The Mathematics of Poker by William Chen, Jerrod Ankenman

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