Optimal sequence for Parrondo games

TL;DR

This paper introduces an algorithm based on backward induction to determine the optimal sequence of games in Parrondo's paradox, demonstrating that a specific sequence maximizes steady state gains and can be adapted for multi-player strategies.

Contribution

It presents a novel backward induction algorithm for optimizing game sequences in Parrondo's paradox, including steady state and multi-player adaptive strategies.

Findings

ABABB... yields the highest steady state average gain

The algorithm can be applied to any finite number of turns

It can be extended to multi-player adaptive strategies

Abstract

An algorithm based on backward induction is devised in order to compute the optimal sequence of games to be played in Parrondo games. The algorithm can be used to find the optimal sequence for any finite number of turns or in the steady state, showing that ABABB... is the sequence with the highest steady state average gain. The algorithm can also be generalised to find the optimal adaptive strategy in a multi-player version of the games, where a finite number of players may choose, at every turn, the game the whole ensemble should play.