[aaaaa]

I am having trouble understanding why we'd push. The FE is really less here with 1 MP raiser.

I'd put the MP2 on AA-JJ, TT, AK-AQ.
I'd put the button on mid-pairs, maybe 77+ hoping to catch a set. Since he didn't raise, I exclude AA-QQ from his range. I'd put him on 77-JJ, AK-AQ.

If you push --
1. MP2 figures you probably don't have an AA or KK since you're pushing and not raising 3X pot.
So MP2 calls with QQ-AA, AK. He folds TT-JJ and AQ.

2. Button looks weak here, don't think he has AA-QQ. He folds 77-JJ and everything except maybe AK, i.e 16 out of 60 possible hands, so he wins very few times against MP2 and we ignore this case.

Most times, you're against MP2 now.

Calls: AA-QQ (18 hands), AK (16 hands)
Folds: JJ-TT (6+1), AQ(16 hands)
Total hands: 57
AA-QQ: 18/57= 32%. You win: 32% * 18% = 6%
AK: 16/57 = 28%. You win: 28% * 55% = 15%

Total win % = 21%. Pot: 7+10+10+73 = 100
Total lose % = 40%. Lose: 73

Folds: AQ, JJ-TT, 23/57 = 40%. Pot = 7+10+10 = 27

EV = 21%*100 + 40%*27 - 73*40% = 2K. That is a real small edge now.