Introduction to Probability with Texas Hold’em Examples

Introduction to Probability with Texas Hold'em Examples illustrates both standard and advanced probability topics using the popular poker game of Texas Hold'em, rather than the typical balls in urns. The author uses students' natural interest in poker to teach important concepts in probability. This classroom-tested book covers the main subjects of a standard undergraduate probability course, including basic probability rules, standard models for describing collections of data, and the laws of large numbers. It also discusses several more advanced topics, such as the ballot theorem, the arcsine law, and random walks, as well as some specialized poker issues, such as the quantification of luck and skill in Texas Hold'em. Homework problems are provided at the end of each chapter. The author includes examples of actual hands of Texas Hold'em from the World Series of Poker and other major tournaments and televised games. He also explains how to use R to simulate Texas Hold'em tournaments for student projects. R functions for running the tournaments are freely available from CRAN (in a package called holdem).

Table of Contents:
Probability Basics Meaning of Probability Basic Terminology Axioms of Probability Venn Diagrams General Addition Rule Counting Problems Sample Spaces with Equally Probable Events Multiplicative Counting Rule Permutations Combinations Conditional Probability and Independence Conditional Probability Independence Multiplication Rules Bayes’ Rule and Structured Hand Analysis Expected Value and Variance Cumulative Distribution Function and Probability Mass Function Expected Value Pot Odds Luck and Skill in Texas Hold’em Variance and Standard Deviation Markov and Chebyshev Inequalities Moment Generating Functions Discrete Random Variables Bernoulli Random Variables Binomial Random Variables Geometric Random Variables Negative Binomial Random Variables Poisson Random Variables Continuous Random Variables Probability Density Functions Expected Value, Variance, and Standard Deviation Uniform Random Variables Exponential Random Variables Normal Random Variables Pareto Random Variables Continuous Prior and Posterior Distributions Collections of Random Variables Expected Value and Variance of Sums of Random Variables Conditional Expectation Laws of Large Numbers and the Fundamental Theorem of Poker Central Limit Theorem Confidence Intervals for the Sample Mean Random Walks Simulation and Approximation Using Computers Appendix A: Abbreviated Rules of Texas Hold’em Appendix B: Glossary of Poker Terms Appendix C: Solutions to Selected Odd-Numbered Exercises References and Suggested Reading Index Exercises appear at the end of each chapter.

About the Author :
Frederic Paik Schoenberg is a professor and graduate vice-chair of statistics at UCLA. He is also co-editor of the Journal of Environmental Statistics. He earned a Ph.D. in statistics from UC Berkeley. His research interests include point processes, image analysis, time series, and applications in seismology and fire ecology.

Review :
"… quite entertaining and fun to read. … I had a very good time reading this book … as a teacher this is definitely a book I would recommend as a pleasant introduction to the world of probability theory." —Julien Sohier, CHANCE, June 2013 "The students will need to understand and have some familiarity with the rules and play of Texas Hold’em. Subject to that, this provides a refreshing new introduction to the subject matter. It is certainly worth considering for your next year’s intake of students." —David J. Hand, International Statistical Review (2013), 81, 2 "Recent trends in probability and statistics reference works and textbooks include placing a greater emphasis on authentic problems and data. To this end, Schoenberg (UCLA) avoids the traditional "balls in an urn" approach to probability, and interestingly ties basic probability theory to Texas holdem poker. The content is challenging but thorough, and the reader needs to think through the poker realities as well as the related probability theory. Introductory chapters stress basic principles of counting, permutations, combinations, and conditional probabilities, but inevitably tie back to Texas hold’em hands. Many of the examples are based on actual tournament results, making the resulting discussions even more authentic. Given the discrete nature of poker hands, it was interesting to see the author tackle continuous data by investigating wait times between eliminations, again maintaining the Texas hold’em theme. More advanced topics show bluffing tied to the Poisson distribution and late player arrival to exponential random variables. Ultimately, the book provides heavily theoretic coverage and calculus-based support of various distributions, but the link to poker is never abandoned. Includes a helpful glossary of Texas hold’em terminology. Summing Up: Recommended. Upper-division undergraduates, faculty, and informed general readers." — CHOICE Magazine JUNE 2012 "it is the laserlike focus of the examples and exercises that sets this book apart from other probability textbooks at this level. … The book is incredibly well-researched — examples are drawn from actual televised poker games, and many explorations of the probabilities in play in a given game situation conclude with a sentence about what really happened, which is a nice touch." —Mark Bollman, MAA Reviews, February 2012