters and Bayes' Theorem 32Exploitive PlayPlaying the Odds: Pot Odds and Implied Odds 47Scientific Tarot: Reading Hands and Strategies 59The Tells are in die Data: Topics in Online Poker 70Playing Accurately, Part I: Cards Exposed Situations 74Playing Accurately, Part II: Hand vs. Distribution 85Adaptive Play: Distribution vs. Distribution 94Optimal PlayFacing The Nemesis: Game Theory 101One Side of the Street: Half-Street Games 111Headsup With High Blinds: The Jam-or-Fold Game 123Poker Made Simple: The AKQGame 140You Don't Have To Guess: No-Limit Bet Sizing 148Player X Strikes Back: Full-Street Games 158Appendix to Chapter 15 The No-Limit AKQ Game 171Small Bets, Big Pots: No-Fold [0,1] Games 178Appendix to Chapter 16 Solving the Difference Equations 195Mixing in Bluffs: Finite Pot [0,1] Games 198Lessons and Values: The [0,1] Game Redux 216The Road to Poker: Static Multi-Street Games 234Drawing Out: Non-Static Multi-Street Games 249A Case Study: Using Game Theory 265RiskStaying in Action: Risk of Ruin 281Adding Uncertainty: Risk of Ruin with Uncertain Win Rates 295Growing Bankrolls: The Kelly Criterion and Rational Game Selection 304Poker Finance: Portfolio Theory and Backing Agreements 310Other TopicsDoubling Up: Tournaments, Part I 321Chips Aren't Cash: Tournaments, Part II 333Poker's Still Poker: Tournaments, Part III 347Three's a Crowd: Multiplayer Games 359Putting It All Together: Using Math to Improve Play 370Recommended Reading 376About the Authors 381About the Publisher 382
