Winning combinations of history-dependent games

TL;DR

This paper extends the understanding of the Parrondo effect by analyzing how two history-dependent, memory-involving games can combine to produce winning outcomes, with new results for random and periodic switching scenarios.

Contribution

It generalizes the Parrondo effect to include history-dependent games and explores the impact of different switching strategies on the paradoxical outcome.

Findings

History-dependent games can exhibit Parrondo effect under various switching schemes

Random switching can lead to winning combinations in history-dependent games

Periodic switching also produces paradoxical winning outcomes

Abstract

The Parrondo effect describes the seemingly paradoxical situation in which two losing games can, when combined, become winning [Phys. Rev. Lett. 85, 24 (2000)]. Here we generalize this analysis to the case where both games are history-dependent, i.e. there is an intrinsic memory in the dynamics of each game. New results are presented for the cases of both random and periodic switching between the two games.