[eastbay]

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Why is it necessary to simulate this? For given stack sizes and blinds, one can directly compute which hands have positive EV for the optimizing player, right?


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Because chipEV != $EV, amongst many other reasons. And even were the simulator and optimizer overkill for this particular problem, I mostly wrote them because they extrapolate to more sophisticated problems where direct methods would be impossible.

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Ah, no, I see. Given the non-optimizing opponent is giving away EV every hand, it may be optimal to pass on certain low EV situations.


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Sure. The classic "why are tournaments different than cash games" thing.

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But then the set of calling hands must optimally be contingent on relative stack sizes and blinds. I get the impression from your post that you are trying to find the optimal set of hands given you are going to suboptimally play the same set of hands regardless of the particular situation.


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In my initial formulation, the strategy remains fixed for the tournament - that's just currently a constraint of the strategy. You're right that this is clearly not perfect; if you've got pot odds after almost taking someone out, you call with more hands. This important effect is ignored. I'll think about how to incorporate it after I get the fixed strategy results giving good answers.

If you can think of a good way to approach it, I'm certainly interested in it.

If you remember my first set of simulations that you dismissed [img]/images/graemlins/wink.gif[/img], I made the game cards-up. Then the criterion for calling was based on a one-parameter combinration of chipEV (known) and "risk" to your stack in the amount of the call.

So I wanted to take a next step with that idea that had a little more applicability. tournament endgame poker is mostly all-in or fold, which is nice, because it is potentially computationally tractable (trying to simulate flop play and beyond is extremely difficult with a zillion variables).

So, I'm certainly open to a better model which is still computable. Maybe you could assume that you know the range of hands that your opponent will push with, and compute a chipEV based on that, and make the counter strategy a function of chipEV and risk once again. That might be a better approach.

The nice thing is, I now have the simulator and the optimizer that I could plug this problem into pretty easily.

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And, oh yes, this has nothing to do with real poker. Shame on you.

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Thanks!

eastbay