Hero opens AAxx (I don't remember suits or side cards) UTG for pot (3.5 BBs), villain 3bets SB (10.5BBs), Hero 4bets, (44BBs or so), villain calls.
Flop (90BBs) with roughly 1 PSB left each.
Qh Qd 2s. Villain checks. I shoved.
I suspect we always stack off, but I wonder if it is better to check-back and hope to widen his range to include some bluffs. Or do we just close our eyes and shove and win the large pot in the middle often enough to be a good play?