In mathematical terminology, this corresponds to the assumption that the win–loss outcomes of each bet are independent and identically distributed random variables, an assumption which is valid in many realistic situations. The fundamental reason why all martingale-type betting systems fail is that no amount of information about the results of past bets can be used to predict the results of a future bet with accuracy better than chance. The martingale strategy has also been applied to roulette, as the probability of hitting either red or black is close to 50%. Additionally, as the likelihood of a string of consecutive losses is higher than common intuition suggests, martingale strategies can bankrupt a gambler quickly. In a casino, the expected value is negative, due to the house's edge. Despite the fact that the gambler usually wins a small net reward, thus appearing to have a sound strategy, the gambler's expected value remains zero because the small probability that the gambler will suffer a catastrophic loss exactly balances with the expected gain. However, no gambler has infinite wealth, and the exponential growth of the bets can bankrupt unlucky gamblers who choose to use the martingale, causing a catastrophic loss.

Since a gambler will almost surely eventually flip heads, the martingale betting strategy is certain to make money for the gambler provided they have infinite wealth and there is no limit on money earned in a single bet. Thus the strategy is an instantiation of the St. The strategy had the gambler double the bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake. The simplest of these strategies was designed for a game in which the gambler wins the stake if a coin comes up heads and loses if it comes up tails. JSTOR ( August 2022) ( Learn how and when to remove this template message)Ī martingale is a class of betting strategies that originated from and were popular in 18th-century France.

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