Defend pre, check flop and turn, and mostly check river with A-high; a small block bet can be mixed in, but checking is slightly higher EV.
Flop 6-6-7 rainbow is very connected and BU’s limp-call range has plenty of 7x and pocket pairs, so we’re slightly behind. With A-high and no real draw, checking range is standard; betting would mostly fold out worse and get called by better.
Turn 2d is a brick; after both players check flop, BU’s turn bet is polarized, but we’re getting about 2.2:1 and need only ~31% equity. A-high with some showdown value and a few outs to improve is a reasonable call.
Turn call leaves BU with ~19BB behind and SPR ~1. River Td gives us a gutshot to Broadway; with SPR ~0.7 and BU’s range polarized, we should mostly check and let BU bluff, but a small block bet can be mixed in. The 7BB block bet is a reasonable sizing, but the solver prefers checking this combo.
Note: River block bet is reasonable but slightly lower EV than checking; solver prefers checking A-high here.