There aren't very many busted draws here, only the spade draws and one straight draw. Throw in the fact that you have the JJ blockers, and that you look showdown bound here. I don't see many bluffs on his part on that board. I don't see many value bets from hands that you have beat either. Nor do I see many hands beating you that will check back. A king is betting.
Checking and folding (C/F) requires a good read on the opponent (and some guts).
Checking and calling (C/C) loses money if my interpretation above is correct.
Betting and folding (B/F) to a raise seems like the natural play without further reads on the opponent.
Betting and calling (B/C) is 100% read based. (What can you beat? Nothing except bluffs!)
I think he will call with
I don't think he has a K. You should have heard from it before. He might very well have an A. He'll call or raise with that.
Versus his A, you neither win nor lose money compared to checking and calling. He doesn't usually have kings, but still, these are betting if you check. Then there are the monsters. Same thing. C/C and B/F have the same outcome.
Now, versus the T, and the PP, the B/F line show profit. These hands will never bluff raise you (they might on $10/$20).
The conclusion is that this guy must bluff hell of a lot for the C/C line to be better than a B/F. If he is the opposite, then C/F is viable. If he is anywhere near normal, the B/F play is correct.
At any rate, the whole thing is a exercise in math once the read based ranges are in place. I haven't done the math for any complicated range on part of the villain.
/Johan =