How strong can the Parrondo effect be?

Abstract

AbstractParrondo’s coin-tossing games were introduced as a toy model of the flashing Brownian ratchet in statistical physics but have emerged as a paradigm for a much broader phenomenon that occurs if there is a reversal in direction in some system parameter when two similar dynamics are combined. Our focus here, however, is on the original Parrondo games, usually labeledAandB. We show that if the parameters of the games are allowed to be arbitrary, subject to a fairness constraint, and if the two (fair) gamesAandBare played in an arbitrary periodic sequence, then the rate of profit can not only be positive (the so-called Parrondo effect), but can also be arbitrarily close to 1 (i.e. 100%).