Basic Gambling Mathematics

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.

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.