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1 results

  • Two-person red-and-black stochastic games

  • Part of
  • Piercesare Secchi
  • Journal:
    Journal of Applied Probability / Volume 34 / Issue 1 / March 1997
    Published online by Cambridge University Press:
    14 July 2016, pp. 107-126
    Print publication:
    March 1997

  • We define a leavable stochastic game which is a possible two-person generalization of the classical red-and-black gambling problem. We show that there are three basic possibilities for a two-person red-and-black game which, by analogy with gambling theory, we call the subfair, the fair and the superfair cases. A suitable generalization of what in gambling theory is called bold play is proved to be a uniformly ε-optimal stationary strategy for player I in the fair and the subfair cases whereas a generalization of timid play is shown to be ε-optimal for player I in the superfair possibility.