Wanna Bet? On Gambling Strategies that May or May not Work in a Casino

Abstract

This article presents a mathematical analysis of a variety of strategies in the setting of casino gambling. The emphasis of this presentation is on the comparisons of mathematics versus common sense and mathematics versus experimentation. Specifically, we examine the difference between a “fair” game and an “almost fair” game in terms of the probability of achieving a predetermined goal. Next, a strategy based on bold play is presented, and the consequences in an “almost fair” game are discussed. The probabilities of achieving the predetermined goal are further explored under the conditions of independently changing each of the parameters to illustrate the differences between common sense and mathematical analysis. Finally, we discuss a case in which a mathematician devised a scheme to defeat a Japanese gambler who bet $200,000 a hand in Trump Plaza Hotel in Atlantic City, New Jersey, December 1989.

Key Words:

• Absorption probabilities
• Difference equations
• Dubins-Savage strategy
• Markov chain
• Transition probability matrix