[KurtSF]

Well, let's try looking at it this way.

If you check, you are giving up the hand - it invites a bet you cannot call. $180 in the pot you are surrendering.

If you bet and are called or raised, you probably cannot put any more money into the pot. So it will be your last bet, and it will either win you the $180 or lose you the size of the bet. $120 is a "reasonable" betsize here.

So then...

Your bet is getting 3:2 on your money (can win $180 or lose $120), so he has to fold 40% of the time to make this worth it. Are you more than 40% sure he has the king?

But what about...

If you bet $60 you're getting 1:3. Note that this looks like a suck-in bet - meant to be called - and will be just as hard for a non-K hand to call as the $120 bet. Are you 25% sure he has the king?

Thoughts?

(I ran into this situation almost exactly recently, and I'm not sure what the best line is so I'm interested to hear. In my case I led the turn strong and stacked off to a raise which turned out to be a bluff and dragged the pot.)