Simple games to illustrate Parrondo’s paradox

Abstract

Parrondo’s paradox is the proposition that two losing strategies can, by alternating randomly, produce a winner. R. D. Astumian has recently created a simple board game to illustrate this counterintuitive phenomenon. We prove that the inherent symmetry of Astumian’s game prevents it from achieving its purpose, and suggest amended versions that do. We also display the additional paradoxical effect of two slow, losing games combining into a fast, winning one.