what hands do you put in his valuerange when you fold river?

He shouldnt have any KK or TT since he checked back the flop and every draw missed the river.

I dont think that this should be a clear fold especially against a decent reg who is a thinking player. YOu have a pretty good bluff catcher and all the draws missed the river. IF he had a big draw it is almost mandatory for him to bet river when he has no showdown value.

Imo his line does make a lot of sense to me because you dont cbet OTF which hits your 3betting range very hard. I would expect you to always cbet here with NFD top 2 or sets. When bet the blank turn i dont think that you have much in this spot especially when you just call his raise OOP. you will always have a big draw or maybe a pair with a draw (which is exactly what you have) imo.

OTR when the baord pairs i think its a good spot for him to bet his air and missed draws here cuz you willl always have a tough time calling in this spot. His sizing could try to fold out top pair or something better. Cant really see a value hand that he would bet so big OTR. I think trips would go smaller to get value from top pair...

BUt still pretty tough spot OTR!

After you check the flop I would consider a turn 3bet jam. This player could fold which is a great result but when he calls we can have the best hand at times and should have good enough equity the times he has 2 pair

Turn jam is probably good (15 nut draws +TPTK), as played calling the river.  Don't think that many players will slow play sets on this flop, 5 completed no draws, hard for him to have a 5x hand that he is raising the turn for value.  seems like a pretty easy call given that all the draws have missed.

Also our hand is pretty face up, so I try to give guys a little credit for thinking and if it looks like we have a top pair type of hand (now two pair), what hands can he really be value betting now (that also check back the flop given that it's a 3b pot).

yea I don't see how we can fold this river when he reps quads.....I do like the turn jam since we do have a ton of equity and we usually have the best hand anyways

Hey, I play lower stakes than you, but here's what I think.

You have 54% equity vs K5 on the turn. Even if he somehow slowplayed TT on the flop you still have 30% equity. He's also going to have a draw there a lot and we force him to fold by 3betting. This is a spot where he doesn't expect us to 3bet almost ever so it makes sense that he would raise liberally with draws. We actually have one of the few hands in our range that can 3bet, and I think we should use it.

River is one of the worst cards in the deck for him to bluff, if you have a soul-read on him that he'll always shut down without the goods...go ahead and fold. But this is far from standard and I can't see anyone here approving a fold, given the amount of air in villain's river starting range and given how up in our range we are (I believe this hand is better for bluffcathing than AAss because of our K blocker).