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

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.