Re: Standard Deviation 24.4 BB/100
 

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You cannot get a bound on the overall error without an estimate on the tail behavior of X, such as a bound on E|X|^4. And my claim is that a genuine and accurate bound like that is impossible after only 6000 hands.

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jason,

I have no idea, but is it possible that E|X|^4 is more stable across different players (playing styles) than E|X|^2 is? In that case, you could get a bound on that using very large aggregate databases (millions, or even tens of millions of hands) and then publish the known result for practical use. No idea if this is feasible, but just curious.

gm

Re: Standard Deviation 24.4 BB/100
 

It's unclear to me how you would do the regression. Perhaps you could illustrate with a simple example. Frankly, I don't see how the number 15 has any relevance here, except maybe as the SD of some Bayesian prior distribution. But if you want to take a Bayesian approach to the analysis, then I'm sure you could do much better than what I'm suggesting, simply by appropriately choosing your prior. For this reason, my intention is to completely avoid any sort of Bayesian analysis.

As for computing a weighted average of your risk of ruin, it sounds like a nice idea. But it looks like you are considering the parameters in the model (for example, the true SD) to be random variables themselves. This is a decidely Bayesian approach. If this is not the case, then perhaps you could elaborate. I am interested in hearing any (non-Bayesian) ideas that might improve this analysis.

Re: Standard Deviation 24.4 BB/100
 

Interesting. I have no idea. But I see no reason to think that E|X|^4 would be more stable. In fact, a "naive" argument suggests it should be less stable. After all, SD is less stable than winrate from player to player, so perhaps stability decreases as we look at higher moments.

Also, I think it would be difficult to test the stability of E|X|^4. We would have to compare its "true" value for many different players. But to get a "true" value for any particular player, they would have to have a large personal database. So all we could really test is the stability of E|X|^4 among players with large databases. And my guess is that "large" here would mean something larger than the database of the typical player who would want to make use of this statistic.