2023/10/13 by Huaijin Liang, Liang, Huaijin, Zengjing Chen +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #60F05 #60J10 #Complex Systems and Time Series Analysis #Computability, Logic, AI Algorithms #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2310.08935
openalex publication_date 2023/10/13 · openalex created_date 2023/10/17 · openalex updated_date 2026/07/28
The 1936 Mills Futurity slot machine had the feature that, if a player loses 10 times in a row, the 10 lost coins are returned. Ethier and Lee (2010) studied a generalized version of this machine, with 10 replaced by deterministic parameter J. They established the Parrondo effect for a hypothetical two-armed machine with the Futurity award. Specifically, arm A and arm B, played individually, are asymptotically fair, but when alternated ran-domly (the so-called random mixture strategy), the casino makes money in the long run. They also considered the nonrandom periodic pattern strategy for patterns with r As and s Bs (e.g., ABABB if r = 2 and s = 3). They established the Parrondo effect if r + s divides J, and conjectured it in four other situations, including the case J = 2 with r >= 1 and s >= 1. We prove the conjecture in the latter case.