you could exploit max bet if they allowed it. you start at $1 and if you lose you double your bet, and when you win you reset your bet back to $1.
The standard deviation of this is fairly large though so that the chance of this happening is very small but nevertheless it isn't zero and what you lose is more than you can expect to win. As sleepychu mentioned, the amount you bet goes up exponentially ($1M after 20 rounds).
Aside: It is sometimes said that in order to do this "double when you lose" strategy, you need to e.g. "stick to red for the entire run". This is false. If I bet red-red-red-...-red-red I am just as likely to win/lose as when I bet red-black-odd-odd-even-...-red
[0] https://en.wikipedia.org/wiki/Martingale_%28betting_system%2...