# 12. Games of Chance

#### Summary

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.

#### Related Topics

• 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.

#### Quotes

• 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