Chaotic Switching in Parrondo's Games: Enhancing Winning Probability

Title: Chaotic Switching in Parrondo's Games: Enhancing Winning Probability

Research Question: Can chaotic switching in Parrondo's games enhance the winning probability compared to random and periodic switching?

Methodology: The researchers used a computer simulation to investigate the different effects of chaotic, random, and periodic switching on Parrondo's games. They employed the Logistic Map, Tent Map, Sinusoidal Map, Gaussian Map, Henon Map, and Lozi Map for generating chaotic sequences. These sequences were used to determine which game (Game A or Game B) to play at each discrete-time step.

Results: The researchers found that the maximum rate of winning could be obtained with all factors properly set, including the coefficient(s) defining the chaotic generator, initial conditions of the chaotic sequence, and the proportion of Game A played. This occurred when chaotic switching approached periodic behavior. They also observed that the rate of winning depended on the specific chaotic map used.

Implications: This study suggests that chaotic switching can enhance the winning probability in Parrondo's games, providing a potential advantage over random and periodic switching. The results may have implications for the design of strategies in other games and systems where mixing different elements can lead to improved performance.

Link to Article: https://arxiv.org/abs/0404016v1 Authors: arXiv ID: 0404016v1