How many hands for Std. Deviation to Converge?

[AaronBrown]

This is not an easy question. There is a theoretical answer if you are drawing from a Normal distribution, but it is not useful in practice for this question. The key is something called "kurtosis," basically, the size and frequency of extreme variations.

If the real question is whether your standard deviation has decreased, the best way to answer it is to look at subsamples from your large database, say 5,000 hands each. If you frequently had runs with standard deviations below 12.81, then the current run is reasonably likely to be the result of chance. But if standard deviations of 12.81 were rare or non-existent in the older database, it seems likely that your standard deviation has really gone down (although not necessarily all the way to 12.81).