looks like a good idea...

but you fold or call the river?
and why?

KJ

I get $148 in the pot and $86 to call for 1.7:1 odds, or 37% to win.

Here's your problem, your opponent is playing like he's got AA or a set. But his play also smacks of a total bluff. Let's ask ourselves, what does he flat call out of position with, then smooth call a board with obvious draws on it, then check raise all in on the turn with?

At first I thought, "he's either got a monster (AA or a set, maybe hit his jacks on the turn but I'm thinking more likely dueces or 6's) or he's completely full of shit because he thinks we are too (you mentioned your LAA table image)." But the more I think about it, he's likely got AJ, KJ, or QJ (much more likely with AJ or KJ than QJ) or 89.

So let's quickly run through the possibilities:

If he's got a set, we're really only drawing to 13 outs (2 diamonds pair the board giving him a FH) so we're about 28% to win and need 2.6:1 just to break even (but we don't play poker to break even, do we?).

If he's got AA, we're a little better - 33% to win and now need just 2:1 for break even. Incidentally, this is the same if he's on the A-high bluff with something like AK or AQ (we can't pair or he's got a better kicker, and our non-dominated card gives him a straight).

If he's on the AJ, KJ, or QJ, then I'd only count one overcard as an out (because the other might pair his kicker, and we don't know which) then we have 18 outs and are 40% to win and need 1.5:1 odds.

And if he's stuck on 89, well, I don't see that happening, so let's just discount it.

I don't even need to assign probabilities to each hand and do the math to tell you this likely isn't a profitable call. But let's do it anyway.

I'd figure 50% AJ KJ QJ
30% set or AA (about the same) and 20% A-high bluff (same winning %'s)



50% * 40% to win = 20%
50% * 30% (avg) to win = 15%

Total winning % = 35%

So a call here is slightly -EV.