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1 results

  • Optimal Strategy for the Vardi Casino with Interest Payments

  • Part of
  • Ilie Grigorescu, Robert Chen, Larry Shepp
  • Journal:
    Journal of Applied Probability / Volume 44 / Issue 1 / March 2007
    Published online by Cambridge University Press:
    14 July 2016, pp. 199-211
    Print publication:
    March 2007
    • Article
      • You have access
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  • A gambler starts with fortune f < 1 and plays in a Vardi casino with infinitely many tables indexed by their odds, r ≥ 0. In addition, all tables return the same expected winnings per dollar, c < 0, and a discount factor is applied after each round. We determine the optimal probability of reaching fortune 1, as well as an optimal strategy that is different from bold play for fortunes larger than a critical value depending exclusively on c and 1 + a, the discount factor. The general result is computed explicitly for some relevant special cases. The question of whether bold play is an optimal strategy is discussed for various choices of the parameters.