[jukofyork]

I am currently thinking about this hypothetical modeling situation:

Player A
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Preflop: Always calls preflop.
Postflop: Folds unless holds nuts.

Player B
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Preflop: Only calls if holding top 13% of hands, else folds.
Postflop: Folds unless holds nuts.

Player C
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Preflop: Only calls if holding at least 1 ace, else folds.
Postflop: Folds unless holds nuts.

Player A's pre-flop hand distribution upon observation over time will be easy to model from the simple fact that it calls 100% of the time [ie: can use stats to work out P(model is always call) {assuming we allready have the hypothesis that Player A always calls...}] and we never need observe the hands they showdown to know their pre-flop hand distribution.

BUT: Player B's and Player C's pre-flop hand distributions will be vastly different, but if only the % of time they call pre-flop is used to attempt to model this ditribution, then Player C's non-linear stratergy will not be observed from this variable alone.

BUT (even more importantly!): If we attempt to model Player B's or Player C's pre-flop hand distributions based on the cards they showdown (ie: WITHOUT any hypothesis about their actual pre-flop stratergy), then our distribution will be VERY wrong based on the fact that stronger initial hole cards are more likely to make it to showdown.

For example, consider Player C's stratergy:

If player C calls with 'any ace' only, then at showdown (assuming he only ever calls down if holding the nuts postflop) we will observe many more AK's than we see A7's, more A2's than we see A6s, more AKs's than AKo's, etc. Even after (infinitly) many samples, our distribution will still be bisased towards the stronger hole cards and thus incorrect.

Any Ideas on how this observered distribution could be 'transformed' to account for stronger hole cards making it to showdown more often (again assuming no hyposthesis, only obervation)?

Also, even considering if we knew exact EV of every holding, could this be used for the 'transform' somehow?

Thanks in advance - Juk [img]/images/graemlins/smile.gif[/img]