Parrondo's games with chaotic switching

TL;DR

This study explores how chaotic switching influences Parrondo's games, revealing that optimal winning rates occur when chaotic behavior becomes nearly periodic, depending on system parameters and initial conditions.

Contribution

It introduces the effect of chaotic switching in Parrondo's games and identifies conditions for maximizing winning rates, a novel approach compared to traditional random or periodic switching.

Findings

Maximum winning rate occurs near periodic chaotic switching

Winning depends on chaotic generator parameters and initial conditions

Chaotic switching can outperform random or periodic strategies

Abstract

This paper investigates the different effects of chaotic switching on Parrondo's games, as compared to random and periodic switching. The rate of winning of Parrondo's games with chaotic switching depends on coefficient(s) defining the chaotic generator, initial conditions of the chaotic sequence and the proportion of Game A played. Maximum rate of winning can be obtained with all the above mentioned factors properly set, and this occurs when chaotic switching approaches periodic behavior.