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Parrondo's games as a discrete ratchet

Toral, R.; Amengual, P.; Mangioni, S.
Physica A 327, 105-110 (2003)

We write the master equation describingthe Parrondo s games as a consistent discretization of the Fokker Planck equation for an overdamped Brownian particle describinga ratchet.Our expressions,besides giving further insight on the relation between ratchets and Parrondo s games, allow us to precisely relate the games probabilities and the ratchet potential such that periodic potentials correspond to fair games and winning games produce a tilted potential.