Imagine you are flipping coins (even odds), and you are making bets on your flips. Here is a popular betting scheme: After you lose, double your bet; and after you win bet one dollar. The idea is that if you lose several flips in a row, you will still come out ahead: -1-2-4-8-16+32=1. Here I lost five flips in a row, and then won $32, and the total is $1. After any string of losses is over, you come out ahead. So you always come out ahead. What is wrong with that reasoning?

The sad fact of life is that this betting scheme loses money faster than most other betting schemes. How can that be, when it always makes money? Well, it doesn’t always make money. There are two problems.

1. The first problem is that in casinos, with other games (besides flipping coins), there is a betting limit. And you reach that betting limit very rapidly when you double your bet every time. Let’s say that the limit is $500. Then you have to lose nine bets in a row (-1-2-4-8-16-32-64-128-256, and your next bet cannot recoup your losses) in order to exceed the betting limit. Nine losses in a row has got to be very rare, right? Not rare enough. Remember that you are only winning $1, every time you win, so you are not one of the big winners in Vegas. Eventually you are going to lose big time.
2. If there is no bidding limit imposed by the house, you still are limited by your own bankroll. You cannot keep doubling your bet when you have only so much money. Just like the house limit problem, you will lose big time.

This betting scheme is called Martingale. It is probably one of the biggest money makers for the casinos.