As I was reading the responses, everyone seems to be thinking that betting the river is for value and checking is for bluffing. Then it occurred, why not bet for "information?" I agree with jrz1972 that if you check, he has the option to check down with a 5, 8, 4, and bet the Q or K(trying to bluff you out of the hand). However, if you bet to make him pay to play, then you can get information on him being that a raise gives him a strong hand, where as a check takes you to the showdown for free - so there is extra value in betting the river. Also, if you bet and he still calls you, then you get an extra bet if you win the hand. The fact that you bet all the way through and then would stop on the King would show weakness. If he raises on the River, after you bet, then at least it is an easier decision to make on what to do next.