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Long bet will lose: demystifying seemingly fair gambling via two-armed Futurity bandit

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  • Zengjing Chen
  • Huaijin Liang
  • Wei Wang
  • Xiaodong Yan

Abstract

No matter how much some gamblers occasionally win, as long as they continue to gamble, sooner or later they will lose more to the casino, which is the so-called long bet will lose. Our results demonstrate the counter-intuitive phenomenon, that gamblers involved in long bets will lose but casinos always advertise their unprofitable circumstances. Here we expose the law of inevitability behind long bet will loss by theoretically and experimentally demystifying the profitable mystery behind casinos under two-armed antique Mills Futurity slot machine. The main results straightforwardly elucidate that all casino projects are seemingly a fair gamble but essentially unfair, i.e., the casino's win rate is greater than 50%. We anticipate our assay to be a starting point for studying the fairness of more sophisticated multi-armed Futurity bandits based on the mathematical tool. In application, a fairness study of the Futurity bandits not only exposes the fraud of casinos for gamblers but also discloses discount marketing, bundled sales, or other induced consumption tactics.

Suggested Citation

  • Zengjing Chen & Huaijin Liang & Wei Wang & Xiaodong Yan, 2022. "Long bet will lose: demystifying seemingly fair gambling via two-armed Futurity bandit," Papers 2212.11766, arXiv.org.
    • Handle: RePEc:arx:papers:2212.11766
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    File URL: http://arxiv.org/pdf/2212.11766
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    References listed on IDEAS

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    1. 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.
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