This is for those who have no idea what the hell Eastbay and others have been talking about in these ICM discussions.
The typical situation is something like this:
You're on the bubble in the BB and it's folded to button who pushes, SB folds, you have a medium strength hand. Should you call, knowing that button will push with a certain range of hands?
The first step is to break down the stack sizes after each possible scenario: 1) you fold 2a) you call and lose 2b) you call and win 2c) you call and split
Then you run each of the stack size scenarios through an ICM calculator and get a dollar value for each (that link will give you a % of the prize pool which also works).
You need to weight (2a), (2b), and (2c) by the likelihood of each, using a poker calculator that can work with ranges of hands. That's the best calculator I've been able to find, though I'm sure there are other good ones.
Now you compare the dollar value of (1) to the weighted sum of (2a), (2b), and (2c). If one is significantly higher than the other, you can be fairly confident that it is the correct play (fold or call).
Here pzhon explains why folding AA is very wrong in a certain situation using this sort of analysis.
Here's a made-up example:
blinds 100/200 stacks are UTG 800 Button 1200 SB 2000 you (ATo) 4000
UTG folds, button pushes, SB folds.
1) you fold UTG 800 Button 1500 SB 1900 you 3800 36.3% of the prize pool
2a) you call and lose UTG 800 Button 2500 SB 1900 you 2800 31.5% of the prize pool
2b) you call and win UTG 800 Button 0 SB 1900 you 5300 42.7% of the prize pool
2c) you call and split UTG 800 Button 1350 SB 1900 you 3950 37.0% of the prize pool
Button has been playing fairly tight, waiting for UTG to make a move first. You put him on any pair, any suited ace, AKo-A8o, KQs-KTs, KQo. Your ATo will lose, win, or split (according to the poker calculator) in the following proportions:
lose: .488 win: .426 split: .086
Calling is worth: .315*.488 + .427*.426 + .37*.086 =.365
36.5% of the prize pool. Compare to 36.3% for folding. This is very close. I bet if someone posted this hand there would be a lot of arguing over what the correct play is. You could probably put the button on a better range of hands than I did. Hopefully this example illustrates the method well enough though.
how to solve certain problems with the ICM (an algorithm)