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.

[rachelwxm]

dethgrind, nice put together.
[img]/images/graemlins/smile.gif[/img]

[The Yugoslavian]

Can the moderators give out best post of the week or something? Because this would *definitely* be it!

I too use the same links (for ICM) and pokercalculator -- I need to improve my play because I am having a very hard time figuring out if I'm really any good at all. Unfortunately pokercalculator only works once after setting it up so I have to install it over and over again (I'm a huge moron I guess), but I too have been unable to find anything better.

Obviously putting your opponent on a range of hands is important. Doesn't eastbay have (or use) a list of push hands for these sorts of calculations (or is this 'push' list something else entirely)?

I've been trying to figure out how big the difference between % of prize pool if folding and % of prize pool if calling needs to be to make it a clear cut decision. Also, since ICM assumes players of equal skill (please tell me if I'm wrong) then even given 100% accurate read of your opponent, don't you need the difference to be more than it is in the example to make the call correct? Is there a way to modify the ICM given that you are a X% ROI player?

Again, great post, you rule!!! [img]/images/graemlins/laugh.gif[/img]

[dethgrind]

[ QUOTE ]
Also, since ICM assumes players of equal skill (please tell me if I'm wrong) then even given 100% accurate read of your opponent, don't you need the difference to be more than it is in the example to make the call correct? Is there a way to modify the ICM given that you are a X% ROI player?


[/ QUOTE ]

LinusKS started a thread about this very issue. It didn't get very far; this is a tricky subject. To answer your questions: 1) probably. 2) not really (yet)

A bit more on question 1: even if everyone were equally skilled, the difference would need to be more than it is in the example for calling to be definitely correct. When it's that close, the ICM numbers are pretty much inconclusive, I think.

[The Yugoslavian]

Thanks for the response!

I think I understand very little of what is actually going on in that thread [img]/images/graemlins/wink.gif[/img].

So, if the difference in the two numbers is .1 then that would be a +$1EV in a 10+1 game? But if there is a difference of .01 then it is only +$.1EV and almost surely insignificant?

[dethgrind]

[ QUOTE ]
Thanks for the response!

I think I understand very little of what is actually going on in that thread [img]/images/graemlins/wink.gif[/img].

So, if the difference in the two numbers is .1 then that would be a +$1EV in a 10+1 game? But if there is a difference of .01 then it is only +$.1EV and almost surely insignificant?

[/ QUOTE ]

I guess I was a bit inconsistent and sometimes used % and sometimes left it as a decimal. A difference of .1 is the same as a difference of 10% of the prize pool, which is huge. $10 in a 10+1 game. A difference of .1% is the same as a difference of .001; this is far too close for the model to be helpful. $0.10 in a 10+1 game.

Remember that ICM calculator link gives you a fraction of the prize pool. The prize pool for a 10+1 game is $100. So if it says 1600 chips have a $EV of .1844, that means $100*.1844 = $18.44 in a 10+1 game.

I don't really know how big the difference needs to be for the decision to be clear. I'd say a difference of .002 or less is almost certainly too close, and a difference of .05 is almost certainly enough to be clear in most cases.

Hope that clears up some confusion [img]/images/graemlins/smile.gif[/img]

[The Yugoslavian]

Yes, of course!

Your message is quite helpful -- I may have been getting confused by the % and decimal numbers but I've got it now.

I was a philosophy major, can ya tell? [img]/images/graemlins/wink.gif[/img]

Then yes, 10% would be way too huge to pass up while .1% (or .001) would be marginal to say the least (especially if your read on the opponent is suspect). .05 (or 5%) must be fairly definitive because it's +$5 decision -- huge for a 10+1 game where even the best players probably won't be able to profit much more than $5/tourny.

I definitely think that shorthanded I need to be rasing allin for value more as there is steal equity, most of the time I won't be dominated (just a slight-somewhat underdog), and the blinds are a significant percentage of my stack. Still, sometimes it's hard going all-in with K4o for value when it seems like such a dog to hands that will call (and at the 20+2 lewel I'm at it is hard to tell who will start calling shorthanded with semi-crappy hands).

Thanks for the help, I will definitely be using the ICM/PokerCalculator combo more in my search for the most +EV (or least -EV) decisions.

Again, thanks for your help!

[NegativeEV]

I echo the others, this is very helpful post. When I try to use the "ICM Calcualtor" link I just see a grey box (I can't use the calculator). Is there anything I'm missing or can I assume that my system is causing me issues?

[dethgrind]

You're not the only one to have this issue. I recommended to someone else with the same problem to make sure they have a recent version of java and a recent web browser. He didn't respond after that, so I'm guessing that was the problem.

[NegativeEV]

Or maybe they were as tech savy as I and didn't know what "recent version of Java" means. I'm confident that my browser is current, but I thought Java was a programming language. How does one get a recent version of Java.

thanks
-EV