The ICM is not all its cracked up to be

[pzhon]

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If you are playing a game like stud where position is determined by a card, then there is a strategy for each table limit which at least breaks even against any opposition. Following this strategy (paying attention to the size of the smaller stack, not who has it) means you will not lose chips on average. Since at the end of the game, you have all of the chips or none, not losing chips on average means you will win with probability at least as great as the fraction of the chips you hold.

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Now, I would be very interested in the proof of the above statement--and in knowing what the optimal heads-up strategy is. Any references for this?

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It's just von Neumann's minimax theorem from 1928. That theorem says there is an optimal strategy (in a 2-player zero-sum game with finitely many pure strategies). Symmetry says the value is 0. This does not say what the strategy is. <font color="white">If you want to allow fractional bets, von Neumann's theorem extends to compact games.</font>

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It seems to me that the strategic options of the small stack become severely limited when his stack is small relative to the blinds.

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If your intuition leads you to think the large stack should accumulate chips heads-up, you should revise or disregard your intuition.

[PrayingMantis]

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It seems to me that the strategic options of the small stack become severely limited when his stack is small relative to the blinds.

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(Edit to say I'm replying to JNash statement, not your post, pzhon.)

This is a rather simplistic way to look at it. In many situations it goes both ways. Actually, in many situations, small stacks will have some tactical advantages against bigger stacks.

As to HU situations, the idea that generally the small-stack is forced into a tighter game (which you mention a few times), and that the big-stack bluffs and steals more, is wrong, for a few reasons. Especially since if they both understand EV, small stack will not play to survive, and therefore will not be easy to bluff. On the contrary. And what you suggest can actually work both ways, again: there are players who will play tighter as big stack HU, because they don't want to double-up the small stack. In these cases, small stack will play a wider range of hands, will bluff and steal more, and force *big-stack* into folding.

[rachelwxm]

zephyr,
Thank you for provide some challenges to ICM. Just like Newton’s law in physics was taken granted for a few hundred years. We need to reexamine ICM from time to time. I think we all agree that it is probably the best tool out there that handles chipev-ev. After reading some of the posts, here is my thought ( I am not a defender of ICM)

1. ICM assume equal skills. Seems most of your critic are about unequal skills assumption of ICM. Of course, every player believes he is better than the field. If you take ICM as a guide of your ROI (-9%), nobody would ever play this game! Then why we still use ICM? Because it is an objective way of measure a fair game.

Take another example u mentioned, two guys HU with equal stack, ICM gives same ev for each two. Let’s say one has a ROI of 35%, the other has 20%. How does the extra added info help you solve the problem? What if one guy w 35% is excellent early-mid stage player while poor HU player? The only FAIR method fit your need is to let those two play HU SNG 100000 games and see average PNL. Can you?

2. I don’t think blind size is a limit of ICM. It at most increases std not average.
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[tubbyspencer]

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Also, I recommend reading the chapter "Freezeout Calculations" in TPFAP. I hope it's okay that I quote the first sentence:
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It is a common conception that your chances of winning a tournament against equally skilled players are equivalent to the fraction of the total tournament chips that you hold

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Sklansky then goes on to explain why this must be the case.


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I went back and read it, and you're right. It explains why your chances of WINNING are exactly proportional to the number of chips you have divided by the total in play.

But the last paragraph of the chapter states

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Unfortunately, there is no equally simple technique to calculate the chances of coming in second, third, etc. based solely on the chip count. There are, however, some good ways of estimating these probabilities.

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Isn't this where the ICM breaks down?

That along with not factoring in the size of the blinds (which has already been mentioned) ?