Is ICM irrelevant once ITM??

[Beck]

I had a situation where the stacks were
6000, 6000 and 3000, and the the 2 big stacks battled it out in a 66%/34% match

6000 chips equals an ICM of 0,3567
The favorite of the hand has a post-hand ICM of 0,34*0,2+0,66*0,46=0,3716, so only a slight increase.

Is my math off, is it correct that yo almost don't gain anything from going to showdown all in, even if a huge favorite, with the other big stack?

[Scuba Chuck]

Well, the problem with your analysis, is that you are doing the analysis with KNOWN hand information. If you were using a hand range for let's the the big stack who went allin first, you could probably find a way for it to be positive EV.

FWIW, the reason your numbers come out to have just a slight increase is probably because the card equity between the two hands is so close to even.

One last thing. Yes, $EV analysis does continue to work ITM.

[Benholio]

Well, what that is saying is that you should usually fold when the other big-stack gets all-in, unless you can be fairly certain to be a good favorite (such as this case). This is what the ICM is telling you, and it is completely relevant.

[mackthefork]

Basically if the 2 big stack go in, it normally disadvantages them both and benefits the short stack, unless of course one of the big stacks is a very substantial favourite.

Mack

[Beck]

Please define "substanbtial favourite"? In my example, one of them would win 2/3

[Nottom]

[ QUOTE ]
Please define "substanbtial favourite"? In my example, one of them would win 2/3

[/ QUOTE ]

I think this just goes to show how much the small stack gains in this spot.

Now this doesn't mean you should be avoidng these kind of spots, because in reality the blinds give back some of that lost EV.

[J-Lo]

I remember Irie saying something like, when you have 1 of the 2 bigstacks ITM, keep pushing into other big stack, because he is giving up when he calls w/ a meteocre hand.

[Beck]

[ QUOTE ]
Well, the problem with your analysis, is that you are doing the analysis with KNOWN hand information. If you were using a hand range for let's the the big stack who went allin first, you could probably find a way for it to be positive EV.

FWIW, the reason your numbers come out to have just a slight increase is probably because the card equity between the two hands is so close to even.

One last thing. Yes, $EV analysis does continue to work ITM.

[/ QUOTE ]

Well, I was expectiong for it to continue ITM, but just can't seem to get it straight.

Yes, I see now that doing it with known hand information is wrong,as it doesn't compensate for all the times, he won't call.
However....
Let's assume the same blind/stack situation, small stack folds, One of the big stacks pushes. Is it correct that the other big stack has to be more than a 60% favourite for it to be a profitable call?
6000 chips PreFlop 0,3567 Post flop 0,4*0,2+0,6*0,46=0,356

[gumpzilla]

[ QUOTE ]
I remember Irie saying something like, when you have 1 of the 2 bigstacks ITM, keep pushing into other big stack, because he is giving up when he calls w/ a meteocre hand.

[/ QUOTE ]

I think this is highly dependent on big stack being a good enough player to recognize this, because if he's likely to call you at some point, then yes, he's giving up money to the shortstack, but so are you.

[J-Lo]

gumpzilla, ex. UTG 2000, you/SB 4000, villain 4000. Blinds at 250-500.

Would you push w/ ALOT of hands if small stack folds? And doing so gives you a great chance at first, even if called, Because u either take first or 3rd (something this forum advocates).

Or the alternate, wait for the short stack to bust out, and push only top 33% of hands.

[gumpzilla]

[ QUOTE ]

Would you push w/ ALOT of hands if small stack folds? And doing so gives you a great chance at first, even if called, Because u either take first or 3rd (something this forum advocates).

[/ QUOTE ]

To nitpick, you either take 3rd or have a substantially better than average chance of taking 1st. Important difference.

[ QUOTE ]
Or the alternate, wait for the short stack to bust out, and push only top 33% of hands.

[/ QUOTE ]

I don't think these are the only two alternatives.

What range of hands you choose to mess around with is going to interplay with what range of hands you think BB is going to call with. If you're in a situation where the player to your immediate left is very loose, then you're just unlucky, I think, because this is a good situation for the shorty if you keep trying to steal the loose guy's BB from your SB.

Of course, you can also choose to pound on the small stack somewhat more. I think the thinking is that the big stack should recognize that he has no interest in busting before the short guy and that this should make him tighter, which is what you want. But all bets are off if this isn't happening.

Regardless, you need to be stealing a lot here, but if I think one of my opponents is going to fold way too rarely I'll probably aim at the other one and tighten up the range with which I push against the loose one.

[Scuba Chuck]

[ QUOTE ]
Is it correct that the other big stack has to be more than a 60% favourite for it to be a profitable call?

[/ QUOTE ]

Well, let's use some math here (since you didn't apply any blinds to your question, let's just assume no blinds).

Let's assume the $55 payouts (where I play).

1st - $250
2nd - $150
3rd - $100

Your stacksizes were 6000/6000/3000

So, let's assume that there is a linear relationship between stacksizes and their percent of the prize pool (which ICM doesn't do).

If the 2nd big stack calls and wins, he will have 12000 chips, or 80% of the equity prize pool. 1st and 2nd is a total of $400. Therefore...

Call and win = $320
Call and lose = $100
Folding = $200

Call = (.4)(100)+(.6)(320) = $232

Therefore, if you're a 60% favorite, calling is profitable. But here's the interesting part. What advantage does he need to have to make calling profitable?

Assume X = winning percentage
Breakeven = Folding (as a percent of the equity prize pool)
Breakeven = 200 = (1-X)(100)+(X)(320) = 100 + 220X
X = 45%

Therefore, he only needs to win this hand 45% of the time.

This should prove to you why ICM gives the smaller stacks bigger ownership of the equity prizepool than the bigger stacks. Because even if having 12000 chips, or 9000 chips more than the second place guy, it's only a 50/50 coinflip before it really begins to even out. For example, if small stack doubles up on first coinflip, then the stacks are 9000/6000. Bigstack now only has 60% of the prize pool.

This all probably doesn't directly answer your question, but my guess is intuitively you can see how the math here is really off. Thus proving, from an inverse perspective, why ICM still applies to tournaments once ITM.

[Scuba Chuck]

Thought I'd continue the math in a second post. Edit: This time, let's apply ICM to the numbers (instead of assuming the linear relationship of stacksize to prizepool).

Stacksizes
6000 - 35.67% of the equity prize pool
6000 - 35.67%
3000 - 28.67%

After a bigstack battle:
12000 - 46% of the equity prize pool
3000 - 34% of the equity prize pool

The remaining difference (as 46% and 34% don't add up to 100) has already been paid out to third place guy. Therefore, let's transpose these numbers to a number that can be comparable to my numbers in my previous post, bigstack now has 57.5% of the remaining prize pool.

57.5% does not equal 80% (numbers from previous post).

Feel free to do the remaining math, to figure out the remaining evidence to your original question.

[Beck]

[ QUOTE ]
Thought I'd continue the math in a second post. Edit: This time, let's apply ICM to the numbers (instead of assuming the linear relationship of stacksize to prizepool).

Stacksizes
6000 - 35.67% of the equity prize pool
6000 - 35.67%
3000 - 28.67%

After a bigstack battle:
12000 - 46% of the equity prize pool
3000 - 34% of the equity prize pool

The remaining difference (as 46% and 34% don't add up to 100) has already been paid out to third place guy. Therefore, let's transpose these numbers to a number that can be comparable to my numbers in my previous post, bigstack now has 57.5% of the remaining prize pool.

57.5% does not equal 80% (numbers from previous post).

Feel free to do the remaining math, to figure out the remaining evidence to your original question.

[/ QUOTE ]

So would that be:
Assume X = winning percentage
Breakeven = Folding (as a percent of the equity prize pool)
Breakeven = 200 = (1-X)(100)+(X)(230) = 100 + 130X
X = 77%

??

[Scuba Chuck]

[ QUOTE ]
6000 chips PreFlop 0,3567 Post flop 0,4*0,2+0,6*0,46=0,356

[/ QUOTE ]

Haha (laughing at self)

Just realized why I didn't understand this part of your post. It would have helped me if I knew you were from Denmark. That math looks about right. So compare that number to folding. Folding ~ 35.6% (using my numbers from other posts - which assumes no blinds). If you bring blinds into this (especially the higher the blinds), I'm sure calling with a 60% advantage is better than folding.

[Scuba Chuck]

[ QUOTE ]
So would that be:
Assume X = winning percentage
Breakeven = Folding (as a percent of the equity prize pool)
Breakeven = 200 = (1-X)(100)+(X)(230) = 100 + 130X
X = 77%

??

[/ QUOTE ]

Beck, you've crossed your wires. You're applying a math equation from the linear explanation, and trying to apply it to the ICM approach.

You need to compare folding to calling. See my other post (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=2234028&page=0&view=c ollapsed&sb=5&o=14&vc=1)

[Beck]

[ QUOTE ]
[ QUOTE ]
So would that be:
Assume X = winning percentage
Breakeven = Folding (as a percent of the equity prize pool)
Breakeven = 200 = (1-X)(100)+(X)(230) = 100 + 130X
X = 77%

??

[/ QUOTE ]

Beck, you've crossed your wires. You're applying a math equation from the linear explanation, and trying to apply it to the ICM approach.

You need to compare folding to calling. See my other post (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=2234028&page=0&view=c ollapsed&sb=5&o=14&vc=1)

[/ QUOTE ]

Knew, I should have made a disclaimer, that I had just gotten home fro ma nightshift and was tired /images/graemlins/smile.gif

So would the correct equation be:
Assume X = winning percentage
Breakeven = Folding (as a ICm measurement of the equity prize pool)
Breakeven = 0,3567 = (1-X)0,2+X*0.46 =
X = 60%

Or am I all wrong trying to make an equation to solve it?

[Scuba Chuck]

[ QUOTE ]
So would the correct equation be:
Assume X = winning percentage
Breakeven = Folding (as a ICm measurement of the equity prize pool)
Breakeven = 0,3567 = (1-X)0,2+X*0.46 =
X = 60%

[/ QUOTE ]

Yes that's correct (assumes a tie is not a possibility). These results are interesting as it makes low pairs, like 88-, only a ~ 55% win probability against the likely pushing range.

TT/AK become the first for sure 60% win probability. Which is interesting as I'm sure many players call hands are probably lower than this.