An Example
Here is a simple example. Suppose you were betting a simple coin toss with a disadvantage, Your probability of winning is 49%, and your prob of a loss is 51%.
But you are going to playa Martingale. If you lose the first bet, you bet 2 units on the seond. If you lsoe that, you bet 4 on the third, etc. If you win any of these bets, you have netted 1 unit overall, and you could back to square 1.
You will do this 10 times. Your probability of losing is very, very small. You have to lose bets in a row, The probability of this happening is (.49)^10 or .119%. If you engage in 840 such cycles, you would expect to lose in only one of them.
But if you do lose, how much does it cost you? It is 1+2+4+8+ � =2^10-1 =1023 units.
In every 840 attempts, you lose 1023 units. In the other 839 attempts, you make 1 unit each time.
You overall win, per 840 starts, is 839-1024. In other words, the times you get �unlucky� and lose you give back all of your winnings and then some.