The use of Martingale systems can be traced back to 18th Century France, when French mathematician Paul Pierre Levy introduced the system to the general populace. However most of the early work on Martingale systems was completed by American mathematician Joseph Leo Doob, who sought disprove the possibility of a foolproof betting system. For a brief period of time martingale strategies became incredibly popular among French gamblers as the system boasted a near hundred percent success rate provided a gambler had infinitely deep pockets.

Martingale systems were developed for many simple gambling games such as heads or tails and roulette. Not so long ago there was a re-emergence of Martingale systems when many sought to profit of the rise of online casinos by selling or promoting such strategies. While Martingale systems are typically associated with various forms of gambling some traders have adopted martingale systems often with a disastrous outcome.

In a simple game of heads or tails a gambler guesses either heads or tails, if his guess is correct he doubles his money. A Martingale system would have the gambler double his bet after every loss, so that our gambler would recover all of his losses and win a profit equal to his original stake. Assuming there is an equal probability that the coin will land on heads or tails and the gambler has an infinite amount of money, there is no chance the gambler will lose. Since his infinite wealth will mean that the coin will eventually land in his favour, meaning he will recover all his loses and make a profit equal to his stake.

The below example demonstrates a good run using a Martingale system:

In the above example our gambler doubled his initial Balance of 100 to 200 in only seven bets. It should be clear how risky such a strategy is, at one point the gambler bet 80 when he had a balance of 120. You should see that all it takes is one winner to get all of your funds back.

Due to the fact that no gambler has an infinite bankroll and with the bet size growing at an exponential rate, it will only take one or more unlucky choices to bankrupt the gambler. It has been suggested that martingales systems are a good example of Taleb distribution with the system appearing to offer steady returns and limited risk but on occasion experiences a huge or fatal drawdown.

The example below demonstrates how a small run of losses can lead to a gambler going broke.