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A Study of Assessment of Casinos’ Risk of Ruin in Casino Games with Poisson Distribution

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  • Ka-Meng Siu

    (Faculty of Applied Sciences, Macao Polytechnic University, Macau, China)

  • Ka-Hou Chan

    (Faculty of Applied Sciences, Macao Polytechnic University, Macau, China)

  • Sio-Kei Im

    (Macao Polytechnic University, Macau, China)

Abstract

Gambling, as an uncertain business involving risks confronting casinos, is commonly analysed using the risk of ruin (ROR) formula. However, due to its brevity, the ROR does not provide any implication of nuances in terms of the distribution of wins/losses, thus causing the potential failure of unravelling exceptional and extreme cases. This paper discusses the mathematical model of ROR using Poisson distribution theory with the consideration of house advantage ( a ) and the law of large numbers in order to compensate for the insufficiency mentioned above. In this discussion, we explore the relationship between cash flow and max bet limits in the model and examine how these factors interact in influencing the risk of casino bankruptcy. In their business nature, casinos operate gambling businesses and capitalize on the house advantage favouring them. The house advantage of the games signifies casinos’ profitability, and in addition, the uncertainty inevitably poses a certain risk of bankruptcy to them even though the house advantage favours them. In this paper, the house advantage is incorporated into our model for a few popular casino games. Furthermore, a set of full-range scales is defined to facilitate effective judgment on the levels of risk confronted by casinos in certain settings. Some wagers of popular casino games are also exemplified with our proposed model.

Suggested Citation

  • Ka-Meng Siu & Ka-Hou Chan & Sio-Kei Im, 2023. "A Study of Assessment of Casinos’ Risk of Ruin in Casino Games with Poisson Distribution," Mathematics, MDPI, vol. 11(7), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1736-:d:1116351
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    References listed on IDEAS

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    1. Corina Constantinescu & Suhang Dai & Weihong Ni & Zbigniew Palmowski, 2016. "Ruin Probabilities with Dependence on the Number of Claims within a Fixed Time Window," Risks, MDPI, vol. 4(2), pages 1-23, June.
    2. Li, Bo & Ni, Weihong & Constantinescu, Corina, 2015. "Risk models with premiums adjusted to claims number," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 94-102.
    3. Wagner, Christian, 2002. "Time in the red in a two state Markov model," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 365-372, December.
    4. Willmot, Gordon E., 1994. "Refinements and distributional generalizations of Lundberg's inequality," Insurance: Mathematics and Economics, Elsevier, vol. 15(1), pages 49-63, October.
    5. Richard Woolley & Charles Livingstone & Kevin Harrigan & Angela Rintoul, 2013. "House edge: hold percentage and the cost of EGM gambling," International Gambling Studies, Taylor & Francis Journals, vol. 13(3), pages 388-402, December.
    6. Thorin, Olof, 1974. "Some Comments on the Sparre Andersen Model in the Risk Theory," ASTIN Bulletin, Cambridge University Press, vol. 8(1), pages 104-125, September.
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