[jgorham]

I have trouble comparing the likelihood of him checking to raise to checking to call (with a worse hand) since both lines are unusual, and both legitimate for NW. So I would probably just put him on a range of (legit) hands and disregard the fact that he checked on the river and make the play that compares best against his hand range.

Even if we put K5s in his range, your equity is really low since there aren't many hands that make sense. After his bet 3bet I give him JTs, A5s, 55, and possibly K5s. And your equity is at about 25%. I don't think the check on the end really changes that hand range since he could check with any of those hands, so I check behind.