I think I found another way to convince you this is false as well. You're assuming that when players have the edge, they'll still use the same strategies (martingale, going all in). But actually, that's not what they'll do. Instead, if I had an edge when playing, I would ALWAYS play the minimum bet. This would insure that I had the opportunity to play as many games as possible, thus making it almost certain that I'll come out on top.

There's absolutely no need to risk all my money, when I can pretty much make guaranteed profits playing small.