Can one overcome a -EV game?

[jason1990]

The number p is the probability of winning one game. I was proving that the probability of having an infinite streak of wins is 0. Having an infinite streak of wins is the same as saying there exists k such that you win all games after the k-th game. I'm not requiring p>0. If p=0, then the probability of winning one game is zero, so the probability of an infinite streak of wins is zero.