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2 results

  • Chapter 4 - Probability and the Casino

  • Jared Poley, Georgia State University
  • Book:
    Luck, Leisure, and the Casino in Nineteenth-Century Europe
    Published online:
    24 August 2023
    Print publication:
    07 September 2023, pp 89-110

  • Summary

    The Blanc casinos were marketed through the cultivation of an impression of honesty and mechanical universality. The study of probability, which arose historically in relationship to the calculation of gambling odds, provided a way to measure the honesty of a casino. Probability, as it was expressed in the context of nineteenth-century resort casinos, was the object of renewed interest among professional mathematicians and amateurs seeking to understand the logic of the games they played. There are three avenues through which this amplified interest in probability was expressed in the nineteenth century: the analysis of “runs” (a long sequence of identical results), the systems that gamblers developed for beating the odds, and the casino as an experimental space for mathematicians in the nineteenth century. Together, these developments suggest that the nineteenth-century casino provided a novel opportunity for inquiry into areas such as the nature of time, the limits of causation, and the science of probability.

  • An optimal betting strategy for repeated games

  • Gary Gottlieb
  • Journal:
    Journal of Applied Probability / Volume 22 / Issue 4 / December 1985
    Published online by Cambridge University Press:
    14 July 2016, pp. 787-795
    Print publication:
    December 1985

  • We consider the problem of finding a betting strategy for an infinite sequence of wagers where the optimality criterion is the minimization of the expected exit time of wealth from an interval. We add the side constraint that the right boundary is hit first with at least some specified probability. The optimal strategy is derived for a diffusion approximation.