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). See Professor Schoenberg discuss the book.
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.
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.
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