Re: To the naysayers
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I'm not sure where I stand on this, though to be honest I can't think of an intuitive reason why stack value would follow some form of S-curve. Or are you intending to try to fit it to just a section of the logistic curve?
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My theory is that it does follow an S-curve, because I believe the value of your stack is related not only to its size, but the rate at which you can continue to grow it, which reduces as your stack gets large relative to the field.
I contend that each chip you add DOES add value, but chips you can invest in a hand are of greater value than those you cannot, assuming you are a winning player.
The trouble with linear models is that they start with the false assumption that everyone is equally skilled. My main goal in this effort is to find a formula that models the things that ICM are missing:
1) Blind size
2) Field size
3) Relative skill
4) Forward-looking equity
I believe the logistic curve provides a way to model all of these things in an efficient and intuitive manner. For example, have another look at the page and consider the growth-rate parameter. I propose setting this to a value proportional to your relative skill level in the field. The result would (hopefully) predict how fast you can continue to grow your stack. And that must say something about your chances of winning the tournament.
My plan is to work with the parameters until I get a curve shaped like I believe the true shape should be. Then I will test it against tourney data I collect.
By the way, I don't intend to focus on the winner-take-all scenario forever. That was just a starting point.
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On a separate note, I have a question for curtains. Are you then of the opinion that we already have a satisfactory model for MTTs in ICM, but that it simply isn't all that useful because of the extra effort involved in using it with so many players, and the vastly larger number of possible scenarios?
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I'd love to hear the answer to this in light of ICM's deficiencies that I list above.
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