Shall I bluff at this river runout?

You should give up here. It’s really hard to get someone to fold top pair on this board after the flush draw bricks. If you ever have a value hand in this spot, you should go huge because Ax is always calling. You also have some showdown value so there is less reason to bluff.

I’m really not a fan of the turn lead here either. Pre-flop and flop are probably too loose but the turn absolutely should be a check/fold.

Id fold flop. Turn bet not sure what story is being told here? A9? River check. Maybe you can check raise as a bluff with the king and no hearts

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I think it takes some fold discipline for AK & AQ to fold, but AJ & AT can't fold their two pairs no matter what. They may tank forever, do some table talk, and cry call at the end, but never folding.

I thought it would be great shame to waste our image, as it is not often we are so card dead to build up this image, and if not due to the weather I might not be dressing in such a 'tight weak' manner. However like DAN GK pointed out, with the busted front door FD, it's not an ideal board to bluff.

Image isn't everything, esp. at 1-2 where people don't notice enough. Having a dress and handbag might help a lot though.

Can see being bored and calling pre. ... it's probably a small mistake, but we've all done it.

Would fold flop.

Turn lead makes no sense to me, you say you 100% check/fold turn ... that seems bad.
Do you always raise TT/44 on the flop?
Would lean heavily call with both hands (and every continue), and then even though it's beluga whale 101 I'd probably x/r turn with A9+ and some flush draws that have more equity on this card (Eg. QJ/J9/J8).
Half pot also doesn't feel like the size I'd pick, if I had any turn leads.

On river we are only beat by Ax/J9/T9 ... snap turn call is less likely to be AA/TT/AT as they'd normally think about raising, could be a good flush draw or maybe AK/AQ/AJ that doesn't want to raise but isn't folding. Seem like a bad hand to turn into a bluff due to showdown, but I'm not really sure where it is in your range either and river bluffs should be more non-FD hands when the FD bricks out ... so with that theory this is better than Jh8h.
Also just generally against bluffing into low VPIP people on AJT9 boards, esp. when they snap call turn and esp. when my turn lead didn't make much sense. Then again if I was V and you bet big on the river I probably still fold a lot without reads.

Preflop: If the villain seems tight and is raising from early position I would fold KJo.

Flop: As played, fold. Your OOP against a tight player representing strength and there's a good chance your pair outs aren't good.

Turn: As played, check/fold. Your opponent could easily hold a pair of aces with a good kicker or any number of other strong hands. Leading for half pot isn't going to push him off any of them.

River: Check. If the card was a total brick or something like a low heart then maybe you could blast away, but here you have showdown value now. If he has something like KTs he won't call you, but there are very few hands better than yours that will fold to a bet. Just check and hope you get to show down your pair.

Just my opinion.

Thanks. You actually raised a lot of good points. This one has also been addressed by an earlier reply, so I will answer this one first
.

On the turn, acting OOP, if I know and I am behind, IF I do not want to give up yet, I will bet with my draw, regardless of FD, SD, anything.
Let's say if I was on a heart draw, I check-call the turn, and a heart arrives at the river. I am going to lose a ton of value because me being on a draw is so obvious, OTR it will only be I bet and V folds, or I check and V check. Check raising is not an available option provided to me.

If leading the bet and getting a flat call is the same price as check-call, why do I check?

And most of the time, betting the turn gives me a cheaper price. As you said, half pot is not the correct price set by a heavy-value or high-equity hand. True, but that's the right price that fit the 'tight weak' image. That's how much a tight weak would bet. The hand is not finished yet, so I am not going to break that image.

Surely check-fold the flop, and check-fold the turn is the standard play, and I 100% agree with that, and I do that the majority of the time.

Not every pot is worth fighting, at that moment I just did not want to give up that one before river. If I was like an other player at the table flopping 3 sets within one hour, I did not need to spend my energy fighting this pot.

AP, whether to bluff the river was more interesting.

I understand the logic, you maybe get some folds and it costs the same as x/c... However doing this assumes nobody ever notices that you keep leading turn with x/c hands, and starts raising a lot of the time you do it. Or even V has a great hand, like AA/TT and raises anyway.
Dito anybody noticing that your turn check range is 100% folding.

Noted with thanks. I will have it in my mind to prevent being exploitable in future play.

FWIW My check-call flop, check turn range includes 44, and that's gonna be a check-raise OTT to target Ax and to charge FD.

That's good to note, too. A lot of the time I try to put myself in V's shoes and think what I would do, but I am also aware that most of the Vs think differently(sometimes very differently) than I do. That's why listening to other players' thoughts in the forum are helpful.