[BruceZ]

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Then I can compute a weighted StdDev over all my observations (i.e. wins and losses) for all sessions. The trouble I am having is how do I interpret the results. I'm not sure what the difference between the three is and how to determine which result I should prefer. Any ideas?

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You don't want to use very short time periods because your results will not be normally distributed. The estimators assume normally distributed data. You really want to go the other way and use sessions that are several hours long, so that the results more closely follow a normal distribution.

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Well, if you have all of the individual game results (I play at home, so I'm not sure how this poker tracking software works), wouldn't you be better off throwing time out the window? Just throw all of your observations into one set and calculate the standard deviation off of that.

Or is the statistic of interest being measured over the time period, and not over the number of game? I'd still consider throwing them all into one pot and calculating from there.

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I'm not sure what you mean by "throw them all into one pot". What is your formula for the variance? When we compute the variance, we must sum over N data points, and the question is how we obtain those N data points. I hope you are not suggesting that we use the result of each individual hand as a data point. Remember, when we compute the variance, we are assuming that our observations are distributed by a normal distribution, and we are attempting to estimate the variance of that distribution. Your results per hand, or even per hour, will not satisfy the assumption of normality.

If your observations correspond to different time periods, or different numbers of hands, then you must take these different time periods or numbers of hands into account properly when you compute your variance. The formula given above shows how to take this into account. If you throw away this information, then you are essentially assuming that all observations correspond to equal time periods, or an equal number of hands, and your result will be incorrect. Even if we have data for every hand, we need to group these results into, say 100 hand samples, to compute a variance in units of bb^2/100 hands. If we want units of bb^2/hr, then we are better to have samples corresponding to several hours, so that the central limit theorem has time to kick in and better validate the assumption of normality.