Well, OF COURSE that selection of hands would show an abnormal distribution.

Any sampling that is a result of choice, is going to be abnormal.

All those hands that you chose not to run to the river and show would be missing from the sample, so any kind of analysis for finding a normal distribution is impossible.

The fact that you would even offer that as the term of the bet, just tells me you don't have a clue about how random sampling for statistical analysis even works, for determining a normal distribution of a random number generator, and the cards that are being dealt.

You need every card dealt, for every hand, for every table, for a crapload of rounds that were played. Not just the ones that you thought would have been good enough to win, regardless of the other players' choices to hold or fold.

-- Smoov