Mathematics of The Big Four Casino Table Games

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 Basic Gambling Mathematics: The Numbers behind The Neon, Mathematics of Keno and Lotteries, and Mathematics of Casino Carnival Games.

"It it is a handbook on different variants of the casino and electronic games, with locations of casino where a particular version is played. All topics are explained in detailed numerical calculations of probabilities and expectations, presented in tables of results, illustrations, and exercises.The gambling in casino and online is estimated at about $100 billion per year industry, and the book studies it from the mathematics and theory of probability points of view. Casino managers can use it to a deeper insight into the games, players can get a better understanding of their favorite games to help them to develop their own strategies, and instructors and students can see it as a valuable manual on gambling mathematics."- Technometrics"This is an extremely well-organized book. It is logically structured, with information that is easy to find.I think there is [a real need for this book]. These are four very important games that make (and can cost) casinos a lot of money, and they need to be better understood.There are three major markets for this book: academics, casino managers, and casino players, with a smaller fourth market of game inventors. Academics can use it in courses dealing with casino management (see below). Casino managers will use it to better ground their understanding of the games. I think that Bollman’s generous inclusion of historical promotions—some of which lasted only briefly—will be extremely helpful to managers. Casual casino players will like it because it will give them insight into their favourite games, and advantage players will read it to assist with their own strategy and analysis."– David G. Schwartz, University of Nevada, Las Vegas"After a brief introduction to elementary probability, this book explores many more variations on the “big four” than I could have imagined to exist, plus numerous side bets. Examples and exercises abound throughout."– Mathematics Magazine, MAA

• 1. Essential Probability. 1.1. Elementary Ideas. 1.2. Addition and Multiplication Rules. 1.3. Combinatorics. 1.4. Random Variables and Expected Value. 2. Roulette 2.1 Roulette Basics. 2.2. History of Roulette. 2.3. New Wheels. 2.4. Electronic Roulette Games. 2.5. Roulette with Cards. 2.6. Side Bets. 2.7. Roulette Betting Systems. 2.8. Exercises. 3. Craps. 3.1. Craps Basics. 3.2. Hazard. 3.3. Street Craps. 3.4. Crooked Dice. 3.5. Controlled Shooting. 3.6. Variations. 3.7. Card Craps. 3.8. Side Bets. 3.9. Exercises. 4. Baccarat. 4.1. Baccarat Basics. 4.2. Card Counting in Baccarat. 4.3. Variations. 4.4. Side Bets. 4.5. Exercises. 5. Blackjack. 5.1. Blackjack Basics. 5.2. Basic Strategy. 5.3. Card Counting. 5.4. Variations. 5.5. California Games. 5.6. Side Bets. 5.7. Exercises. Answers to Selected Exercises. References.