[Phil153]

Note: I'm sure there are better statistical methods of working this out, but since no one else answered this should give a quick and dirty answer.

Since he can't play more than around 2000 hands/day, there will be many days where he finishes a loser but not down 10 buyins. So I'm going to restate the question and assume:

1. He never loses for the day after reaching 1 buyin (50BB)
2. He will play up to 2000 hands if he hasn't reached one buyin.
3. He is a 10BB/100 winner with a 50BB/100 standard deviation.

I don't know how to incorporate (1) into the calculations, but you can work out a lower bound by determining how often he'd be a winner if he played 2000 hands every day.

With a 95% confidence interval, his distribution will look like:

20*10 ± 1.96*20*50/ sqrt(20) = 200BB ± 438BB

So the distribution ranges from +638BB to -238BB, with a mean of 200BB. Thus, roughly 67% of his days will be winning days. If he stops each day as soon as he reaches 50BB, this will push this number significantly higher, as it cuts out the days he reaches 50BB and ends up losing. It's easy to see how this could push his daily win% to over 80%.

There are other factors that could add credence to his figures and bring the total closer to his 90% figure:

1. His winrate includes period of tilt and poor play, and is actually higher than stated when he's playing good. Sheer determination and the goal of getting unstuck may make him a play better poker. Given that he's something of a Fairly Aggressive Guy, this seems very likely.

2. His table image deteriotes after losing for a while, and he is able to exploit this and artificially increase his winrate to get back up.

3. The quality of his reads and/or domination of a table increase with time spent there.

4. He has a higher winrate when playing a deep stack.

So I don't think it's an example of running good at all, seems pretty standard results for a Fairly Aggressive Guy (or even a Very Aggressive Guy, as may be the case here) playing a stop-win method.