Martingale is an age old “money management” system, that originated as a betting system in 18th century France. The idea behind it is simple: allow the trader to have huge, exponential growing drawdown, in order to regain lost capital ; the betting system rule is to double the stake when you have a loss.

The trick about the martingale is that it gives the impression that the probability of the next loss reduces as we advance thru a streak of losses. For instance, we had 6 losses and we ask ourselves what would be the probability to have 7 losses. If we note the states by L for losses and W for wins, then we’d have our 7 losses as one possibility (LLLLLLL) out of 2^7 (128) cases. That means 1/128. As we go further down, the number continues to shrink even more, as our drawdown increases exponentially.

As you can see in the table, as you’re getting hammered by the exponentially growing drawdown, the probability for the ruin to continue is shrinking.
The problem is, however, that the possibility of a win after 6 losses (as in our case) is the same, still one possibility (LLLLLLW) out of 128 cases. That is, what matters is the individual probability of a win.

That means, in the case of a casino wheel, that the probability of the next loss is the same. There is nothing in the mechanics of the wheel to prevent losing in the future. The probability of a win remains constant (18/37) , 48.65% (one zero wheel case).

The probability is different than the one in the table, because the one in the table is calculated before the entire streak. Those 128 cases referred for the 7th tryout include also WWWWWWW or WLWWLLW for instance, but in the case of the martingale, the LLLLLL already happened, and the probability of the next tryout to be a loss is as much as the probability for the first one.
In trading, the situation is just slightly different. It starts out being basically the same. The market can go any of the two directions: either up, or down, with a 50% probability on both. That is, because the market moves randomly. You can see the same thing in the option theory: an ATM option will have a 50% delta to reflect the same thing. Or, if you trade binary options, the large majority of platforms out there are one click based – the option is created with the market price at the time of the click being the strike price of the option so that it starts as a bet, with a 50% chance.

To translate the martingale strategy in trading, we consider a single trade, with a take profit and a stop loss. Therefore can be only two events : either it touches the take profit or the stop loss.

One application of the martingale would be for the trader to try to exploit the momentum. When the momentum occurs, the probability – at least the perceived probability – of a move in a definite direction would be higher than 50%. That’s why we call it momentum – it’s when the market doesn’t seem random anymore. However, one has to ask, how much money would you leave on the table if momentum doesn’t pay off and you end up losing several steps in a loss streak ?

One important element that can influence probability is the spread. The smaller the spread, the more impact it has. Why ?