Parrondo’s Paradox: Winning Two Games You’re Guaranteed to Lose

From io9:

JM Parrondo is a casino and con artist's worst nightmare. In the 1990s, he invented two games that are sure to lose you everything. They're both mathematically designed to make you go broke, but play them one after another and you are guaranteed to win.

Parrondo's Paradox was dreamed up in the 1990s by physicist Juan Manuel Rodriguez Parrondo. It spawned a whole new approach to games — specifically, a distrustful approach to games by those who were sure the odds were stacked in their favor. The paradox is simple: two games, if played separately, will always result in you losing your shirt. They're played with a biased coin to make sure of it. If you switch off between them, though, you'll win a fortune. Suddenly, your loss turns into a win.

The first game is simple and always the same. You flip a coin, knowing that the two-faced, lying, no-good cheater you're playing against has weighted it so that your chance of winning is not fifty-fifty. Instead your chance of winning is (0.5 - x), with x being whatever the cheater dared weight it with. If you win, you get a dollar. If you lose, you lose a dollar. Since whenever "x" is more than zero you'll lose slightly more than you'll win, you are guaranteed to lose over the long run.

More here.