[Josem]

[ QUOTE ]
Say a few weeks ago you sat down at a table with Graycat HU, and after the session you asked yourself did that guy see my holecards. The a priori distribution is whatever probability you thought he had of seeing your hole cards before you sat down with him. 1 in a million? 1 in a billion? or whatever.

[/ QUOTE ]

I don't understand; this does not make sense to me. Why does have a pre-existing estimate of the chance you were cheated matter?

[ QUOTE ]
Then you analyze the session to adjust that a priori probability based on the data. But in doing so, you need to realize that your data is biased, because you don't do this analysis after every session. But if you sit at a table with Graycat right now and play until he quits you (or play until a prescribed number of hands, and throw out the sample if he quits you earlier), and analyze based on those results, good or bad, then you won't have selection bias.

[/ QUOTE ]

My criteria to minimise selection bias will be every accessible heads up hand history vs him. While there will be "selection bias" in favour of hands played with people who browse 2p2 and similar sites (and thus, able to provide the data), I don't see how such a bias is likely to distort the outcome.

We're studying a phenomenon that has already happened. Judging by the crazy chip dumping after this thread became public, any future play will be contaminated by this very study/thread/publicity.