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
