Risk of Ruin (ROR) Analysis in Casino Games Using Poisson Distribution

Lancelot Julsen Josua; Meivin Mulyo Prawiro; Jumadil Saputra; Siti Hadiaty Yuningsih

doi:10.47194/orics.v5i2.312

Authors

Lancelot Julsen Josua
lancelot20001@mail.unpad.ac.id
Universitas Padjadjaran, Jatinangor, Indonesia
Meivin Mulyo Prawiro Universitas Padjadjaran, Jatinangor, Indonesia
Jumadil Saputra Faculty of Business, Economics and Social Development, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia
Siti Hadiaty Yuningsih Department of Mathematics, Faculty of Mathematics and Natural Sciences, National University of the Republic of Indonesia, Bandung, Indonesia

Keywords:

Risk of Ruin (ROR), house advantage, poisson distribution, binomial random walk.

Abstract

Gambling in casino games is an uncertain business because it creates two possibilities between the hope of winning or the risk of losing. The risks faced by casinos are usually analyzed using the Risk of Ruin (ROR). The main focus of this study is to apply the mathematical model of ROR using the Poisson distribution to model random events in gambling by considering the house advantage (a) and the law of large numbers. This study discusses the relationship between variables, such as maximum bet limits and cash flows and examines how these factors affect the risk of casino bankruptcy. In its business characteristics, casinos operate as gambling business entities and utilize the house advantage to achieve their financial benefits. House advantage indicates the profitability of the casino. However, the uncertainty of this gambling can pose a risk of bankruptcy for them. In this study, the house advantage is included in our model for several popular casino games. In addition, a set of full-range scales is defined to facilitate effective assessment of the level of risk faced by the casino, considering its regulatory context. This study also uses the binomial random walk model to describe the race between the casino and the gambler, where each step has two possible outcomes, namely winning or losing. The results of this study are expected to provide insight into the risk in calculating risk in optimizing betting decisions and reducing the risk of bankruptcy.

References

Cai, X. (2022). The House Edge and the Basic Strategy of Blackjack. In SHS Web of Conferences (Vol. 148, p. 03038). EDP Sciences.

Coolidge, J. L. (1909). The gambler's ruin. The Annals of Mathematics, 10(4), 181-192.

Dickson, D. C. (2016). Insurance risk and ruin. Cambridge University Press.

Kaufman, P. J. (1995). Smarter trading (Vol. 22). New York: McGraw-Hill.

Newall, P. W., Walasek, L., & Ludvig, E. A. (2022). Risk communication improvements for gambling: House-edge information and volatility statements. Psychology of Addictive Behaviors, 36(4), 358.

Siu, K. M., Chan, K. H., & Im, S. K. (2023). A Study of Assessment of Casinos’ Risk of Ruin in Casino Games with Poisson Distribution. Mathematics, 11(7), 1736.

Vince, R. (1991). Portfolio management formulas: mathematical trading methods for the futures, options, and stock markets (Vol. 1). John Wiley & Sons.