Hi Justin,

The confidence interval calcs that people do only apply to a Normal distribution with mean and variance equal to the mean and variance of our special BB/100 distribution.
Since our BB/100 distribution is not normal, these first two "moments" are not enough to figure out exactly what our confidence intervals are. So, our calculations introduce an error. How big is the error?

Let's go to the extreme and say that we were interested in BB/1 (BB/hand). Our mean, let's say, is 0.0200 (this would mean we had a winrate of 2.00 BB/100). And let's say our standard deviation is 1.5 (which would result in an SD/100 of 15). This means that a one sigma event would put us between -1.48 and 1.52 BB, and a five sigma event (which happens less than once in a million trials on average) would be between -7.48 BB and 7.52 BB. Clearly this is way off. We win (and even sometimes lose) more than 7.5 BB well over once in every million hands. So our confidence interval calcs for BB/1 are way off because the real poker distribution is nowhere near Normal and can NOT be approximated well using just its first two moments (mean and variance).

So where does that leave us with BB/100? How much error do we introduce in our confidence interval calculations by assuming BB/100 is Guassian? Good question. I'm not sure. I think you will still see remnants of the longer flat tail on the positive side and the shorter, steeper tail on the negative side (a by-product of the fact that you can win a lot more in one hand than you can lose). But I suspect it will be close enough to normal to not worry about it.