Preflop spots are so boring... zzz....
Villain's Range: QQ+
AKs Equity vs. Villain's Range: 34.6% (1.89:1)
on your Shove (assuming you're called 100%): 1.14:1
Just on that alone, its a fold. But a 20/15 isn't the nittiest nit on the planet, so I have a hard time believing that he only 3-bets QQ+ from the small blind against a cut off steal. And if he starts folding things like JJ, AK to a shove, then shoving should be quite profitable.
With the set-miner in the pot, it becomes a trivially easy 4-bet IMO. I just can't put the SB on that tight of a range after 60 hands. But then again, I don't play FR.
There's a good hold'em manager article dealing with facing a 3-bet. It essentially lays out what he has to 3-bet in order for you to 4-bet/call profitably for one buy-in. And in order for 4-bet/calling AKs to be profitable, we need him to 3-bet at least 3%. That is a range of exactly JJ+ & AK. So unless you know stone cold that he never 3-bets those against a cutoff raise, then we should be 4-bet/calling or just 4-bet shoving here. If he ever 3-bets TT, AQs, ect., then this is an auto-stack.
I think the only decision here is call or 4-bet. And since the BB is deep and calls 3-bets with implied odds hands, I think we can easily rule out calling, since we don't want to put in ~150bb's bad against the BB. This of course depends on how well you play postflop, but in general I think it sounds like its going to be hard to put the BB on a range.
So yeah, I don't hate folding. Its not a huge mistake. However, I think shoving is the best play. If I had to score them on a scale of 1-10 with 5 being break even, 1 being spew, and 10 being omfg profitz then I'd say they fall about here: