From io9:
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.