Games of chance hold an honored place in probability theory, because of their conceptual clarity and because of their fundamental influence on the early development of the subject. In this chapter, we explore some of the most common and basic games of chance. Roulette, craps, and Keno are casino games. The Monty Hall problem is based on a TV game show, and has become famous because of the controversy that it generated. Lotteries are now basic ways that governments and other institutions raise money. In the last four sections on the game of red and black, we study various types of gambling strategies, a study which leads to some deep and fascinating mathematics.

- Introduction
- Poker
- Simple Dice Games
- Craps
- Roulette
- The Monty Hall Problem
- Lotteries
- Red and Black
- Timid Play
- Bold Play
- Optimal Strategies

- Poker Experiment
- Poker Dice Experiment
- Chuck-a-Luck Experiment
- Craps Experiment
- Roulette Experiment
- Monty Hall Game
- Monty Hall Experiment
- Red and Black Game
- Red and Black Experiment

- Introduction
- Poker
- Simple Dice Games
- Craps
- Roulette
- The Monty Hall Problem
- Lotteries
- Red and Black
- Timid Play
- Bold Play
- Optimal Strategies
- Answers to Selected Exercises

- For several of the models in this chapter, the gambler either wins or loses, independently from game to game, and with the same probability. Such random processes are studied in detail in the chapter on Bernoulli Trials.
- Many of the games we have studied in this chapter can be viewed, in statistical terms, as sampling from a finite population. The chapter Finite Sampling Models has a thorough discussion of such sampling models.
- One of the simplest strategies for varying bets is studied in the discussion of the Petersburg Problem.

- Gambler's Anonymous is a support group for compulsive gamblers.
- The Mathematics of Games and Gambling by Edward Packel is a good introduction to the mathematics of various games of chance.
- The Theory of Gambling and Statistical Logic, by Richard Epstein is more advanced analysis of a variety of games of chance.
- Games, Gods, and Gambling by Florence David is an excellent history of the interplay between probability and gambling.
- The Gambler, by Fyodor Dostoyevsky is a classic fictional study of a compulsive gambler
- Cardano, the Gambling Scholar by Oystein Ore is an fascinating biography of the colorful Cardano.
- Inequalities for Stochasitc Processes (How to Gamble if You Must) by Lester Dubbins and Leonard Savage is a classic work on gambling strategies and the the game of red and black in particular.

Is this a game of chance?

...Not the way I play it, no.

--Response from WC Fields to a question from one of his many victims.The easier a game is to understand the greater the house advantage

--The Wizard of Odds