Re: Testing ICM -- some questions for discussion
 

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As a lawyer, I'm continually surprised by how much information you can get by simply asking. Assume that an online site were willing to assist. What and how much information would you be looking for?

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The size of the blinds at the time the match gets to be HU seems like it would be a relevant factor.

One issue that interests me about the data collection is how many data points one should take from each tournament. Let's say I play 20 hands heads up against my opponent; should we use this as 20 data points? My gut feeling is no, we shouldn't, because any deviations from average behavior become magnified.

As an oversimplified, unrealistic example of what I'm talking about, say I get heads up with blinds of 100, my stack being 2000, villain's stack being 8000. Now let's say he's ridiculously tight, so tight, in fact, that he'll fold anything but aces. Now I should win this just about all of the time, and so I'm going to skew the data horrendously if you take multiple data points from this tournament that show my small stack overcoming a major disadvantage and winning.

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Intuitively I agree that only one data point is permissible on independence of observations grounds. I'm not sure how to prove it, but I'm not sure that it needs proving.

eastbay

Re: Testing ICM -- some questions for discussion
 

If the linearity theory is indeed false, it would not be hard to disprove. You only need to do an analytic or simulated solution for three data points under one set of conditions. If you find a non-linearity in those (which I'm sure can be done given a correct choice of data points), then the equity function must be non-linear. In other words, you basically only need one counterexample.

On the other hand, I would think "proving" the s-curve hypothesis would be quite difficult.

Re: Testing ICM -- some questions for discussion
 

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If the linearity theory is indeed false, it would not be hard to disprove. You only need to do an analytic or simulated solution for three data points under one set of conditions. If you find a non-linearity in those (which I'm sure can be done given a correct choice of data points), then the equity function must be non-linear. In other words, you basically only need one counterexample.

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I'm not clear on what you mean by this. The whole point of the exercise, as I understand it, is to see how well the analytical models match up against reality. Whether or not some specific model predicts linearity isn't really the question, but it seems to me that you're suggesting doing calculations to determine just that.

Re: Testing ICM -- some questions for discussion
 

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The whole point of the exercise, as I understand it, is to see how well the analytical models match up against reality

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To me, data collection simply tests the assumption of symmetric players. If you assume symmetric players, the problem can be solved analytically (or approximated via simulation).

Re: Testing ICM -- some questions for discussion
 

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To me, data collection simply tests the assumption of symmetric players. If you assume symmetric players, the problem can be solved analytically (or approximated via simulation).

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In what model? I still think you're missing the point.

Re: Testing ICM -- some questions for discussion
 

Seconded.

Don't confuse models with reality. The whole point of making measurements is to validate a model, whether it be a relatively simple ICM or a more involved full-scale simulation.

eastbay

Re: Testing ICM -- some questions for discussion
 

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One issue that interests me about the data collection is how many data points one should take from each tournament. Let's say I play 20 hands heads up against my opponent; should we use this as 20 data points? My gut feeling is no, we shouldn't, because any deviations from average behavior become magnified.

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Intuitively I agree that only one data point is permissible on independence of observations grounds. I'm not sure how to prove it, but I'm not sure that it needs proving.

eastbay

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I don't see how this would create a bias in the data. You would be doing this for every tournament so the fact that you have 20 points of data from one tournament where one player was exceedingly tight is countered by the fact that you have hundreds of points of data from just a few dozen tournaments where players were reasonably loose.

Re: Testing ICM -- some questions for discussion
 

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I don't see how this would create a bias in the data. You would be doing this for every tournament so the fact that you have 20 points of data from one tournament where one player was exceedingly tight is countered by the fact that you have hundreds of points of data from just a few dozen tournaments where players were reasonably loose.

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But consider that in loose contests, it's likely to end faster, so you will have proportionally fewer data points for the same number of SNGs. I think the simplest thing is just to take one data point per tournament.

Re: Testing ICM -- some questions for discussion
 

We agree to disagree.

Re: Testing ICM -- some questions for discussion
 

Can you please explain in the most simple English possible what precisely it is that you're going to do, perhaps by laying out in detail what calculations you think you can perform and what they'll demonstrate?