Stopping Strategies and Gambler's Ruin
Department or Administrative Unit
In this paper we show how to answer the first questions (probabilities of success and ruin) using recurrence relations. Then we introduce the language and methods of random variables, showing how these probabilities can be used to solve the duration question. A key will be two identities due to Wald, for which we give elementary proofs at the end of the paper.
Harper, J. D., & Ross, K. A. (2005). Stopping Strategies and Gambler’s Ruin. Mathematics Magazine, 78(4), 255–268. https://doi.org/10.1080/0025570x.2005.11953340