Live 1-2

2 limps
Player with very wide limping range(think 74o) raises button to $12(I think he is raising his broadway holdings here, including things like T9s)
Hero has AcKs SB and makes it $40, folds to button who calls... we are $260 deep after his call

Flop QsTs8c
I plugged this into solver, and am a bit surprised to see a high bet freq(75% bet and 25% check). I did plug that the button is flatting AK preflop which probably is a large difference between live and online.

I decided to check the flop and he checks back

Turn is a Qh
Do we continue to check down here, or is there a reason to be turning this into a bluff? Pio seems to like a 50% turn bet, but I think alot of the check backs are going to be showdown oriented and I dont see us having much fold equity. We do have some showdown ourselves and can probably call a turn bet if it happens having 2 overs, a gutter, and being ahead some of the buttons bluffs/air. Its a bit contradictory to say his checkdown indicates showdown, but then choose to call a turn bet, but I think its possible he could bet a hand like AJo on turn, or A9s, or KJ that didnt bet flop, or have same hand, so imagine we need to call a turn bet

he does check back

River is a 5c
We check
He bets $50, we fold at this point, thinking a hand like AJ, if going to bet, would do so before being able to check down A high on the river. Also, KJ is filtered on earlier streets, so it just seems to be very pair heavy, with maybe a very very small region of air..... Thought it was close though