A review of Parrondo's paradox

Abstract

Inspired by the flashing Brownian ratchet, Parrondo's games present an apparently paradoxical situation. The games can be realized as coin tossing events. Game A uses a single biased coin while game B uses two biased coins and has a state dependent rule based on the player's current capital. Playing each of the games individually causes the player to lose. However, a winning expectation is produced when randomly mixing games A and B. This phenomenon is investigated and mathematically analyzed to give explanations on how such a process is possible. The games are expanded to become dependent on other properties rather that the capital of the player. Some of the latest developments in Parrondian ratchet or discrete-time ratchet theory are briefly reviewed.