optimizing calling all-in in a heads-up, all-in or fold poker model

[PrayingMantis]

[ QUOTE ]
But now I'm concerned about your (and OP's) observation that a calling strategy's optimality is a function of play from the SB. Possibly strongly so.

So how about this:

Otherwise full-scale, preflop all-in or fold tournament poker with a fixed blind. Given a blind size and an opponent's strategy (choosing from some reasonable set of benchmarks), can we formulate a counterstrategy with a small number of parameters, and optimize the parameter set for countering such an opponent?

Benchmark opponent strategies:

1) Always push, always call (a weak benchmark opponent)
2) Push top 50%, call top 50% (a better benchmark opponent)
3) Push top 75%, call top 25% (a "gap" player)

Some counter strategy assumed forms, off the top of my head, inspired by your calling strategy form:

1) Push top N%, call top N%. Optimize N for $EV.
2) Push top N%, call top M%. Optimize N,M (is there a gap? how big?)
3) Push N*S/T%, call N*T/S%, where S is your stack and T is total chips.
4) Push f(S/T)%, call g(T/S)%, optimize functions f,g over some low-dimensional parameterization.

(All "top N%" references mean avg win rate against a randomly chosen hand)

Is this going somewhere?

[/ QUOTE ]

This looks more interesting than your original model, IMO, and much more "realistic" (despite the fact that the blinds are equal and fixed).

One question: will it be possible (or how difficult will it be), to also try and test hero's strategy as a "direct" function of opponent's (and part of hero's himself)?

For example: If opponent pushes top A%, and calls top B% (where you state 50/50, or 75/25 or any other two numbers), can you state N% (for hero's pushing standarts) and see how optimal M% (hero's calling standarts), is a function of A,B and N? or vice-versa, i.e., how optimal N is a function of A,B and M?

I don't really know exactly how your model is executed, so in other words, I'm asking whether it is possible to decide that for each set of simulated tournies, A and B of opponent's will be two fixed random numbers, N will be a fixed random too, and only M will be a variable, so you can maybe figure optimal M for maximizing $EV, as a function of A,B and N, and try it later (this approximation of f) on other fixed A's, B's and N's, in more and more sets of simulated tourneys?

PrayingMantis

[Mergualdo]

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Hmm. I don't follow you.

[/ QUOTE ]

I think I'm saying the same thing as Bozeman and Praying Mantis.

[eastbay]

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This looks more interesting than your original model, IMO, and much more "realistic" (despite the fact that the blinds are equal and fixed).


[/ QUOTE ]

Not equal, just fixed.

[ QUOTE ]

One question: will it be possible (or how difficult will it be), to also try and test hero's strategy as a "direct" function of opponent's (and part of hero's himself)?

For example: If opponent pushes top A%, and calls top B% (where you state 50/50, or 75/25 or any other two numbers), can you state N% (for hero's pushing standarts) and see how optimal M% (hero's calling standarts), is a function of A,B and N? or vice-versa, i.e., how optimal N is a function of A,B and M?


[/ QUOTE ]

I think this would be reduced to a curve-fitting exercise through some trials values, which would probably be good enough to see the general trendlines.

eastbay

[Bozeman]

Oops, I meant instead 1/(A*S/B+1), where A is the variable in the the strategy.

Maybe e^(-A*S/B) would be better.

Craig

[Moonsugar]

Because I know. The situations come up all lthe time. Period.

[Moonsugar]

For instance, check:

http://forumserver.twoplustwo.com/sh...;sb=5&o=14