Parrondo's paradox

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Parrondo's paradox is a paradox in game theory that describes how a combination of losing strategies can become a winning strategy. It is named after its creator, Juan Parrondo, who discovered the paradox in 1996. A simple example involves two coin flip games: Game A uses a biased coin that loses 50.5% of the time, while Game B switches between two different biased coins depending on whether your current winnings are even or odd. Though both games individually favor the house, alternating between them creates a net winning strategy. This occurs because the alternation causes players to spend more time in the favorable states of Game B, while Game A's consistent bias helps reset the system into those advantageous conditions. Parrondo devised the paradox in connection with his analysis of the Brownian ratchet, a thought experiment about a machine that can purportedly extract energy from random heat motions popularized by physicist Richard Feynman. However, the paradox disappears when rigorously...

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