The ICM is not all its cracked up to be

[zephyr]

There has been a recent resurgence in the volume of posts that use the ICM for analysis. Most of these post have been well thought out with the hand analysis' verging on brilliance.

However, I just wanted to mention a note of caution. Although the ICM is a clever variable transformation from CEV->$EV, it should be noted that it is by no means a perfect mathematical representation of this aspect of the game. A proven mathematical transformation from CEV->$EV is very very far away.

Also, I think results obtained from doing an analysis as illustrated in dethgrinds recent post should only be taken as a very rough estimate. I think the thought process is good, with the critical step being the range of hands that you put your opponent on. Personally, I'd always trust my gut over the number I crunch though.

I'm not trying to critize the ICM as a method of analysis, but am just pointing out the fact that it is only a rough estimate.

Only my opinion,

Zephyr

[Solitare]

My vote for the biggest weakness in the ICM is that it doesn't take into account the size of the blinds. For instance, if you have 500 on the bubble I would think your EV is larger if the BB is at 50 than if the BB is at 200.

I think this is particularly relevant to the SnGs we play given the blind structure.

[RacersEdge]

What exactly does ICM say?

[stupidsucker]

Although I agree that the ICM can certainly use some adjustments, its not perfect ... but..

It's still the best weapon we have to calculate $EV opposed to chip EV. You cant come on here and say its bad and not give reasons why or try to make suggestions on how it can be made better. Got any better ideas?

It lacks in a few areas.

#1(as stated by a previous poster) The blinds make a difference. They make a fairly huge difference.

#2 Skill level has been mentioned before, but this is near impossible to factor in. My roi is about 30% ITM about 40% so I know that my %of the prizepool is higher then 10% when I start, but how can you weigh this?

#3 Stealing fear. I dont think it takes into account certain plays like big stack stealing when you are on the bubble and a short stack is there against some mid stacks

All things aside, I see the ICM as one of the best tools we have. With time will come improvments. A lot of work went into making it(I assume). I know one of the people involved with creating the ICM and I trust his math skills much more then I do my own.

[zephyr]

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You cant come on here and say its bad and not give reasons why or try to make suggestions on how it can be made better. Got any better ideas?

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I'm entitled to come on here and say whatever I feel like. But alas I wasn't posting on the qualifications of those who proposed the ICM, nor do I want to get into a debate over whose math skills are the best. I agree that it is a powerful tool for transforming CEV into $EV, but the point of my post was only to remind people that it is nevertheless a very crude and over simplistic technique.

In addition to the points mentioned by you I think one of its biggest pitfalls is its assumption of linearity.

Say it's heads up with each opponent holding 5000 chips. ICM says that with equal skill, each opponent has a 50% chance of getting first and a 50% chance of getting second. I agree with this. Next, if opponent 1 now holds 7500 chips to the others 2500, the ICM would give opponent 1 a 75% chance of finishing 1st and a 25% chance of finishing second. I do not necessarily agree with this.

I have a problem with: chance of finishing 1st = Chips/Total Chips

Why do we choose a linear relationship?
What other options do we have?

In the simple case of two players heads up I think that

chance of finishing 1st = f(stack size, blind size, position, skill level, opponents tendencies, play of previous hands, etc.)

Where some of these quantities are not quantifiable.

I'm not terribly familiar with the derivation of the ICM, but am certain that a great many assumptions are made. I'm curious to hear for what range people believe it’s valid. Say for example:

4 players: 1-2000, 2-3000, 3-1500, 4-3500,

ICM gives Opponent 4 $EV=0.31

How accurate is this? Within what confidence range? 95% of the time will you be between 0.29 and 0.33 or between 0.25 and 0.37?

Has anyone conducted experimental trials on it? Say recording the chip count when it gets down to 3, calculating your $EV from the ICM and then comparing this prediction with the actual outcomes?

Again, I agree with you that it is currently the best means of going from chips to $. It just tickled me the wrong way when people began posting matter of fact solutions to situations that by nature do not have precise solutions. I'm no longer familiar with the progress of game theory as it relates to games of incomplete information, but don't think that it’s advanced to the point where such problems can be solved analytically in a general sense.

Only my opinion,

Zephyr

[AleoMagus]

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I'm no longer familiar with the progress of game theory as it relates to games of incomplete information, but don't think that it’s advanced to the point where such problems can be solved analytically in a general sense.


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Why, when it can be done for so many other poker problems?

The point is, we are not talking about a game of incomplete information once we specify all the incomplete variables.

If, for example, I assume in a situation my opponent will call with EXACTLY 17.9% of hands in a bubble scenario, the artificiality of ICM rests primarily with this assumption, not with the theory itself (though it may well be flawed also).

I guess that I just think you are criticising the wrong thing. I can see how criticisms might be levelled against the kind of reasoning I gave in the Blind stealing theorem discussion. For anyone unfamiliar with what I'm talking about, I gave a fairly precise set of push-stealing hands assuming roughly equal stacks between SB/BB and being folded to in the SB.

Well, I most definitely might have been wrong about those hands as a general guideline, because they were in no way aimed at solving a general kind of problem.

I assume EXACTLY what my opponent will call with in that spot. How is it a problem of incomplete info if I make this assumption?

If we look at a more mundane, pot equity calculation in a ring game holding a flush draw vs a made hand, we also make exact calculations and nobody ever complains about those calculations in this game of 'incomplete info'. Why? Because we make precise assumptions about all of the incomplete info, thereby filling in the blanks. If we want, we can even put a confidence level on a range of possibilities in order to fill in the missing data, just as we do when using ICM.

What am I saying exactly? Your 'gut feelings' about a situation do not invalidate ICM. They merely augment the assumptions that you put into the equations.

Any thoughts?

Regards
Brad S

[zephyr]

Perhaps you are not entirely familiar with game theory (not that I am an expert), but the reason for using it in the game of poker for example is that it eliminates the need to make rational judgments of what the opponents hold.

The examples that you stated in your post are not actually examples of game theory, but are rather examples of basic mathematics.

Calculating pot equity, or using the ICM are not examples of game theory. While these give mathematical approximations to parts of the game, game theory offers a solution to the game as a whole. I know the boys over at the U of A in Edmonton are doing a fair amount of research on these topics.

In theory a computer could be programmed to play poker perfectly. When I say perfectly, I don't mean that the computer would necessarily win the most $/hands, but that the computer would be impossible to beat. Of course the computational power needed for this is very very far away, and may never be realized.

Although many of us want to believe that poker is infinitly complex, it is really only a finite game. The hypothetical game theory computer would not adjust based on its opponents, would not model them, would not use pscychological ploys. It would play strictly according to game theory and would be impossible to beat.

On the topic of incomplete information: poker is a game of incomplete information by nature. Whether we put our opponent on a hand or range of hands it does not change the fact that the game is one of incomplete information.

Back to the ICM. I don't know why everyone believes that the ICM is theoretically correct. I'm certain that its developers would never claim that. It's an approximation, and the main point of my original post was to remind people of that fact when using it for hand analysis. How good of an approximation? I don't know, but think it's a very relevant question.

As always only my opinion,

Zephyr

[zephyr]

By the way,

Thank you for your guide. It got me started on the right track when I began playing online a year ago. I'm in your debt.

Zephyr

[AleoMagus]

I should not have cut and pasted that quote at the beginning of my response to you becasue it seems to have confused things. I was not intending to defend 'game theory' as a whole (though I do think some of what you have said about it are wrong).

I was merely trying to defend the ICM and the calculations we have been doing using it's results

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Again, I agree with you that it is currently the best means of going from chips to $. It just tickled me the wrong way when people began posting matter of fact solutions to situations that by nature do not have precise solutions.


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It is perhaps this quote that I should have used, which immediately preceeded it. You claim we cannot make matter-of-fact conclusions about these problems because the situations do not have a precise solution by nature.

The thing is, if we precisely define the 'incomplete information' in these problems, we can make matter of fact conclusiuons.

Does this mean the conclusions are matter-of-fact correct? ...well, not exactly.

It means they are correct so long as our assumptions are correct, nothing more.

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On the topic of incomplete information: poker is a game of incomplete information by nature. Whether we put our opponent on a hand or range of hands it does not change the fact that the game is one of incomplete information.

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OK... but you seem to say this as a justification for you claims about there not being precise solutions to these kinds of problems.

I'll try to give a more concrete example of why I think this is wrong.

Imagine a game where I pick a number between one and ten and you wager on what number it is. This is the 'incomplete info'.

You know nothing about my number picking tendencies so you assume randomness. This is the range of possibility assumption (numbers 1-10)

I give you 20-1 odds on your guess if you want to make the wager. Should you 'call' or not?

Matter-of-factly, I'll say that you should call. Precise answer, incomplete info or not

Regards
Brad S

[dethgrind]

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I have a problem with: chance of finishing 1st = Chips/Total Chips


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In fact, this is the only assumption that is constant in every tournament finish probability model I've seen. All of which are contained in this highly mathematical post by Bozeman a while ago.

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.




[ QUOTE ]
Although the ICM is a clever variable transformation from CEV->$EV, it should be noted that it is by no means a perfect mathematical representation of this aspect of the game. A proven mathematical transformation from CEV->$EV is very very far away.


[/ QUOTE ]
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It just tickled me the wrong way when people began posting matter of fact solutions to situations that by nature do not have precise solutions.

[/ QUOTE ]

I agree wholeheartedly. Putting your opponent on a range of hands is often quite an approximation. Adding the additional approximation of the ICM could very well produce the wrong conclusion for a given situation. I think it's valuable to put something like this in your post: "if I'm correct that my opponent will have this range of hands, the ICM says this move is better by this %." I think it's dangerous to say, "the ICM says this, therefore it is the right play."

I'm glad someone has expressed some skepticism about the ICM. I'm kind of curious what Mason Malmuth and other big shots think about the kind of analysis that has been going on here.