To my emerging collection of paradoxes, I now add another: the joyfully alliterative Parrondo’s Paradox, which states that “Given two games, each with a higher probability of losing than winning, it is possible to construct a winning strategy by playing the games alternately.” The paradox was discovered in 1999.
This article from the New York Times written shortly afterward describes one of Parrondo’s experiments with two games involving weighted (non random) coins: “when a person plays either game A or game B 100 times, all money taken to the gambling table is lost. But when the games are alternated — playing A twice and B twice for 100 times — money is not lost. It accumulates into big winnings. Even more surprising, he said, when game A and B are played randomly, with no order in the alternating sequence, winnings also go up and up.”
When visualized, these games take on a rachet-like shape — a shape central to the explanation of trivial phenomena, like the Brazil Nut Effect, and more fundamental matters, like the design of enzymes and proteins.