ICM theory question

[dfscott]

This is a question about calculating ICM.

Let's talk about how to calculate the following situation:

Blinds 100/200
UTG (t1150)
Hero (t1390)
SB (t2010)
BB (t675)

Preflop: Hero is Button with A[img]/images/graemlins/heart.gif[/img], J[img]/images/graemlins/club.gif[/img].
UTG folds, Hero ???

Ok, I'm deciding whether to push or not. So, as I understand it, the first step is to calculate what your chip stack will be if you 1) fold, 2) push and everyone folds, 3) push and someone calls and you win, 4) push and someone calls and you lose, and 5) push and someone calls and you split.

Am I right so far?

Assuming I am, it looks like you'd also have to go a step further, since you have to consider the following scenarios for 3-5: 1) SB folds, BB calls, 2) SB calls, BB folds, and 3) SB calls and BB calls.

So, now you're talking about 11 different scenarios, right? It looks to me like it's:

1) Folding
2) Push and all fold
3) Push and only BB calls and you win
4) Push and only SB calls and you win
5) Push and both blinds call and you win
6) Push and only BB calls and you lose
7) Push and only SB calls and you lose
8) Push and both blinds call and you lose
9) Push and only BB calls and you split
10) Push and only SB calls and you split
11) Push and both blinds call and you split

But then, it looks like it could go even further. In option 11, you might split with just one of the hands, or it might be 3-way. So doesn't that add yet another 2 scenarios?

Then, once you get all the chip counts done, you have to go back and run your hand against the three possible scenarios (vs SB, vs BB, and vs both blinds) to get the win percentages, right?

Maybe I'm missing something, but it looks like this can get complicated pretty fast...

eastbay, if your tool can handle all this, I think you have a customer.

[eastbay]

My tool covers the important ground here, but it currently does not consider the 3-way cases, and it also uses an equity valuation rather than explicitly accounting for split pots.

I'm confident these produce small effects in the majority of cases that really aren't important. However, I intend to lift both of those restrictions in the future, starting with the multi-way cases.

It is also not limited to 2 players behind. You can analyze a push from UTG at a full table, if you want. And yes, it does get very tedious and labor intensive fast. But this is what computers are good at.

eastbay

[dfscott]

[ QUOTE ]
My tool covers the important ground here, but it currently does not consider the 3-way cases, and it also uses an equity valuation rather than explicitly accounting for split pots.

I'm confident these produce small effects in the majority of cases that really aren't important. However, I intend to lift both of those restrictions in the future, starting with the multi-way cases.

[/ QUOTE ]

Both my calculations and well as play results would seem to bear this out.

[ QUOTE ]
It is also not limited to 2 players behind. You can analyze a push from UTG at a full table, if you want

[/ QUOTE ]

So in the example above, your tool would take the following scenarios into account:
1) Folding
2) Push and all fold
3) Push and only BB calls and you win
4) Push and only SB calls and you win
6) Push and only BB calls and you lose
7) Push and only SB calls and you lose

It would not consider the following:
8) Push and both blinds call and you lose
5) Push and both blinds call and you win

And it would basically ignore these as insignificant:
9) Push and only BB calls and you split
10) Push and only SB calls and you split
11) Push and both blinds call and you split

Correct?

[eastbay]

[ QUOTE ]

So in the example above, your tool would take the following scenarios into account:
1) Folding
2) Push and all fold
3) Push and only BB calls and you win
4) Push and only SB calls and you win
6) Push and only BB calls and you lose
7) Push and only SB calls and you lose

It would not consider the following:
8) Push and both blinds call and you lose
5) Push and both blinds call and you win


[/ QUOTE ]

Right. That's the multi-way case that isn't yet implemented but will be. The showdown probabilities get very involved here, and I don't want to make the thing too pokey by calculating or estimating them each time. I prefer a full precomputed enumeration table lookup.

[ QUOTE ]

And it would basically ignore these as insignificant:
9) Push and only BB calls and you split
10) Push and only SB calls and you split
11) Push and both blinds call and you split

Correct?

[/ QUOTE ]

It doesn't ignore them so much as account for them by adjusting the win percentages. A tie is like winning half the time. It's not exactly right but it tends to make very small differences in the result. In the name of purity I'll probably compute the tie case explicitly at some point.

eastbay

[jcm4ccc]

You're making this much too complicated. It's not necessary to consider every possible scenario, and to calculate your expected winnings down to the 4th decimal.

You're analyzing two scenarios:

1. Fold

2. Push

Fold is easy. Under push, I would analyze only the most common situations:

All fold
SB calls, you win
SB calls, you lose
BB calls, you win
BB calls, you lose

You have to make an educated guess as to what the SB will call with, and what the BB will call with. After that, it's pretty straightforward.

I'm sure you can get more precise numbers if you analyze all these other situations that you outlined, but it will make little difference in the overall numbers, and no difference as to whether you push or fold.

[spentrent]

Is it naive of me to think "It's 5-handed, I have an average stack and A f'n J. Those blinds are mine!"

[Elektrik]

[ QUOTE ]
Is it naive of me to think "It's 5-handed, I have an average stack and A f'n J. Those blinds are mine!"

[/ QUOTE ]

That's my train of thought...I'm really hoping this post is asking to quantify the value of pushing here, not whether it should be pushed.

[ilya]

[ QUOTE ]
Is it naive of me to think "It's 5-handed, I have an average stack and A f'n J. Those blinds are mine!"

[/ QUOTE ]

It's 4-handed.

I think this is a great spot to push. BB might feel like he has to call you with a lot of pretty weak hands; even if he folds, you've made sure that the short stack has gotten shorter instead of possibly getting his BB back. Yes, the SB can bust you, but neither BB nor UTG are so short that you can play it safe.

[spentrent]

[ QUOTE ]
[ QUOTE ]
Is it naive of me to think "It's 5-handed, I have an average stack and A f'n J. Those blinds are mine!"

[/ QUOTE ]

It's 4-handed.

[/ QUOTE ]

Oops. I thought Joe Blinds couldn't tell if his stack were 100 or 200.

Blinds 100/200
UTG (t1150)
Hero (t1390)
SB (t2010)
BB (t675)

[yecul]

Push looks good to me. Short handed, so you likely have the best hand. No one has many chips in relation to the blinds. SB will fold unless he has a big hand in which case you're screwed. BB might call as he's shorty, but his calling range is wide, so you would probably still be ahead.

Folding seems like a bad move unless you're happy to just back ITM. Calling would be weak. Raising is tough because any raise would be ~half your stack anyway.

Push.