[rory]

I think I instantly check-call the river. The 7 is a great card for you-- any draws he could have had missed. If he had some sort of gutshot and picked up a flush draw or something on the turn, he also missed. He may be more likely to bluff a busted draw with the 7 hitting, because it looks scary to you. He won't bet K high here and he also might not bet a small pair, fearing that you have a pair but are scared of the board pairing.

My guess was that he had either a 4 (which he might not bet) a busted draw or a 7 on the flop. The 7 makes it a lot less likely he has a 7 and also that he will bet a 4. I think you will see a hand like T6 or maybe 59 or like any overcard+gutshot combo with two diamonds, possibly two hearts he decided not to raise and that sort of thing way more than 1:6 times to make the river call pretty easy. I can't see him really having a K here too often, unless he has a suited king of hearts or diamonds with some card in the gutshot range on the flop. So betting is totally wrong-- I think I saw some responses saying bet.