The Martingale

You're in the casino and place a $1 bet on red. It doesn't come up, so you place a $2 bet on red, so that if you win you pick up $4 - everything you've staked so far, plus a dollar. It misses again, so you bet $4 - the $8 you'll surely win THIS time covers all you've staked - $1 + $2 + $4 = $7, plus a dollar to win. Red's bound to come up eventually, so eventually you'll make your dollar. It's a foolproof system! It's called the Martingale, and - unfortunately - it doesn't work very well.

The word martingale derives from the town on Martigue in Provence, southern France. In Martigue, where trousers were traditionally worn fastened at the back. "A la martingale" soon came to mean 'in a ridiculous fashion' and is applied in exactly that sense to the system above.

The problem with the Martingale is that your bet size gets very big very quickly - as you can see below.

Bet number: Stake size
1: $1
2: $2
3: $4
4: $8
5: $16
6: $32
7: $64
8: $128
9: $256
10: $512

After losing ten bets in a row (which will happen a little fewer than once in a thousand times*), you'll be looking to gamble over $1000 dollars to win just one in return - and the odds you're getting are still a little worse than evens. Yes, you're bound to win your dollar in the end - as long as you have an infinite bankroll. Eventually, you will simply reach a point where you don't have enough to carry on playing, and you have to stomach a devastating loss.

* Actually, in a casino the odds are slightly worse than this because of the house edge. In an American casino with two zeroes, the probability of red is about 0.47 rather than the 50% implied by the odds. That makes the probability of ten losing red bets in a row about one in 610.