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1 results

  • Favorable red and black on the integers with a minimum bet

  • Part of
  • Kevin Ruth
  • Journal:
    Journal of Applied Probability / Volume 36 / Issue 3 / September 1999
    Published online by Cambridge University Press:
    14 July 2016, pp. 837-851
    Print publication:
    September 1999

  • In a superfair red and black gambling house where the player must bet at least 2 units at each stage, a gambler wishes to maximize the probability of reaching a goal integer N before reaching zero. For win probability p > 1/2, when N is even, an optimal strategy is to bet 3 units when you have 3 units or N − 3 units and to bet 2 units otherwise. When N is odd, there are two strategies which are optimal depending on the value of the win probability p. When p is smaller than a certain value, p*, the above strategy is optimal, and when p is larger than this value, the timid strategy is optimal.