GAMBLING THEORY AND STOCHASTIC CONTROL.

Abstract

Reference is made to the discrete-time gambling theory of L. E. Dubins and L. J. Savage which treats many colorful examples such as red-and-black and roulette. These examples can often be reformulated in continuous-time as diffusion control problems. The question of how the gambler can play to minimize the expected time to reach the goal is considered. The discussion covers: discrete-time goal problems; continuous-time goal problems; discrete-time red-and-black; red-and-black with a house limit; casinos; and minimizing the expected time to the goal.