Thus the strategy is an instantiation of the St. Petersburg paradox. 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.
This effect scales up to any amount of starting capital: there is a large chance of gaining a little bit of money and a small chance of losing all your money. As a result, many gamblers will turn a small profit playing the martingale system, but the rare gambler will suffer complete losses.