Hi,

If there are 3 remaining and the payout is 50/30/20, blinds are 3000/6000 and stacks are:

BTN: 250000
SB: 20000
BB (Hero): 110000

Why does the nash push/fold calculation say we should:

BTN PUSH 46.6%
SB CALL 39.7%
BB OVERCALL 16.9%

But then if SB folds BB should only call 2.3%?


I understand the 2.3% but I don't understand why we should overcall 16.9% vs a BTN push and SB call?? Is it because we have a chance of knocking out the SB also? Just seems weird to me, I've never thought of calling WIDER vs two.

Can someone inform me what I'm missing? Thanks

In addition to knocking out SB, you 2x+ up and go HU with chip lead. When you don't overcall you go HU with deficit no matter other if you bust shorty or he does.

But aren't we at risk of busting 3rd? I would have thought ICM points in the direction of letting the leader bust the shorty and just stay out the way... but I see what you're saying... I've just never thought of it this way...

The stacks can end in a few ways.

Obviously the cases where the short stack doubles or triples, just update the ICM calculator and see what the new situation is. But in the cases where the short stack busts your situation is only improved by also taking chips off of the leader. In cases where BTN folds and you bust the short stack you are still in a 2:1 chip disadvantage. When you double through you go HU with the 2:1 advantage.

ICM points to protecting your chips. This means folding a ton, but also leads to the opposite in spots which are not folds. Spots which can shift you into the chip lead heads up are much more rare and much more valuable than watching a shorty bust.

This is one of the spots I think I am bad at, but because I will over call too much!

I guess I feel the need to clarify the above.

When you are in your top 19%, versus 40% and 30% ranges, you are calling because you have the hand to call. This should show why it is important to call at the bottom of your 19% rather than making a bunch of hero folds waiting.

It's strange because my default has always been to fold when someone is at risk of busting if I'm about to move into HU play whether I'm 1st, 2nd or 3rd in chips. So this is new to me. Overcall wider when we can bust shorty and take the chip lead. Is this always true though?

No.

It is a result of adding up your equity in each prize position. By folding you are only forcing 0% likelihood of taking $20 to get x% of the 50 and 1-x% of the 30.

There exist cases like this where your range v range equity is good enough that after the chips move around you have a nonzero chance of 3rd but since your chance of first goes up so much (coupled to your HU opponents going down) that the sum of your equities in each position is greater than when you have zero chance at 3rd.

EV=(x)(50)+(y)(30)+(z)(20) - (100%)(Buy in).

Folding gives you z=0.
x = proportion of chips in play when you get HU.
y=1-x and is essentially your second place equity.

Your total EV is the sum of all events. So based on your range v range equities and assuming that shorty buts and you go HU...

Your call has 40% equity to go HU with 63% of the chips in play.

So (.40)(.63)($50)+(.4)(.37)($30)+ (.6)($30)+(0)($20)* = $35.04 - Buy in

Compared to the fold case where you have
(1)(.28)(50)+(1)(.72)(30)+(0)(20) = $35.6 - Buy in

This is not fully correct since we are neglecting the cases where you bust and shorty triples as well as cases where you win the side pot and shorty triples. This should however give you a better idea of how I think this is showing up in your ICM calc. I assumed ranges of 47,40 and 17, rounded all proportions to a few decimals and neglect complicated cases which might add the difference to overcalling.

Excellent, thanks for this, I wonder how I could use this in a live setting... probably just the knowledge gained by studying these situations is enough to help.. hmm ... cheers