What do you do?

Simply: I check behind.

Lets see his expected range for limp-call and check both flop and turn. I dont expect any monsters, that would be limp-raised for sure.

Small pairs, like 44-TT.

Suited connectors, 67s-KQs.

Boadway cards: like KJ, KQ maybe also QTs. Even that QTs is on the edge.

Ax cards, like A5-AQ.

We represent very wide range. Our preflop raise could have been a bluff, and we never called/raised after that.

So, should we raise?

We should always have a reason to raise. Bluff or value bet?

For bluff we want stronger hand to fold.

I dont see a single hand beating us in his range, which he would fold to reasonable raise. And for sure I dont want to bluff-shove and hope he has Ax (that he could fold). That is just small part of his range. And the pot size is just not worth it. And we are not getting extra values if he folds weaker hand.

For value bet we need weaker hands to call.

But at this situation, he will fold most of hands we are beating.

He will check/raise us with strong hands, and we dont want to call that, not even try some bluff catching now.

He will call with Ax probably, but its tie with most of those.

So its a check. Even we are giving him free card for straight/flush draws.

Lets keep my thread extras in "Brad Pitt movie" aread. I think this one is appropriate now: