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John Quigley
Matthew Revie


This paper presents an investigation into the properties of a stochastic process whereby the value of a fund grows arithmetically and decays geometrically over discrete time periods. While this general structure is applicable to many situations, it is particularly prevalent in many casino games. This investigation was motivated by a request for support by a casino operator.  Statistical models were developed to identify optimal decisions relating to the casino game concerning setting the initial jackpot, the probability of winning each prize, and the size of the prizes. It is demonstrated that all moments of the process converge asymptotically and the limiting distribution is not Normal.  Closed form expressions are provided for the first moment as well as investigate the quality of approximating the distribution with an Edgeworth Expansion. The case that motivated this initial investigation is presented and discussed.

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