[Oblivious]

Surely you arent arguing that there is no such thing as a 500bb downswing for winning players.

If we assume the probability distribution for streaks to be gaussian (a bell curve), we would see that the more extreme winning or losing streaks would be less probable. This probability distribution would be defined for all streaks, no matter how large. So if you play long enough, you will eventually encounter a losing streak of 500bb, 1000bb, and even 10000bb. Mind you, "long enough" might require hundreds of thousands of years... most of our careers dont last that long.

The fact that you brought up the qualification of "winning player" is strange to me. Even losing players have very large rushes upward. I agree with you that a winning player, starting with 500bb, would most likely never go broke if his earnings were added to his bankroll. This isnt the case for a losing player. But if a winning player starts a career with 500bb, and withdrawls money such that his bankroll is never over 500bb, he will eventually go broke provided his career is long enough.

Somewhere, the idea of convergence should be included in this argument, but Ive become a bit rusty since my course in Analysis.