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If i interpret your results correctly, under the assumptions your model is correct, if you have 100.000 streaks of 100 hands each, one of those will show a win rate of 284bb/100 just by chance? How many hands are there in ppls PT-databases (which would be the population) and what is the probability that every once in a while we will find a maniac with those winnings without cheating?
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I edited my post, because I'm not used to the 1 in x thinking. The chance to run that good is 1 in 20 million hands actually, because the other time you will be on the losing side. The player I used for this analysis has won more than 1 million this year on pokerstars so far on 25/50 NL.
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And what if you increase the standard deviation a little? I mean, this kind of maniac could have a SD of 100 right? That would make it even more probable that such good streak could occur right?
EDIT: I just saw that the had a SD of 270ptbb/100 and that it was 190 hands. That will give completely different estimates. It would be very interesting if you could present a new analysis with those paramters.
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The sample size of 5 100 hand intervalls is just too small to provide any meaningfull result. However if you calculate it for 400, 500, 300, 1000 and 400 bb/100 hand classes using the one outlier of 1000, we get a mean of 520, a standard deviation of 277.5 and a 90% chance that the bb/100 lies between 63.5 and 1777.9 bb/100 for any 100 hand intervall. If we don't use the outlier and only 400, 500, 300, 400 we get a mean of 400, a standard deviation of 81.6 and a 90% chance that the bb/100 for a 100 hand intervall lies between 265.7 and 534.3 bb/100.
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your model also assumes that winnings are normally distributed. Do you think this is a good assumption and in what way do you think violations th normality would affect the estimated probabilities?
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I just assumed that it was a normal distribution and after checking it actually is one. Here is the graph:
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My guessing is that you will find a very high probabbility that such streak would occur in ppls PT databases, more than once.
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On heads-up NL 25/50 a 284bb/100 hand intervall is possible every 20 million hands. However to get a 481bb/100 hand intervall you have to look at approximately 2000 trillion hands.
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Thanks for the update. There is a big problem though with your approach that you might not have thought about.
Your are trying to estimate a persons win rate from a small sample of hand where he obviously runs extremely hot. This means that the cards did not fall in a very representative manner and your confidence interval is only valid when you hit your cards that good.
I suggest that you use another approach instead. Say that this person has a negative expected winning of -20ptbb/100 with a SD of 270ptbb. What are the probability that such a player makes 284ptbb/100 in 190 hands? And when you have that probability, try to estimate the probability that such person could be found in the poker community's collective PT-.DBase for High stakes poker.