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#21
05-09-2005, 12:16 AM
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Re: Testing ICM -- some questions for discussion
Sure. My understanding is that the issue in question (the linearity of the equity function) is basically the same as saying that someone with x% of chips in a HU freezeout with someone of equal skill will win x% of the time. My point is that if that premise is false, to disprove it does not require extensive data collection. All you have to do is to construct a scenario where someone with x% of the chips wins something other than x%.
That says nothing about the s-curve or any other possible shape for the equity function. But if it can be done, it shows that the function is not linear in all cases. 
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#23
05-09-2005, 12:26 AM
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Re: Testing ICM -- some questions for discussion
[ QUOTE ]
What I said is not a matter of opinion. [/ QUOTE ] No, but some of it is incorrect, specifically the part about the whole point of making measurements being to validate a model.
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#24
05-09-2005, 12:28 AM
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Re: Testing ICM -- some questions for discussion
[ QUOTE ]
. All you have to do is to construct a scenario where someone with x% of the chips wins something other than x%. [/ QUOTE ] This is a very vague statement. We can construct scenarios where opponents have equal chips but one always loses, because the other one has AA. This isn't what you mean, but you haven't nailed down what you mean. What eastbay and I are trying to get at is that you can't nail down what you mean in any way that will answer the original question. Any calculation or simulation you make will have to assume certain strategies, certain values of the blinds, etc., and now you're not really talking about heads-up poker, you're talking about a model of heads-up poker.
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#25
05-09-2005, 12:29 AM
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Re: Testing ICM -- some questions for discussion
[ QUOTE ]
[ QUOTE ] What I said is not a matter of opinion. [/ QUOTE ] No, but some of it is incorrect, specifically the part about the whole point of making measurements being to validate a model. [/ QUOTE ] Uh... whatever. Do you know what ICM is? Do you understand what validating a model means? eastbay
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#26
05-09-2005, 12:40 AM
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Re: Testing ICM -- some questions for discussion
OK. I see what you are saying. My understanding was that Sklansky's assertion was basically that over a large number of trials those things really didn't matter, so long as the players were of equal skill. If this is not what he is saying, then you are correct -- what I said can't be done.
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#27
05-09-2005, 12:49 AM
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Re: Testing ICM -- some questions for discussion
[ QUOTE ]
Do you understand what validating a model means? [/ QUOTE ] Yes. I have been doing academic research for the last 9 years, developing and validating models and publishing the results. There are lots of reasons to take measurements and lots of ways to validate models. They are not one and the same. Like I said, we agree to disagree.
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#28
05-09-2005, 12:53 AM
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Re: Testing ICM -- some questions for discussion
[ QUOTE ]
[ QUOTE ] Do you understand what validating a model means? [/ QUOTE ] Yes. I have been doing academic research for the last 9 years, developing and validating models and publishing the results. There are lots of reasons to take measurements and lots of ways to validate models. They are not one and the same. Like I said, we agree to disagree. [/ QUOTE ] By definition there is only one way to validate a model: make measurements. You may be confusing validation with verification or you may use the word in some kind of sloppy way which considers model to model comparison "validation." I don't, I expect anyone who is involved in academic research to know better. eastbay
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#29
05-09-2005, 01:16 AM
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Re: Testing ICM -- some questions for discussion
For lack of a better thread to put it (this is enough of a triviality that I don't feel it merits its own complete post), here's an argument regarding heads-up linearity. It's not a very complicated argument at all, but it at least backs up the intuition that % stack should equal % win in a particular case. This is the kind of thing that seems very intuitive to me, but I'd never looked at any kind of argument for why it had to be.
The case that I'm considering is simple move-in poker - two players, with stacks x and y (assume without loss of generality that x > y), both go all-in every turn. Since they are pitting two random hands against each other, each has a 50% chance of winning each confrontation. We can now easily show that the equity formula E(x) = x / (x + y) is consistent. Half of the time stack x wins, half of the time stack x ends up in a new game with stacks x - y, 2y. So, E(x) = .5 + .5 E(x - y) = . 5 (x + y / x + y) + .5 (x - y / x + y) = x / (x + y) Notice that if we choose some kind of screwy function, like E(x) = 1 if x > y, 0 otherwise, for example, we don't necessarily get this consistency. So it's a strong argument that % stack = % win works for this particular situation. Also, it's important to note that this just assumes a relatively braindead strategy of pushing and calling every time; an actual game is more nuanced, which is where the argument comes in.
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#30
05-09-2005, 01:38 AM
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Re: Testing ICM -- some questions for discussion
This thread is in full hijack mode largely because of me, so this will be my last post on the subject.
Yes, I am all too familiar with verification and validation. I understand everything you have said, and I disagree with the points I noted. You think I am completely wrong, and I am fine with that. Life would be boring if we all agreed on everything. All the best. [img]/images/graemlins/smile.gif[/img]
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Linear Mode
