A betting system developed in 18th century France that is used to theoretically guarantee winning money in casino games like craps, roulette, or blackjack, named after a successful 19th century gambler who frequented the casinos of the French Riviera. The basic method is to start with a minimum bet. If you lose, double the bet and try again. If you win, go back to the minimum bet. The theory is that you always bet enough to win back the money you lost from your previous bets.
For example, if you start with a minimum bet of $1, lose four times, and then win, the pattern goes:
Bet Result Total
1 loss -1
2 loss -3
4 loss -7
8 loss -15
16 win +1
So every win should earn you $1, no matter how many intervening losses there are, and regardless of the odds and the house percentage, because eventually you'll win it all back. Simple, right?
Wrong!
Why doesn't this work in practice? Two reasons. First, casinos always have limits to the amount you can bet. So if the table minimum is $1 and maximum is $1000, it only takes 9 consecutive losses (1/512 probability for an even money game) to reach the maximum bet.
The other reason is that your bankroll is not infinite. If you play long enough, you will hit a bad streak, and even if the casino didn't have a limit, you do. This system would only work if you have an infinite amount of money to bet, and the casino were willing to take any bet you placed.
There are many other systems based on the Martingale, and in fact martingale is now an eponym that describes any betting system that employs similar tactics.
Just remember, no betting system will beat the house percentage in the long run, so your best bet is not to make one.
Sources:
http://www.jimloy.com/gambling/marting.htm
http://www.ace-ten.com/strategy/intermediate/effective.html
http://store.traders.com/-v06-c07-marting-pdf.html