2nd Edition

Basic Gambling Mathematics The Numbers Behind the Neon, Second Edition

By Mark Bollman Copyright 2024
    322 Pages 38 B/W Illustrations
    by A K Peters/CRC Press

    322 Pages 38 B/W Illustrations
    by A K Peters/CRC Press

    322 Pages 38 B/W Illustrations
    by A K Peters/CRC Press

    Basic Gambling Mathematics: The Numbers Behind the Neon, Second Edition explains the mathematics involved in analyzing games of chance, including casino games, horse racing and other sports, and lotteries. The book helps readers understand the mathematical reasons why some gambling games are better for the player than others. It is also suitable as a textbook for an introductory course on probability.

    Along with discussing the mathematics of well-known casino games, the author examines game variations that have been proposed or used in actual casinos. Numerous examples illustrate the mathematical ideas in a range of casino games while end-of-chapter exercises go beyond routine calculations to give readers hands-on experience with casino-related computations.

    New to the Second Edition

    • Thorough revision of content throughout, including new sections on the birthday problem (for informal gamblers) and the Monty Hall problem, as well as an abundance of fresh material on sports gambling
    • Brand new exercises and problems
    • A more accessible level of mathematical complexity, to appeal to a wider audience.

    1. Fundamental Ideas. 1.1. Historical Background. 1.2. Mathematical Background. 1.3. Definitions. 1.4. Axioms of Probability. 1.5. Elementary Counting Arguments. 1.6. Exercises. 2. Combinatorics and Probability. 2.1. Advanced Counting Arguments. 2.2. Odds. 2.3. Addition Rules. 2.4. Multiplication Rules and Conditional Probability. 2.5. Exercises. 3. Probability Distributions and Expectation. 3.1. Random Variables. 3.2. Expected Value and House Advantage. 3.3. Binomial Distribution. 3.4. Exercises. 4. Modified Casino Games. 4.1. Wheel Games. 4.2. Dice Games. 4.3. Card Games. 4.4. Casino Promotions. 4.5. Exercises. 5. Blackjack: The Mathematical Exception. 5.1. Rules of Blackjack. 5.2. Mathematics of Blackjack. 5.3. Basic Strategy. 5.4. Introduction to Card Counting. 5.5. Additional Topics in Card Counting. 5.6. Exercises. 6. Betting Strategies: Why They Don’t Work. 6.1. Roulette Strategies. 6.2. Craps Strategies. 6.3. Slot Machine Strategies. 6.4. And One That Does: Lottery Strategies. 6.5. How To Double Your Money. 6.6. Exercises. Appendix A: House Advantages. Answers to Selected Exercises.


    Mark Bollman is Professor of Mathematics and chair of the Department of Mathematics & Computer Science at Albion College in Albion, Michigan, and has taught 116 different courses in his career. Among these courses is "Mathematics of the Gaming Industry," where mathematics majors carefully study the math behind games of chance and travel to Las Vegas, Nevada, in order to compare theory and practice. He has also taken those ideas into Albion's Honors Program in "Great Issues in Humanities: Perspectives on Gambling," which considers gambling from literary, philosophical, and historical points of view as well as mathematically. Mark has also authored Mathematics of Keno and Lotteries, Mathematics of Casino Carnival Games, and Mathematics of The Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.

    Praise for the First Edition

    "This book successfully transforms an already fun topic into an even more enjoyable read."
    —Mathematical Reviews, MAA

    "This is a fantastic guide to gambling math, both for the beginner and the experienced gambler (or mathematician). As Bollman’s math proves, there’s rarely a sure bet, but Basic Gambling Mathematics comes pretty close."
    —David G. Schwartz, University of Nevada, Las Vegas, USA

    "Basic Gambling Mathematics: The Numbers Behind the Neon is a must-have book for anyone interested in gambling mathematics. It not only covers all of the most popular casino games (blackjack, craps, roulette, keno), but is also a treasure trove of fascinating variants and novel games from casinos all over the world."
    —Mike Ferrara, University of Colorado Denver, USA