[LinusKS]

[ QUOTE ]

We don't know whether Johnny is a winner or a loser. If he plays 7000 hands, dutifully does his confidence interval calculations, and then announces the 3BB - 10BB interval, we have to revise our initial estimate that he's most likely a loser. We do the sums (allow me to guess some answers here) and calculate that if he was a loser, there's a 2% chance of him registering that sort of winrate. If he's a winner, there's a 60% chance of that winrate range coming up.

So, consider 100,000 players. 99,000 of them are losers; of those guys, only 1980 will come up with such confidence intervals after their first 7000 hands. 1,000 players are winners and 600 of them will have such an interval. So, the chances that Johnny is actually a (temporarily) lucky loser are 1980 / ( 1980 + 600 ) or 77%.

Does that make you feel better?

[/ QUOTE ]

What he said.

(Minus the "feel better" part.)

Seriously, though, I'm the last thing from a math expert, but I think the Bayesian analysis is exactly right.

If you assume there's a large number of losers, and a small number of long-term winners, lucky losers will tend to outnumber true winners, even over a pretty good number of trials. Meaning confidence-interval analysis will tend to be misleading, at least when applied to a "random" player.

Yes?