[rigoletto]

Hi Eric

Thank you for taking the time. It does look like I'm wrong on this, but if I'm learning that's all good. But I still need to wrap my brain around something:

Your assertions would also seem to imply that DERB can not run a confidence interval on his own stats. I mean, we have determined that confidence intervals doesn't apply. Let's for arguments sake assume that the 100K hands we are talking about are all the hands DERB has ever played; how can the confidence interval then apply to one analysis and not another.

Aren't we confusing a (very small) sample of players (only DERB) with the sample of hands. Granted there is a relationsship between his sample of hands and the key numbers we chose him from, but does this really mean that a sample of 100K hands are rendered meaningless just because we went looking for a LAG that is a winning player?

Let's imagine I where to look up 30/18 (or there about) players with a good winrate in a huge database and I find 100 of them. Now running a confidence interval on this sample of 100 players and their 4 key stats will tell me that they are likely winners because that's why I picked them (the confidence interval is meaningless like in your coin example). But when I look closer I find that 99 of these players stat's are based on less than 100 hands while one is based on 100K hands. Doesn't this make a difference! Intuition tells me that the key figures from the guy with 100K hands are more reliable than from the 100 hand guys. It also seems to me that doing a confidence interval on the 100 hand guys will tell us that they could be anywhere from big loosers to big winners, while the confidence interval on the 100K hands points to a winner.

I can't really find a good coin analogy for this one.