Basic Gambling Mathematics

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.