-EV w/Most Pot equity?

[jackaaron]

Just wanted to make sure this is possible. I could obviously be doing the math wrong.

But, the situation is this.

You have 105k. CL has you covered.

Two short stacks have 30k, and 35k. Those two go all in, and the CL goes all in, and you have AK, and you are thinking of going all in (full table, 14 left in a tournament).

Let's assume you know that the shorties will push with the top 30% of hands, and so will the CL.

Hand Pot equity Wins Ties
30% 22.61% 128,469 16,358
30% 22.58% 128,376 16,212
30% 22.56% 128,417 15,852
AK 32.25% 181,608 26,159

You have 32.25% pot equity in this situation. However, making the call would be -ev. I added up the two short stacks, plus 105 from the CL, and 105 from me. That's 275,000. 32.25% of that is 88687 which is less than the 105,000 that I'm putting in, so that's -ev, correct?

[jay_shark]

It's positive EV to make the call assuming you put your opponents' on the top 30 % of all hands .

To make things easier , assume 3 players put in $1 which means that you have to win at least 25 % of the time to make the call correct .

If this specific situation is negative EV for you , then it must be negative EV for the other three players since their pot equity is less , but this is a contradiction since it cannot be negative EV for everyone .

In fact , you may even call with ace-9 and the call will still be good since you're at least a 50% favorite against the CL which is where most of your EV is coming from . AK is more than enough and should be an automatic call .

Also , I don't think the CL will necessarily call with the top 30 % of hands . I'm only working under the assumptions you've made .

[Tom1975]

You've oversimplified this. There's a main pot with 120k which is the one you have 32.25% equity in. There's also a 3-way side pot with 15k and a 2 way side pot with 140k. You have to figure your equity in all 3 pots then add them together. Your equity % will be higher in the side pots since you have fewer opponents in them.

It's also worth noting that in tournaments that just because a play is EV+ does not mean it's always in your best interest to make it.

[jay_shark]

A-9 may be slightly negative EV as I haven't checked it .
Certainly a-10 wins 24% of the time which in this case is still positive EV since it is ahead of CL by quite a bit .

Do you understand the point to be made here ?

[jackaaron]

Even though there are side pots, it still comes out as getting less as a percentage of pots than you are putting in total.

I guess I don't understand (yet) because I'm putting in 105k of my stack, although I'm getting a little over 32% from each side pot, it adds up to less than I'm putting in. So, it seems -EV as a result of this, but I must be missing something.

Also, re: Jay Shark, I don't think the 1.00 example is good, because I have a very specific example here. Two people are very short, and one has me more than covered. I think if we were all equal stacks, then this would obviously be +EV, and I wouldn't have the question.

Edit....WAIT...Should I not only do side pots....BUT...ALSO change my pot equity?

I'm assuming .3235, however, when it's just me and the CL in the biggest pot of them all, I have WAY more than that in pot equity....

EDIT 2....Okay, Okay. GOt it. Sorry. Whomever told me about the side pots, I wasn't calculating them correctly. This would be massively +EV by about 28k or so.

Thanks!!!

[jay_shark]

brain freeze

[DWarrior]

This will actually be a very complex calculation.

You have to calculate each pot (main, 2 sides) individually.

The second sidepot of CL vs you will be 70k.

Hand 0: 63.718% 61.55% 02.17% 4236784404 149223576.00 { AKo }
Hand 1: 36.282% 34.11% 02.17% 2348230524 149223576.00 { 55+, A2s+, K5s+, Q7s+, J8s+, T8s+, 98s, A7o+, A5o, K9o+, Q9o+, J9o+, T9o }

For 140,000
Equity: 89,205.2

Note that 34.11% of the time you will lose to CL and that means you no longer have dibs for the remainder of the pots. 2.17% of the time you will be splitting the 140k second sidepot and then moving on to the other sidepot and main pot and battling the shorties. 61.55% of the time you will win the 140k and then go up vs the shorties for side and main.

If you assumed their ranges were independent of one another, and that battling for each pot was independent of one another, this calculation would be relatively easy.

However, when you win against CL, your odds of beating shorties go up, which severely complicates the problem.

We can go in reverse order (from main up):

(using your numbers, they don’t add up to 1)
30k shortie: 30% 22.61% 128,469 16,358
35k shortie: 30% 22.58% 128,376 16,212
CL: 30% 22.56% 128,417 15,852
You: AK 32.25% 181,608 26,159

32.25% of the time you scoop 275k
22.56% of the time CL wins and thus scoops, you lose 105k
22.58% of the time 35k shortie wins main+side1, so you’re guaranteed to lose 35k. You still have equity in the 140k sidepot2, but I cannot calculate it.
22.61% of the time 30k shortie wins main, so you’re guaranteed to lose 30k. You still have equity in both sidepots, but I cannot calculate it.

All I can say is your equity is definitely greater than 88687.5.

The problem with AK though is that sometimes it becomes a –EV hand when enough villains take enough of your outs.

Example:
AKo vs TT = ~coinflip
AKo vs AKo vs TT = TT 65.5% fav

I'm still almost positive that AKo is a +EV call in that spot (assuming their ranges are all 30%, which is extremely unrealistic)