[elindauer]

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Your assertions would also seem to imply that DERB can not run a confidence interval on his own stats.

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Yes, I wrestled with this as well.

First of all, let's note that just because your confidence interval calculation is invalid, it doesn't mean that DERB is a loser. I happen to think it's likely he is a losing or break-even type player and he's on a major hotstreak, but I haven't given any proof of this. This is just speculation based on the few hands I've seen posted. All I've "proved" is that a confidence interval calculation is invalid in this instance when it comes to pinning down this guy's true win rate.


Ok, moving on. DERB of course chose his own stats randomly beforehand, so he does have an unbiased view of his own stats. So he believes, correctly, given the information he has, that he is 99.7% likely to be a winner.

I think the reason we can put him at a much lower percentage than this is that we have more information than DERB, or at least, than the hypothetical DERB that just naively runs a confidence interval on his play with no other thought. Here are the things we know that his simple calculation does not take into account:

1. he is the farthest outlier in a large sample of datamined players. This virtually guarantees that he is on the very high side of the variance. It's virtually impossible that this one guy has a true win rate ten times higher than anybody else and is running bad. Right? In his simple worldview, he is just as likely to have below average results as the very best.

2. we can analyze the hands he's playing and see that he's making substantial mistakes that aren't consistent with someone winning this much money. The poker information contained in the hands we see him play is much more convincing and "converges" much faster than the rather naive confidence interval calculation DERB is doing himself. I made another post on this a while ago. If you look at the hands and see that a player is making major mistakes, that's a much better indicator than a confidence interval of a player's true win rate. DERB is making these mistakes himself so he probably cannot recognize them as a major indicator that he is just one of the 1 in 600 players or so that will run this good, and not the world beater his confidence interval calculation suggests.

Hope that helps.
-Eric