Parrondo's paradox

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Parrondo's paradox is a game idea: two losing games can be turned into a winning one when you switch between them in a clever way. It was found by Juan Parrondo in 1996 while studying how systems can extract useful work from random motion, a concept tied to ideas like the Brownian ratchet.

Two simple losing games show how this can work:

- Game A uses a biased coin that makes you lose more often than you win. Played alone, it loses in the long run.
- Game B uses one of two biased coins depending on whether your current total (your capital) is even or odd. Each coin by itself also leads to losses over time.

But if you alternate these losing games in a certain pattern—such as AABB (or other specific sequences)—the combination can become winning. The trick is that switching creates moments when Game B has a better payout, and Game A helps push you back into those favorable states. In short, the dependence between the two games lets their combination beat the losses of each game on its own.

Parrondo’s paradox has been explained with various methods, including Markov chains and other theoretical tools. It is widely considered counterintuitive: two bad games can produce a good one when arranged in the right order. The idea has been explored in biology, finance, engineering, ecology, and many other fields, making it a topic of active study.