Building a Bankroll For Newbies, Version 2.0 (rather long)

[MrWookie]

I just posted this in FRNL. Someone had referenced the portion of this post that talks about the confidence that you're a winner, and I added this to the discussion. I figured I'd add it here for the benefit of my Micro homies:

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The first part of this post is horribly out of date, but the last part is a good approximation. It's still an approximation, though, since the distribution of the total number of BB you win in 100 hands is not Gaussian. It's actually a skewed distribution with the peak below your avg. win rate, but a big long tail into the large win rates, at least for limit. NL might be a little different, but I don't think it would be by too much. Actually, IIRC, it may have been most probable to lose slightly for 100 hands, but the fact that you can win so big makes up for it. This was based on Josh.'s (IIRC) 1M-ish hand database -- he had a thread in one of the higher stakes limit forums: MHSH, MSLHE, or HSLHE. As you look at a BB/1000 or a BB/5000 or BB/10000, the distribution of BB you win over the specified sample gets more and more Gaussian, but we didn't have a 100M hand database to really know where things really got Gaussian.

With this in mind, if you were to calculate the probability that you're a winning player using the method I outlined in that thread, it will tend to be an overestimate. Given the skewed nature of the distribution, there's more area under the curve (more probability) on the low end than the Gaussian approximation gives credit for. I don't think there's a specific mathematically-motivated probability distribution that would better describe BB/100 data, but I'm not totally sure on that one. With a truly massive database (10-100M hands), we could probably come up with a good guess for one heuristically by just trying a bunch of curve fits and seeing which ones work best. Such a curve would probably use fit parameters that weren't exactly the mean and SD we pull out of PT, but we would probably be able to derive some formulas to convert the usual mean and SD into the fit parameters of this curve. Anyway doing this is out of reach for me at the moment given how (comparatively) little poker I play. Also, you kinda have to wonder just how much merit getting an extra significant figure on the confidence you have that you are a winning player is worth.