Estimating true winrate when 'sklansky bucks' winrate is known

[Hielko]

I know how I can construct a confidence interval when I know the number of hands played, the sample variance, the and sample winrate. Does anyone know how the accuracy of the confidence interval can be improved when the 'sklansky bucks' winrate is know?

For those who don't know the term yet: the sklanksy bucks winrate is the winrate you would obtain when you would earn exactly your pot equity in every hand that has a showdown and it can be calculated using the PokerEV software.

For example, I have played 17,087 hands of 25NL this month and earned 559,69 dollar giving me a winrate of 6,55BB/100 and I have a standard deviation/100 hands of 39,20BB. Using this data one could construct a confidence interval that is centered around 6,55BB/100. Now we also know my equity adjusted winrate (706,61$ - 8,3BB/100). I guess that using this winrate instead of the sample winrate would improve the confidence interval, but by how much? Would you need an 'equity adjusted' variance where the variance is always zero in a pot with a showdown?

[Christian_Peters]

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Does anyone know how the accuracy of the confidence interval can be improved when the 'sklansky bucks' winrate is know?

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Now we also know my equity adjusted winrate (706,61$ - 8,3BB/100). I guess that using this winrate instead of the sample winrate would improve the confidence interval, but by how much? Would you need an 'equity adjusted' variance where the variance is always zero in a pot with a showdown?

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What do you mean by 'improve' your confidence interval? I assume you just mean that you would obtain a narrower interval.

Treat winnings from hands as independent, normally distributed. Now, it's a very cool idea to calculate a standard deviation for the winrate, so you can get an idea of normal and abnormal variance - it's normally distributed data so you can easily determine, for example, this session represents a loss that is in the 98th percentile of all my sessions or something like that.

I'm confused about why you would want to adjust for equity. If you build a confidence interval on hands that are adjusted for equity, then what does the confidence interval really tell you about your sessions? I'm not sure exactly how you would interpret something like that - maybe 'this is a mean and stdev. that I should theoretically have.' But then why even adjust your data at all?
What was it that you had in mind here?