River situation in 3-bet blind battle

[DonkBluffer]

Villain is on 2 of my tables, which are both 3-handed. Don't have much of a read yet, but he's fairly LAG preflop. Assume he's a thinking player.

$2500 effective stacks. BTN folds, villain raises to $60 in SB, I make it $200 in the BB w/ JTs. He calls.

Flop: K96r. Check, bet $265, call.
Turn: K. Check, check.
River: T. Check, then I bet $450.

How's this for a valuebet? I figured villain would have a worse pair a large % of the time.

Then villain check/raises all-in for about $1600 more. Now what?

[AAismyfriend]

This is close. The fact that you would likely never play a K like this makes me think it's closer to a call than a fold. Also, river is an easy value bet.

[DonkBluffer]

Yeah, at first I thought: he almost always has a made hand. He either has a worse pair (nines, sixes, random pocket pairs) or he has a better hand than me. He would not check/raise all-in with the worse made hands, but he might check/call with them.

But from villain's perspective, if he's holding a pair <tens, I could be bluffing, in which case he'd win the pot whether he check/calls or check/raises. But I could easily be value betting AA, QQ, JJ and Tx, making a check/call look less attractive, but he has some FE if he check/raises. Isn't a check/raise superior to a check/call for villain?

And if that's true, isn't bet/folding wrong here?

[AAismyfriend]

These hands are really tough to give a good answer too, as making the right decisions in these scenarios depends a lot on past history, reads, and the flow of the game. I wouldn't fault you for calling or folding in this spot, as good arguments can be made for both options. Have you seen him take this line before as a bluff?