Originally Posted by tunah

(I'm going to assume the BB folds here, since no info is given about his range. If you flat-call he may come along, and he may show up with a monster in any scenario, but I can't work these out precisely...)

Fold
EV = 0

3bet 30x
He has 6 combos each of 66-QQ in his range, 3 each of AA-KK (since you hold blockers) and 9 of AK, for 57 total hands, of which 6 call. When called we only have 18.5% equity in a 61BB pot of which we pay 29.5BB. When he folds we win 5.5BB.

EV = 51/57 x 5.5 + 6/57 (-29.5 + 0.185 x 61) = 3.0BB

(Note we're exploiting his fold-to-3bet tendency, shoving over is +EV with zero equity because he folds so much. We should choose to do this with e.g. 87s instead of AKo because it has better equity when called). edit: This isn't true, we have more fold equity with AK because we have blockers to his calling range. Thanks spoon!

3bet 10x
He has the same 57 hands, but this time 21 of them shove. Our equity against his shoving range is 38.8%. We have to call 20BB to win a total pot of 61BB so we only need 32.7% equity, this is a call. So we have 38.8% equity in a 61BB pot of which we pay 29.5BB, and when he folds we again win 5.5BB.

EV = 36/57 x 5.5 + 21/57 (-29.5 + 0.388 x 61) = 1.33BB.

(This isn't great, he doesn't fold nearly so much, and we end up still behind his wider stack-off range but having to call because of pot-odds).

Call
This is obviously fuzzy, it depends on (your opponent's perception of) your calling range, and both players' postflop tendencies.

But the implied odds are likely to be in his favour - if he holds a medium pocket pair he's probably going to be able to get away when an A or K hits. Whereas if you hit and he gets a set or AA, you could lose your stack. You're out of position and he has this initiative.

Overall I suspect you'll struggle to get 'your half' of the pot back, making calling -EV.

So best option seems to be 3-bet shoving, and in fact doing it with ATC until EP or BB adjust.