[poincaraux]

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I'm curious. Given that QQ is only a small favorite against AK, how often do you need to see JJ-22 or Ax for this to be profitable?

Given the way it played, I probably fold, because I expect to see AA, KK or AK most of the time here, and JJ pretty rarely. When you're up against AA or KK, you're crushed, and those times you're up against AK, you're really not giving up much equity.

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PoBoy:
I've never seen anyone post about how exactly to do a weighted EV calculation, but I think I'm doing them correctly (someone please correct me if I'm wrong!)

Let's say he has two classes of hands here, and that he treats each hand within a class identically. That is, whatever he's going to do with JJ, he's going to do the exact same thing with 44.

AA,KK,AK: 6+6+16=28 combinations, we own 38% of the pot
JJ-22: 6*10=60 combinations, we own 81% of the pot

There was $0.85 in the pot, you raised to $1.50 and he re-raised to $10. Let's make it simple and assume that you'll push and he'll call. At that point, you'll be risking ($20.40 - $1.50 = $18.90) to win ($20.40+$0.85+$1.50=$22.75) (let's ignore the rake).

Here's the way I thought about this at first: let him have AA,KK,AK x% of the time and JJ-22 (100-x)% of the time. Then, we need to end up with 18.90/(18.90+22.75) = 45% of the pot. So, we need

x*0.38 + (1-x)*0.81 = 0.45.
x*0.38 + (100-x)*0.81 = 0.45.
.38x + .81 -.81x = .45
.43x =.36
x = .36/.43 = .84

That is, he only needs to have JJ-22 16% of the time for us to break even. That's pretty sweet.

I don't think that's quite the right way to think about it, though. Instead of saying "well, I think he'll have JJ-22 x% of the time here," I think it's better to say "well, I think he'd do this x% of the time with JJ-22. So, let's say he does this 100% of the time with AA,KK,AK and x% of the time with JJ-22. I think the right way to weight things is to say that he has 28 combinations of AA,KK,AK and 60*x combinations of JJ-22. does this sound right to people??. That gives (28+60x) total combinations, and we can say

(28/(28+60*x))*0.38 + (60*x/(28+60*x))*0.81 = 0.45.

Edit: note: I switched the meaning of x in my equations. In the first one, it went with his winning hands, but in this one it goes with his losing hands. Sorry about that.

Solving that tells us that we need x to be greater than or equal to 10%. It makes a lot of sense that this is lower than the 16% we got earlier: there are more combinations of JJ-22, but we were weighting them equally before.

So, that's my longwinded way of saying this:

He only needs to do this 10% of the time for you to push with QQ.

Someone please tell me if this looks right.

Note: I forgot that you included Ax in his "bad" range .. the math's the same, but you'll be farther ahead because there will be more hands that you're ahead of.

-poincaraux