This reminds me of "doubling" in Roulette. If you bet $1 and win you profit $1. If you lose, bet $2. If you win you win 2 - 1, if you lose you bet 4 and perhaps win 4 - 2 - 1 = $1. With an unlimited supply of capital you will earn positive returns for any reasonably positive probability of winning even if significantly less than 50%. Similar to the Parrondo's example the result requires bets that depend on capital which depend on previous iterations of the game and so the different games are not truly independent.
That's the Martingale System (http://en.wikipedia.org/wiki/Martingale_system), and it fails because no one has an unlimited supply of capital. Lose 20 times in a row and you've lost $2,097,151 since your last win. And you will eventually lose 20 times in a row. Since you're only winning $1 every time you win, you'll have to play many times to win any significant amount of money.
