This is from the Wizard of Odds website. Everything on this site is based on the mathematics of gambling.
This is the from the "Truth about betting systems" article:
The Martingale (double after every loss) system
Every week I receive two or three e-mails asking me about the betting system by which a player doubles his/her bet after a loss. This system is generally played with an even money game such as the red/black bet in roulette or the pass/don't pass in craps and is known as the Martingale. The reasoning behind those who believe it is that by doubling your bet after a loss, you will always win enough to cover all past losses plus one unit. For example if a player starts at $1 and loses four bets in a row, winning on the fifth, he will have lost $1+$2+$4+$8 = $15 on the four losing bets and won $16 on the fifth bet. The losses were covered and he had a profit of $1. The fallacy is the promise of guaranteed winnings by using the Martingale. Occasionally the player will lose several bets in a row and will reach a point where he doesn't have enough money to double.
In order to prove this point, I created a program that simulated two systems, the Martingale and flat betting, and applied each by betting on the pass line in craps (which has a 49.29% of winning). The Martingale bettor would always start with a $1 bet and start the session with $255 which is enough to cover 8 losses in a row. The flat bettor would bet $1 every time. The Martingale player would play for 100 bets, or until he couldn't cover the amount of a bet.In that case he would stop playing and leave with the money he had left. In the event his 100th bet was a loss, he would keep betting until he either won a bet or couldn't cover the next bet. The person flat betting would play 100 bets every time. I repeated this experiment for 1,000,000 sessions for both systems and tabulated the results. The graph below shows the results:
http://www.wizardofodds.com/gambling/scam.html
If you still don't believe him he's put his money where it mouth is. (taken from the bottom of that scam.html page)
The Wizard of Odds Challenge
Despite all the evidence I have supplied I continue to get challenges via e-mail from people who believe their individual systems are the exception to the rule and really work. These challenges usually come with a request that I waste my time writing a free simulation program to prove or disprove the author's system. Contrary to what some may think, I do not sit around all day with nothing to do but test betting systems. So in an effort to give the true believer a fair chance to prove me wrong, I will bet your $2,000 against my $20,000 that your system won't win a negative expectation game over a billion trials.