[jason1990]

[ QUOTE ]
That's actually what I meant. I am not sure it is, though. Doesn't brownian motion assume equal step sizes?

[/ QUOTE ]
Well, I'm not exactly sure what you mean by this. Since Brownian motion is continuous, there are no "steps," of course. But BM can be realized as the scaling limit of a random walk with equal step sizes, if that's what you mean. However, you don't have to have equal step sizes to get BM in the limit. Only independent steps with mean zero and finite variance. This is the Invariance Principle: the scaled random walk converges to BM regardless of the underlying distribution of the steps. So if the result of your j-th poker hand is m + X_j, where m is your win rate and X_j are i.i.d. mean zero random variables with finite variance, then the limit of the sums of the X_j's will be BM and the m will give you a drift. (This is very hand-wavy, of course. In particular, note that you must scale the X_j's to get BM, but you don't want to scale the m.)

[ QUOTE ]
what if the question was a 25BB downswing rather than 100? Clearly the long term normal approximation will fail, right?

[/ QUOTE ]
I agree. Similarly, the usual risk of ruin formula will not be accurate if you only have a 25BB bankroll. I would only use the BM model if (a) I was asking about "big" events (big swings, long term profits, etc.) or, as in this case, (b) I just wanted to have fun playing with BM. [img]/images/graemlins/wink.gif[/img]