Martingale
The martingale betting system (from the French martingale) is a gambling strategy in which a player increases the size of each bet after a loss until a win occurs. Although the strategy may seem to guarantee a profit, it does not give the player a mathematical advantage.
In stochastic process theory, a martingale is a random process for which the best mean-square prediction of a future value, conditional on all currently available information, is its present value.
In short: in gambling, a martingale is a system of increasing bets after losses; in mathematics, it is a stochastic process with no predictable upward or downward drift.
Betting-system example: You bet ₽100 and lose, then bet ₽200 and lose again, then bet ₽400 and win. The final win recovers the previous losses and yields a net gain equal to the original stake, but the required bets grow rapidly.
Stochastic-process example: If your bankroll changes by a fixed amount with each toss of a fair coin, with equally likely gains and losses, its expected future value—given the information available now—is equal to its current value.