Intermediate Poker Mathematics

Mark Bollman is a Professor of Mathematics and chair of the Department of Mathematics & Computer Science at Albion College in Albion, Michigan, and has taught 120 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, Mathematics of The Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette, and Basic Gambling Mathematics by CRC Press.

1. Counting The Cards. 1.1. Poker Hands. 1.2. Elementary Probability Through Texas Hold’Em. 1.3. Combinatorics. 1.4. Counting 5-Card Hands. 1.5. Lowball Hands. 1.6. Wild Cards. 1.7. Random Variables. 1.8. Betting. 1.9. Exercises. 2. Stud Poker. 2.1. 5-Card Stud. 2.2. 7-Card Stud. 2.3. Razz. 2.4. Exercises. 3. Draw Poker. 3.1. Introduction. 3.2. Gameplay Considerations. 3.3. Lowball Draw Games. 3.4. Italian Poker. 3.5. Draw Poker at Home. 3.6. Poker Dice. 3.7. Exercises. 4. Texas Hold’Em and Its Variants. 4.1. Basic Gameplay. 4.2. Different Decks. 4.3. Omaha. 4.4. Pineapple Poker. 4.5. Prop Bets. 4.6. Exercises. 5. Advanced Card Counting. 5.1. Why Five?. 5.2. Hand Rankings Revisited. 5.3. Extra Possibilities. 5.4. Historical Games. 5.5. Alternate Decks. 5.6. Deck Composition More Generally. 5.7. Exercises. 6. Beyond Hold’Em. 6.1. Lowball Games. 6.2. Division Games. 6.3. Stud Games. 6.4. Exercises. 7. Poker-Based Carnival Games. 7.1. Hold’Em Derivatives. 7.2. Stud Poker Variations. 7.3. Division Carnival Games. 7.4. Three Card Poker. 7.5. Four Card Poker. 7.6. California Games. 7.7. Exercises. 8. Video Poker. 8.1. Basic Gameplay. 8.2. Variations. 8.3. Optimal Strategy. 8.4. Additional Game Options. 8.5. Exercises. A. Elementary Probability Formulas.