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Casinos will normally post a maximum and a minimum stake for a roulette table and this is sometimes done for recreational play, too. Typically, for each spin of the wheel, if a player the total amount of a player's inside bets must exceed the minimum stake. The listed maximum stake usually shows only the maximum allowed for a single number "straight up" bet. The maximum stakes for other types of bet increases proportionately e.g. The maximum bet allowed for a pair of numbers is double the maximum straight-up bet, the maximum allowed for a corner bet is 4 times the straight up maximum and so on. So that really the limitation is on the amount that the casino can lose!
Even if there isn't a betting limit, and if you have an infinite credit limit, it still doesn't really work, it just doesn't really fail either. If the martingale strategy is continued indefinitely and without regard to betting limits, your bankroll will hit arbitrarily high positive and negative values. The expected value is still negative, but the variation is so high that it your bankroll won't stay either negative or positive.