Changes

This would seem to be true even when playing against a "house percentage" (e.g. a roulette wheel with 0 and a 00 slots on which nobody wins), which should instantly raise suspicions.

This would seem to be true even when playing against a "house percentage" (e.g. a roulette wheel with 0 and a 00 slots on which nobody wins), which should instantly raise suspicions.

The flaw in the martingale is the assumption that the series of bets can continue for as long as is needed to reach that eventual win. In fact, the run of bets is limited either by the amount of money the gambler has or by casino betting limits.  

The flaw in the martingale is the assumption that the series of bets can continue for as long as is needed to reach that eventual win. In reality, the run of bets is limited either by the amount of money the gambler has or by casino betting limits.  

For example, consider a gambler who has only $70 and tries to follow the system above. If there is an (imaginary!) fair roulette wheel, the probalities are:

For example, consider a gambler who has only $70 and tries to follow the system above. If there is an (imaginary!) fair roulette wheel, the probalities are: