- Membership
- Publications
- Meetings
- Community
- Programs
- Students
- High School Teachers
- Faculty and Departments
- Underrepresented Groups
- MAA Awards
- MAA Grants

- News
- About MAA

Publisher:

Chapman & Hall/CRC

Publication Date:

2012

Number of Pages:

189

Format:

Paperback

Price:

49.95

ISBN:

9781439827680

Category:

Textbook

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by , on ]

Mark Bollman

02/26/2012

I like a book that is what it says it is, and *Introduction to Probability with Texas Hold’em Examples* is a fine example. The title says it all: this book treats the standard topics of elementary probability, all of them illustrated with examples drawn from Texas Hold’em poker. The mathematics is appropriately rigorous, complete with improper integrals, density functions, and limits everywhere that they should be — it is the laserlike focus of the examples and exercises that sets this book apart from other probability textbooks at this level.

One weakness of this choice is that some fundamental topics of probability — for example, permutations and independent events — aren’t as amenable to a Texas Hold’em approach. Nonetheless, the commitment to drawing examples from this mathematically rich game is impressive. When introducing Bayes’ Theorem, the classical example of medical testing is used, but this is an extremely rare exception. 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.

That said, this is not a book from which to learn Texas Hold’em, and the author makes that point clear in the first paragraph of the preface. While there’s a quick run-through of the rules in an appendix and an invaluable glossary of important terms in another, the intended reader of this book is someone already knowledgeable about the game and who is looking for insight into the mathematics behind it. At the same time, this is as good a resource as exists for a reader in the reverse situation: someone looking for or interested in a collection of applications of known mathematics to Texas Hold’em.

Mark Bollman (mbollman@albion.edu) is associate professor of mathematics at Albion College in Michigan. His mathematical interests include number theory, probability, and geometry. His claim to be the only Project NExT fellow (Forest dot, 2002) who has taught both English composition and organic chemistry to college students has not, to his knowledge, been successfully contradicted. If it ever is, he is sure that his experience teaching introductory geology will break the deadlock.

**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**

- Log in to post comments