My first thought was a scared set or the same hand which would obviously be quite rare.

If he's a nit, he's only 3 betting KK pre so he'd only have 1 set combo and even nits will bet there. 

I think I'd call if we hadn't already had a huge chunk of our stack taken out. As played here I probably tank/fold.

I'm totally ok with turn lead here, too.

Given the range you assign him, why would bet turn?

Plus I have good equity against his range on the turn after he checks the flop. I don't think he would bet the river with AA or AK he would just check behind, he played a hand with AK where he rivered trip K and just called all 3 streets against QQ.  

River seems easy bet-fold. He is bluffing close to 0% and not likely to valuebet light (AA, AK). His line looks like a some pot-controlled hand (AA, AK) with sd-value that he is pretty likely to call again on the river. 

With given reads I would fold pre against 3bet. 

If we check the river, fold against that bet-size seems fine. 

Agree with Jugi, I like bet/folding

What sizing would you guys go with for a bet/fold?

So our read is that he is such a nit that he will only valuebet KK on the river and check behind AA and AK? Than we can exclude AQ from his pf 3betting range... an also AK a lot of the time imo.  I dont know, I see nits playing AA like that and vb river since AA are "safe" now(no diamond, no str8 etc...).

But if he really only bets KK there I like fold pf and bet/fold river as others have stated...

5555/fold riv, ez game

Interesting spot for sure. First of all, your play. What would you say his exact range is PF? Based on your description of the villain it seems like he's a QQ+, possibly AK 3 betting type of guy. What does he think of you? Do you think he's able to adjust his 3b range based on your tendencies? Like if you're opening tons, is he able to recognize that an widen his 3b range? Based on the assumption that his range is QQ+ and some AK, we're not doing so hot pre. Blockers weight him a bit more toward KK, which is helpful to know, but dubious to willing proceed against. Our pot odds are good though, but our hand is weak given the context (OOP vs a range that exclusively dominates us). 

Getting to postflop, I'm concerned with the continuity in logic as the streets play out. Why did you bet the turn? It seems illogical based on the range we're assigning him. We're likely still beat, though clearly have equity (Ad) in the pot, but betting puts as at risk of getting raised off our equity, or as least off of a price we'd prefer to pay. I think you check for a bit of pot control, as well as to let his bluffs, the few/none that he has, bluff. Your turn bet suggests you like your hand, then on the river you don't like it when it's strength has improved, on a river card that does nothing to change his range, except eliminate any chance he has QQ. You also say he could have a set of KK or 77. KK I definitely think is plausible all the way from preflop to the river: He 3b preflop because he has an awesome hand. He checked top set on the flop because he could still be behind a flush, and is scared to face a Ch/r. (Also adding a bit of deception to his hand strength). But 77, he cannot have. All of a sudden he's 3bing that pre? That seems extremely unlikely that 1. he would 3b it and 2. he would get to the river this way with a set. I think each are very unlikely individually, and of course much less so in tandem. I'm not saying you can't reevaluate mid-hand and change previous assumptions, just that in this instance, the new conclusion doesn't seem correct. Turn, again afraid of the possible flush, so he calls. River, bingo full house, time to bet big and get my man. So I could see that. In fact, it seems to be the single most likely holding all things considered. Something like KQ or KcQd could be a candiate too. Could he be bluffing? With what? It's tough to find a reasonable combo for such. JJ or JJd that is trying to make you fold AK or something? I'm not sure. I think he tends to have it when he 3bs, tends to have it when he bets big on the river after taking a tricky line, and tends to have it cuz he's old! Final note, having the Ad is crucial in so many ways. Most of all for the fact that it takes away a lot of the bluffs he's representing with his river bet / betsize. 

Hey Tom! Thanks for the reply. I just read your initial response to the OP. I first read the OP, and then replied without reading the responses to make sure I didn't bias my thoughts with popular opinion. There's some great stuff to touch on here!

His sets: Yep, we're on the same page with this concept: he doesn't have 77 in his PF range, therefore it cannot be in his postflop range. Disclaimer - of course we can always reevaluate, but in general and concept-wise we agree here.

"Turn lead is okay". A bet is either for value or it's a bluff. There are occasional times where this line isn't black and white, but rather blurred and somewhere in the middle. Such times could include, betting to maintain the lead as the hand continues, betting for protection, betting to prevent a likely worse action from occurring, and things along those lines. But, generally speaking, and much more often than not, a bet is either a value bet or it's a bluff. 

In the case of this hand, when/if we bet the turn, what is our bet? Are we betting because we think we have the best hand? Are we trying to make him fold a better hand? In this situation it's pretty ambiguous on the surface,  which type our bet is or should be. It's almost a candidate to be in the rare middle ground type of hand, but I think we can firmly categorize it upon deeper review. Based on reading the hand (details in my first post here) and what can happen when we bet and when we check, checking becomes the better option here to me. In this case it's almost like our hand isn't good enough to value bet vs his range, but we also don't feel the need to bluff with it, so instead we can check. Checking allows us to realize nut equity at a likely reasonable price, free if he checks or the size of whatever presumably standard size bet he makes. Checking allows us to let him bluff, and then bluff catch with immediate showdown value and fine equity to improve our hand strength drastically. Checking allows us to put less money in the pot when we're behind. 

This is a long-winded and specifically detailed way of saying that before you take an action in a hand, understand the reasons why you took this action, and why you didn't take other action. In this case, why is "a turn lead okay"?

As for your logic behind saying a turn lead is okay, I think it's pretty clever. Why not pace the betting if we can, name the price so to speak? I do think this will happen a lot of the time in a situation like this, for the reasons you states. But I also think we need to take a broader view of this spot. For example, what happens the times when he does raise our turn lead? Maybe he feels our size or our appearance at the table indicates we have a weak or medium strength hand, and he's confident his KKK is best, and he raises us. This is a disaster. I think that with checking we get to avoid that disaster, and we get the benefit of him bluffing (with like JJ only, ha?) thrown in. Your logic is there! I think it could be developed a bit further, and I think it could even benefit from an exercise. Maybe assign him percentages for each time an action happens? Like If I bet XX on the turn, he will call 80% and raise 20%. If I check the turn, he will bet 50% of those times. Etc. I think in doing so it might give you an additional way to conceptualize the spot, and see how each possibility of it plays out, before recombining all of that insight into the big, total picture. 

I like how you described the river situation. I strongly agree with that. There's just a fair amount of ambiguity in a spot like that, which is annoying! But I think we did our best to break it down with the information at our disposal, and I'm relatively confident that folding the river as played here is correct, and we'll be shown kings full here a lot.

Thanks man! I will make a concerted effort to post more. I need to figure out a way to make smaller posts though, haha. Then I'll be able to get a lot more out there. GL. 

Something I thought stood out was the 3 bet sizing.

Given the "nit" perception of the villain, I think his range could actually be wider than QQ+ because of his sizing.  I would expect an older nit to size his pre 3bet more toward 3-3.5x there with a stronger range.  Especially in the WSOP main on day 1.  Did he have a ton of chips and decided to play against his image on the BTN? Possibly.  As a player who doesn't always play true to the optimal lines, I could play this hand as check call the whole way with runner runner Qs, but I definitely agree with other posters, once you lead the turn, a river bet/fold-to-raise is best.