[jason1990]

Not the bankroll fluctuations, but the bankroll itself. This is in the introduction to the article I linked to in the Poker Theory thread. Whether it's an accurate model or not, I'll leave for others to debate. Although I will say that I believe it is a good model when it comes to questions about the "long run." Also, such a model does generate the "usual" risk of ruin formula that folks toss around, so that may be evidence that at least some other people think it's a useful model.

I've played with this a little more. If T is the first time you see a 100 BB downswing, I want to compute

E[e^{-aT}]

for arbitrary a>0. This is the Laplace transform; it should allow us to compute moments of T and, with a computer package, may even explicitly determine the distribution of T. Unfortunately, I can only work out that

E[e^{-aT}] = E'[e^{-bT + cX*(T)}],

for some (explicit) positive constants b and c, where the notation is as in that other thread. This is no good, since I only have a formula for

E'[e^{-bT - cX*(T)}].

In other words, I think I can analyze upswings, but not downswings. I may give up on this soon, since I'm probably spending too much time on it.

Edit: If forgot the "e^"s in my E' expectations.