Inducing Call% thresholds from observations

[jukofyork]

If we assume a very simple-minded limit player who uses a single threshold to decide upon either folding preflop or calling all the way to the river (eg: if the player's preflop handrank is < X he will call, else he folds), then which of these methods used to induce the threshold will converge quicker:

<u>Method A: Using observed action frequencies only</u>
1) Observe the player playing and keep a record of the number of times they fold and the number of times they call.
2) Induce the threshold by calculating: calls/(calls+folds)

<u>Method B: Using observed hand rankings only</u>
1) Every time a player calls, note the hand rank of the cards they called with (0=best / 1=worst).
2) Work out the mean hand rank you have observed the player calling with.
3) Induce the threshold by doubling the mean (eg: an observed mean of 0.1 would indicate they are using a threshold of 0.2, etc).

NOTE: If he folds we don't get to see what he is folding, but because he calls all the way to the river we always get to see what he initially called with (hence why method B is possible).

NOTE: Ignore the fact that the handranks are not uniformly distributed between 0 and 1 (assume they are for this).

I haven't really thought about this very hard/carefully yet, but it seems that intuitively Method B should converge quicker than Method A. If this is true, then:

A) How can this be quantified?

B) If we were told what the player was folding then could a "Method C" be created which converged even quicker?

C) Can the frequency method and the handrank method be combined to converge even quicker than either on their own?

Juk [img]/images/graemlins/smile.gif[/img]