Re: ICM problems
Well, there are a couple of other simplifications in the model that distort the conclusions, but I don't know how to fix them (at least formally). One problem is that the model treats someone's advantage over the field as fixed over time; in reality, the skill level of the players will increase with time as the weaker players tend to be eliminated more. This implies increased chip value early on, since more chips are needed to take full advantage of certain situations that will be less likely to occur later.
As regards inferior players recognizing coin-flip situations, I think the problem for them is more 'meta' so to speak, in that the vast majority of them don't realize they are inferior. Further, most inferior players won't understand the theory outlined above, though from observation it does seem that most people instinctively understand that if they're playing against someone like Daniel Negreanu their best chance is to gambol it up and go all-in even if the odds might not be the best.
Anyway, if we assume that most players overestimate their skill in a systematic way *and* that they understand the 'coin flip aversion' results of the above model on some level, it has further (perverse) implications for optimal play. (You can obtain the same results if you assume simple irrational loss aversion on the part of most players). The conclusion is that if you can threaten opponents with elimination of their entire stack, you can force them to back down from coinflip type situations (even ones where they might have a slight advantage). This means that you need a big stack yourself. If your stack is small compared to the one you are threatening the curve is too flat (not convex enough locally) to encourage folds in marginal situations. This once again suggests increasing marginal chip utility if you're a shorter stack, with decreasing utility if you're already big enough to threaten others (but the stack sizes keep increasing...). It's also consistent with the real-world observations of my brother, who plays professionally.
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