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The only person that would kick you out of a casino for using Martingale wagering techniques are the people who rely on your finances.
Yes, the Martingale strategy is legal on betting sites. This strategy, which originated in 18th-century France and is commonly used in games of chance that offer a 50/50 bet, involves doubling your bet after each loss so that the first win would recover all previous losses plus win a profit equal to the original stake.