What's the magic formula?

[hmkpoker]

There's some kind of formula that (given a sample size and BB/100 and probably SD/100) allows you to calculate a range of "actual" BB/100 within a given confidence range...for example, a 95% confidence of a range of 1 to 5 BB/100 with for a BB/100 of 3 and a SD of 15BB/100 at 15k hands (just making numbers up, but you see what I mean)

How can one calculate this?

Does it change if one plays short (6-max) limit rather than full ring limit?

[AaronBrown]

Let WR be your long-term expected win rate per 100 hands and SD be the standard deviation per 100 hands. After N hands, your confidence interval for actual win rate is:

WR - k*SD/SQRT(N/100) to WR + k*SD/SQRT(N/100)

where you set k to get the desired level of confidence:

k = 1, confidence = 68%
k = 2, confidence = 95%
k = 3, confidence = 99.7%

You can use Excel to compute the confidence as 1 - 2*NORMSDIST(-k).