Discrete–time ratchets, the Fokker–Planck equation and Parrondo's paradox

Parrond's games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature. Here we review two recent approaches, based on the Fokker–Planck equation, that rigorously establish the connection between Parrond's games and a physical model known as the flashing Brownian ratchet. This gives rise to a new set of Parrond's games, of which the original games are a special case. For the first time, we perform a complete analysis of the new games via a discrete–time Markov chain analysis, producing winning rate equations and an exploration of the parameter space where the paradoxical behaviour occurs.

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