Parrando's paradox

The paradox is illustrated by two games played with coins weighted on one side so that they will not fall by chance to heads or tails.

In game A, a player tosses a single loaded coin and bets on each throw. The probability of winning is less than half.

In game B, there are two coins and the rules are more complicated. The player tosses either Coin 1, loaded to lose almost all the time or Coin 2 loaded to win more than half the time. He plays Coin 1 if his money is a multiple of a particular whole number, like three.

If his money cannot be divided evenly by that number, he plays Coin 2. In this setup, the second coin will be played more often than the first.

''Sure enough,'' Dr. Abbott said, 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.

Because these results seem so surprising, the outcome is paradoxical -- Parrando's paradox. Switching between the two games seemed to create a ratchet-like effect. With its saw-tooth shape, a ratchet allows movement in one direction and blocks it in the other.

From a New Your Times article -> Paradox in Game Theory: Losing Strategy That Wins.