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Demystifying the Two-Armed Futurity Bandit’s Unfairness and Apparent Fairness

Author

Listed:
  • Huaijin Liang

    (Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, China
    These authors contributed equally to this work.)

  • Jin Ma

    (School of Mathematics, Shandong University, Jinan 250100, China
    These authors contributed equally to this work.)

  • Wei Wang

    (School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250014, China
    These authors contributed equally to this work.)

  • Xiaodong Yan

    (Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, China
    These authors contributed equally to this work.)

Abstract

While a gambler may occasionally win, continuous gambling inevitably results in a net loss to the casino. This study experimentally demonstrates the profitability of a particularly deceptive casino game: a two-armed antique Mills Futurity slot machine. The main findings clearly show that both non-random and random two-arm strategies, predetermined by the player and repeated without interruption, are always profitable for the casino, despite two coins being refunded for every two consecutive losses by the gambler. We theoretically explore the cyclical nature of slot machine strategies and speculate on the impact of the frequency of switching strategies on casino returns. Our results not only assist casino owners in developing and improving casino designs, but also guide gamblers to participate more cautiously in gambling.

Suggested Citation

  • Huaijin Liang & Jin Ma & Wei Wang & Xiaodong Yan, 2024. "Demystifying the Two-Armed Futurity Bandit’s Unfairness and Apparent Fairness," Mathematics, MDPI, vol. 12(11), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1713-:d:1405881
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    References listed on IDEAS

    as
    1. Samantha J. Hollingshead & Christopher G. Davis & Michael J. A. Wohl, 2023. "The customer-brand relationship in the gambling industry: positive play predicts attitudinal and behavioral loyalty," International Gambling Studies, Taylor & Francis Journals, vol. 23(1), pages 118-138, January.
    2. Chen, Zengjing & Epstein, Larry G., 2022. "A central limit theorem for sets of probability measures," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 424-451.
    Full references (including those not matched with items on IDEAS)

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