AA is close to TT. Tiny dif if some bigpairs limped pre. So what when it is equal do we want to fold or call 100% because TT=AA? I offered an aproximately unexploitable range for call, ofc we can throw coin instead, mix ranges some way etc.

Yes board is rather dry. But here are we 3in, lets say one one with 9x second with SD/Ax gutshot. Now they have 13 outs together. Something like one V having FD+gutshot, such draw needs respect.

if you think he is capable of having 45 in this spot then maybe you can bet and fold to a raise.
There are 6 combinations for having sets in that spot ( assuming he has a set of deuces or threes).
There are 4 combinations of 54 suited hand that may have limped pre.

But when you think about it, if he has 54 in that spot, then he could have called with 65 on the flop and continued on turn because he gained some equity.Since the river is an 8, u are beat a lot in this spot, even if u assume he as suited connecters on the river.

i think u have to check/fold.

It's much more interesting (and probably more accurate) if you think Villain could have limp/called his button with the offsuit combos of 54 and 65 as well. Then he has potentially 16 bluff combos and up to 22 value combos, and on the river we are left guessing whether he decides to pull the trigger with his bluffs.

If we think he only has suited combos of both, then he has potentially 4 bluff combos and 9 or 10 value combos (9 if you think he needs a backdoor flush draw to call flop with 65s), which means check/fold becomes a better option.

CallMeVernon thats an interesting way to look at it. I assumed he only had suited connecters in that spot but probably you are right when you say we should assume he could be limping 65 and 54 off as well.

CallMeVernon I counted rather SCs for SD and Ax with gutshot. I also feel that this spot otr is underbluffed, I dont mind overfold it a bit.
Thats why I offered folding TT-QQ and call with KK+ 99, which is given the potsize overfold.
Only dont want to give free card ott nor x/f 100% otr.

If you think you can expect a river betting range to be weighted towards value, more so than the pot odds you're getting, the correct play is to fold ALL your bluff catchers, not just some of them.

X river is not the best river card it improves his value range slightly so a bet is going to be considerably less EV wise compared to a check now.

Also he can still have his slowplays given i don't expect villain to have a raising range on this board which means even more value hands. If he is as good as you say then it is too thin to value bet 3 streets w/TT... AA yes it's fine being this deep in this spot.

Pretty sure v has some SDV hand tho what worse hands will call i honestly think if we triple barrel v will fold hands we are ahead of some of the time.

Checking is going to be more +EV w/TT in this spot then betting for thinnish value unless he absolutely LOVES to hero-call rivers light.

It's close with QQ+ im betting for v tho.

grunch. The only draw is 45. I'm assuming V folds A9 on the turn, and probably raises it PF some of the time.

I would check and evaluate, but most likely fold if he bets. If he got to the river with a marginal 9x hand that you are ahead of, he is probably going to take the free showdown. If he bets, it's going to be 22 and 33 most of the time. If he bets small enough that you can throw a few combos of 45 into his range and make it profitable, then you can call.