Does ICM amd/or Computers Count Each Opposing Stack SpecificallY - Poker Theory

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Does ICM amd/or Computers Count Each Opposing Stack SpecificallY

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04-29-2024 , 09:35 PM

David Sklansky

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Join Date: Aug 2002 Posts: 17,116

Or does it merely count (before the hand starts) your stack, plus input prize money, the number of players left, and the total number of chips facing you. In other words, does it come to a different conclusion if you have 10K and four players have 12K each, than it would if the stacks were 25K, 12K, 8k, and 3k? If, as I suspect, the ICM and solvers don't distinguish between these cases (at least for those times when some players have already folded or the hand hasn't started yet) then I have something to write about in my next Card Player column.

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04-30-2024 , 01:05 PM

tombos21

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Join Date: Sep 2018 Posts: 2,061

ICM distinguishes between those two things.

It calculates the probability of every stack placing in every position.

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04-30-2024 , 04:17 PM

David Sklansky

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Join Date: Aug 2002 Posts: 17,116

I don't think you answered my question. I wanted to know if it took into account the difference in correct strategy based on, among other things, how close last place is to busting out. In other words does it assume the second highest stack is less likely to tangle with the highest stack if the smallest stack is tiny, as compared to when the total chips of the three smaller stacks add up to the same thing but the smallest stack is bigger.

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04-30-2024 , 05:47 PM

tombos21

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Quote:

Originally Posted by David Sklansky

This isn't what you asked in the original post.

But no, ICM doesn't account for collision rates, the size of the blinds, the player's strategies, positions, etc.

ICM is just a function that converts stacks into placement probabilities in a vacuum. It is known to slightly underestimate the value of the chiplead for the reasons you've posted.

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04-30-2024 , 06:03 PM

tombos21

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Imagine each player is dealt a random number between 0 and 1.

They take that value and raise it to the power (average stack / their stack). This new number is their final score.

The player with the highest final score wins first place. The player with the second-highest score wins second place, and so on.

The probability of placing 1st, 2nd 3rd, etc, in this game, is identical to your ICM probability. Note that it doesn't look at anything other than the size of each stack.

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04-30-2024 , 06:24 PM

David Sklansky

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Join Date: Aug 2002 Posts: 17,116

Quote:

Originally Posted by tombos21

OK. But the point is that the tiniest stacks that may have already folded changes the strategy and thus changes the results. If the stacks for 500,300,200 prizes and the stacks are 10k, 10k, 5, 5, and 5 and you are in the small 100 blind and the other big stack is the big blind you should push with everything since the big blind can only call with aa or kk since he is risking about 400 to win about 100 and you are only laying 33 to 1. This would even be true if you had a few dollars less than the leader.

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05-01-2024 , 01:57 PM

tombos21

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Join Date: Sep 2018 Posts: 2,061

Quote:

Originally Posted by David Sklansky

To clarify, ICM doesn't determine strategy. It's just a utility function - a thing that changes the value of outcomes. We plug that utility function into a solver to determine strategies.

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05-01-2024 , 05:01 PM

David Sklansky

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Join Date: Aug 2002 Posts: 17,116

Quote:

Originally Posted by tombos21

To clarify, ICM doesn't determine strategy. It's just a utility function - a thing that changes the value of outcomes. We plug that utility function into a solver to determine strategies.

My original question included solvers. Are there any solvers that take into account the fact that there are tiny stacks out of the hand that change your strategy against a big stack?

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05-01-2024 , 08:13 PM

GreatWhiteFish

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Join Date: Oct 2013 Posts: 346

Quote:

Originally Posted by David Sklansky

My original question included solvers. Are there any solvers that take into account the fact that there are tiny stacks out of the hand that change your strategy against a big stack?

There are. Hold em Resource Calculator is capable of calculating ICM-adjusted strategies both pre-flop as well as post-flop. You enter the payout structure, stack size distribution including positions on the table, and HRC calculates ICM-adjusted equilibrium strategies.

One interesting caveat is that while a chip-EV GTO strategy is "unbeatable," the ICM-adjusted strategy presumes that you're playing against rational opponents who will fold appropriately based on ICM considerations. If our opponent commits ICM suicide for example by calling our shove too wide it can cause a loss of EV for both them and us.

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05-02-2024 , 10:57 AM

#10

plexiq

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Join Date: Apr 2007 Posts: 2,557

Quote:

Originally Posted by David Sklansky

My original question included solvers. Are there any solvers that take into account the fact that there are tiny stacks out of the hand that change your strategy against a big stack?

Yes, ICM based solvers will take all remaining stacks into account, not just the ones that are still live in the current hand. That includes players that folded, or even ones that are on another table entirely.

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05-02-2024 , 03:25 PM

#11

David Sklansky

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Join Date: Aug 2002 Posts: 17,116

Quote:

Originally Posted by GreatWhiteFish

One interesting caveat is that while a chip-EV GTO strategy is "unbeatable," the ICM-adjusted strategy presumes that you're playing against rational opponents who will fold appropriately based on ICM considerations. If our opponent commits ICM suicide for example by calling our shove too wide it can cause a loss of EV for both them and us.

Actually, in situations where the first player should push with bad hands while the second player should fold to him with good hands, a rational second player should push out of turn since he is forced to keep the money in. Bet your favorite solver doesn't take THAT into account.

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05-03-2024 , 01:17 AM

#12

GreatWhiteFish

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Join Date: Oct 2013 Posts: 346

Quote:

Originally Posted by David Sklansky

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