The ICM is not all its cracked up to be

[AleoMagus]

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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 %."

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These kinds of caveats are completely built into any analysis that I have seen on here lately. If this is unclear to people, then they do not understand the analysis in the first place.

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I think it's dangerous to say, "the ICM says this, therefore it is the right play

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Again, the real danger is not that people are making claims like this, the real danger is interpreting the claims that are being made in this way.

In all cases, about decisions being guided by ICM, the ONLY thing that the ICM is giving us is a CEV to $EV conversion. Nothing more.

Once we have that, all the calculations we use are the same 'range of possibility' type calculations we always use in situations that don't require the ICM at all (ring games). These calculations do not always turn out to give sound guidelines for play, but the fault lies in our assumptions about these ranges of possibility, not the calculations themselves.

This is to say that when we are wrong with this sort of analysis, our mistakes lie in our assumptions about things like (for example) what hands a reasonable opponent will call a 10xBB all-in raise with in the BB when on the bubble and covered slightly.

I don't want to sound like too much of a religious believer in mathematical models here, because really, I'm not. I simply think that people are confusing the ICM with a lot of the calculations we are performing with it's results.

As far as worrying about the approximations involved in these calculations, I don't know what to say. That's what this game is about. Forming an informed and educated guess about what an opponent holds and then making calculated decisions based on those conclusions.

Sometimes we can come up with a very small range of possibilities with a high degree of certainty and often we cannot. We do what we can though, and when our gut tells us that the result of such analysis is incorrect, what it is most likely telling us is that one or more of our assumptions are wrong. That or we are deluding ourselves.

Regards
Brad S

[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

[zephyr]

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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

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What number do you guess? What assumptions do you need to make? This is where game theory comes into play to give you an unbeatable strategy in this situation. That being to randomly choose a number between 1 and 10 (say by rolling a 10 sided die), thus giving your opposition no way of outwitting you. Do you need to make any assumptions about your opponent? NO! You would play the game if your opponent gave you greater than 10:1 odds and not otherwise. This is a very simple game of incomplete information with a trivial solution. Similar situations arise in poker. The situations that people have been analysing with the ICM are not such situations.

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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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My original post was designed to get people to question some of the asssumptions that are inherent to the ICM. There are many assumptions that were made when the ICM was developed that are NOT correct, thus it is impossible to make matter of fact correct decisions when using it.

Given the following situation, 4 players, 1-2500, 2-2500, 3-2500, 4-2500. Suppose you are opponent 4 in the big blind(400), 1 and 2 fold and opponent 3 pushes. Opponent 3 shows you KQs, and you hold AJ. Should you call?

First lets consider it as a cash game,

If you fold you are left with 2100.

If you call:

56.19% chance of winning -> $5000
0.46% of a tie -> $2500
43.35% chance of losing -> 0

So you expect a stack of 0.5619*5000+0.0046*2500 = $2821.

So you call knowing that your decision is matter of factly correct. Hence this problem has a trivial solution.

Now lets look at the same situation in a SNG.

If you fold: 1-2500, 2-2500, 3-2900, 4-2100 for a $EV using the ICM of 0.223.

If you call:

Win: 56.19% -> $EV of 0.3833
Tie: 0.46% -> $EV of 0.25
Lose: 43.35% -> $EV of 0

So this gives us 0.5619*0.3833+0.0046*0.25 = 0.216.

So by this analysis we fold thus giving ourselves a $EV of 0.223 instead of 0.216 had we called. But can we be certain that the fold is the correct move? Is it matter of factly correct? The answer is no, because the ICM has built in assumptions that may or may not be true.

Only my opinion,

Zephyr

[zephyr]

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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

[/ QUOTE ] Sklansky then goes on to explain why this must be the case.

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Slansky's argument is expectionally weak in TPFAP. I agree that with equal stacks and equal skill, each player has an equal chance of winning. His method for analysing unequal stacks is crude and unconvincing, however.

Don't get me wrong, I think that there is a very good chance that chance of finishing 1st = % of total chips, but have yet to find a substancial proof of that.

Only my opinion,

Zephyr.

[eastbay]

This is all fine and good, but I think the point remains: do you have a better idea?

Otherwise, your post seems to be useless quibbling.

eastbay

[dethgrind]

I feel kind of silly arguing this particular point any further, but here goes anyway:

Sklansky and Malmuth (actually Mark Weitzman) offer various plain english explanations for why the chance of finishing 1st = % of total chips in TPFAP and GTAOT. Their target audience is poker players with a basic understanding of some math concepts, not theoretical mathematicians. If you really want that thoroughly rigorous mathematical proof, you could do a quick google search for the gambler's ruin problem. Here is a good explanation of the problem. Here is a proof.

You might argue that poker doesn't really fit that model, or that multiple opponents change the results. Fine. Run some tournament simulations. I can give you some code if you like. You won't be surprised by the results. That won't give you proof, but at least you'll discover that you won't be able to find a significant counter-example.

You really ought to have at least one decent piece of evidence if you want to question this very basic result that has been accepted by so many very smart people.

[zephyr]

Thank you for the information in your post. It is well received.

I've been curious if anyone has done an analysis on how accurate the ICM is using tournament data. Do you know of any such investigations?

Zephyr

[Bigwig]

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Could I get a link to all this ICM business? Is it software? Help me out.

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Could someone please answer this question?

[lastchance]

ICM is independent chip model. It accurately (well, to our best guess) describes how chip EV (how many chips we have) = $EV.

This is the ICM calculator.

[stupidsucker]

Let me do my best to wrap this up.

The ICM is by no means an exact sum or perfect calculation telling you exact $EV based on chip EV. It is however a great tool in the right hands.

Everyone that has a clue about poker knows that a lot of x factors go into chip ev to $EV. The ICM can not calculate the x factors, and I dont know if anyone will ever come up with one that does. The X factors are something you have to have a brain and figure on yourself. The ICM is just a guide to tell you some bare bones facts/approximations.

And yes you are free to come here and belittle anything you want, but if you cant come up with anything constructive to add or any "better ideas" then what points do you have?

Bottom line...

The ICM is a great tool if you have the knowledge to use it properly. Some of that may take imagination. If you require prefection then poker probably isnt even a game for you. Math may be the biggest part of poker, but its not the only part, and it never will be.