I was reading the Martingale betting system on wikipedia and there is something not completely clear to me. The article says at some point
However, the gambler's expected value does indeed remain zero because the small probability that he will suffer a catastrophic loss exactly balances with his expected gain. It is widely believed that casinos instituted betting limits specifically to stop Martingale players, but in reality the assumptions behind the strategy are unsound. Players using the Martingale system do not have any long-term mathematical advantage over any other betting system or even randomly placed bets.
I don't quite understand this. If you keep doubling, it is true that you might encounter catastrophic losses, but the probability that you get 5 heads in a row is 1/32, quite low, and it decreases to zero exponentially. Thus, to me it seems that it should be rare , assuming that the probability of head is .5, to have to play more than 6/7 rounds in real life.