[pococurante]

I think this can be simplified to some extent, and still get numbers that are semi accurate.

In your average pot, you either gain $1 or lose $1. Over 100 hands, you average a $16 profit. Therefore, you win 58% of the hands and lose 42% of them.

So to find the odds for 1000 hands...

sqrt{(1000*.58*(.42)}
sqrt(243.6)
standard deviation = 15.61
expected wins = 580
actual wins (for a $500 loss) = 250
# of deviations = 14.7

Something that's 7 deviations away from the EV has odds of about 1 in 385,000,000,000 of happening... so you can imagine what 14.7 deviations means.

So anyway, according to these numbers:

68% chance to be within $15.60 of your expected $160 profit
95% chance to be within $31.20
99% chance to be within $46.80

Now that I see the results... those are too consistent for how poker really works. I realize now it's because I didn't count the variance on your 58% winrate, and the variance on the $1 pot size. If I had to guess... just double the above numbers (65% to be within $31, for instance) and that sounds reasonable.

Bottom line: no way in hell are you going to lose $500 in 1000 hands. Unless you're the type to tilt and then move way up in stakes so you can win it back faster... then it's all but guaranteed to happen.

It's pretty obvious when you look at the basic facts, too. With those kinds of pots, what are you playing? Probably 10nl. Who the hell has a 50 buyin downswing in 1000 hands? Unless you're tuff_fish, losing a buyin every 20 hands is pretty hard to do.