how to solve certain problems with the ICM (an algorithm)

[dethgrind]

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.