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It doesn't sound like these models are doing the same thing.
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To what little I've seen of yours, it seems it does. You calculate 1st place equity by whatever equation you have, ICM uses the (mychips)/(allchips) formula and therefore has no skill bias. ICM takes it the next step and applies this formula to 2nd place, 3rd place, etc. by removing players one at a time.
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That might be good for joining them together. Or it might make them totally incompatible.
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I think they're incompatible, but the ideas from ICM can be carried over to your model.
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1) The effect of the graduated payout structure on the values of chips in the stacks.
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ICM takes care of this. I assumed you knew what ICM was, but if you don't,
here's a calculator and a short explanation.
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2) The effect of skill on the value of chips in the stacks.
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ICM doesn't take this into account by its basic linear 1st place equity equation. It has been suggested that you could arbitrarily add a certain % of chips to a good players stack, but it hasn't been well explored as far as I know.
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Based on your description above, it sounds like your method is complicated and computerized and calculates EV for chip stacks, particularly when those stacks are pretty large compared to the chips in the tournament (like 5%?) I would be very surprised if, say, a 2x starting stack is worth much less than twice a 1x starting stack.
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It does get fairly computationally intensive for large numbers of players. However, we use it all the time in the STT forum for 4-5 player situations where the money pays the top 3 and its results seem to make a lot of real world sense. Early in the tournament, I think ICM predicts you need a 53-55% chipEV advantage to call an allin in order to be breakeven $EV wise. This gap widens considerably as your approach the bubble (4 players).
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My method could care less about the payout structure; it basically wants to measure the effect of skill on the tournament. So if you are better than your opponents, your chips are worth more than their par value. How much more? That's the question.
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I think this is why your model as is would break down as you approach the money. But I think this issue can possibly be resolved...
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But it relies on an abstraction of doubling up N times to get all the chips in the tournament as its value function. So unless you can think of a good way to change that to "finish in these other places," you may be out of luck.
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Well let's say you assume you have a 2x buyin equity (this is very high for a STT, but that's irrelevant for now). That means someone else in the tournament has a -2x buyin equity (Edit: This should be: everyone else has a combined total of -2x a buyin, but just assume it's just one really bad player for now). Everyone else can be assumed to be breakeven. Say for the sake of argument it's a single table tournament with 10 people with the standard 50-30-20 payout structure. You can calculate the first place $EV of each player using your model given their stack sizes and their respectable equity variable. Well, to calculate the remaining positions, assume player A got first. Now from there subtract him and his chips out of the tournament. Now you have a "new" tournament. Calculate your equity again there for yourself and everyone, except now its for a 2nd place prize and the probability of it happening is multiplied by the probability of A getting 1st in the first place. Repeat and you solve the equity for all positions and all players.
The main difference between your model and ICM is how you calculate your chances of getting 1st place; yours takes into account a skill advantage, classical ICM does not.