Puzzles

Two losing games can be combined into a winning one

Imagine two separate gambling games, each individually rigged so you lose money on average over time. Play only Game A, and you lose. Play only Game B, and you lose. But if you switch between them in a particular pattern, or even at random, the combined strategy can turn into a long-run winner. How can two losers make a winner?

Reveal the answer

Game B's rules depend on your current capital, so switching games changes which game's bias dominates at any given moment, letting the combination escape the losing trend either game has alone. Physicist Juan Parrondo devised this apparent paradox in 1996; it's since been used to model phenomena in evolutionary biology, financial trading, and randomness-driven physical systems.

Juan M. R. Parrondo, Parrondo's paradox — First presented 1996; formalised by Harmer and Abbott, Nature, 1999

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