I was thinking about win rates and bankroll considerations and did a little research on Current Win Rate (CWR) vs. True Win Rate (TWR) and came up wit the following:
Confidence Interval for Calculating True Win Rate
Obviously, the more hands you play and the lower your variance for any given stakes, the closer your Confidence Interval (CI) converges on your TWR.
Using HEM you can find your Standard Deviation in bb/100 or BB/100. I've used BB/100 since that is the same as PTbb/100, which seems to be the norm for win rates. Look for you StdDev down the left-hand column and match it with the number of hands played accross the top and find your confidence interval.
If your number of hands is somewhere in between two columns, you can interpolate between columns to get an approximation.
The table provides the Confidence Interval (CI) for a 90% confidence that your TWR is in the range between:
CWR -CI <--> CWR + CI
OR;
(CWR - CI) < TWR < (CWR +CI)
The way I see it, you will be doing at least as well as the lower bound of your TWR. So, if you have a high win rate, subtract the confidence interval from that number and you have the bottom end of the range for your TWR.
If it's positive, you are probably a winning player.
If your range of win rates extends into a negative lower bound, it doesn't mean you are a losing player. It's just that there is some non-zero probability that you are.
Likewise, if your CWR is negative, you'll find that the upper bound may be positive and there is some non-zero probability that you are a winning player.
I will soon add a 95% CI and 50% to the linked page to provide higher and lower confidence intervals.
I think the most usable aspect of these numbers is with respect to bankroll management. If you find you have a very wide spread of possible win rate, you need to take that into consideration when determining what bankroll you need to survive your Risk of Ruin (RoR).
I used the lower end of my range for TWR in the formula below:
BR = StdDev^2/(Kelly Fraction * TWR),
I use a Kelly Fraction of 0.5 (because I play mostly PLO and my SD is very high). A Kelly fraction of 1 is also commonly used, but seems to balla for my tastes. (My guess is it's good if your TWR range says you are killing the micros, though.)
My numbers basically say I need to have a 37 buy-in BR. If I use a Kelly Fraction of 1, I get 18 buy-in's. This could work at PLO25, since my current win rate is like 20BB/100, but I wouldn't feel confident having that small a BR if I wasn't running as hot as the sun or playing at higher stakes, so I'd stick with 0.5 for the KF. YMMV.
GL