Re: Modeling hand distributions from shown-down hands
As a purely theoretical matter, even if a player's strategy is constant and nonrandom, you could not deduce it even from an infinite set of observations. You obviously could deduce the situations in which the player goes to showdown, with a large enough sample you would observe all of them. This would allow you to make some inferences about folded hands, for example if a player ever shows A9, then you know she doesn't always fold A9 preflop.
But suppose a player always bets 72o preflop and folds it postflop, and always folds 73o preflop. You would have no way of distinguishing this from a player who does exactly the reverse. Neither hand will ever be revealed, and since they are exactly as common, there's no way to tell the difference based on frequency.
Therefore, unless a player shows down every hand, you will have to make some strategy inferences from reasonability assumptions, even with an infinite sample.
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