Hero is effective stack with about $600.

V is Old-ish guy. We recognize his face but don't remember playing with him before. He comes from a broken game and covers. First or second hand so no reads.

OTTH: Hero opens UTG to $12 with QQ, one call and V 3 bets to $31 from MP. His undersized 3 bet shows strength but I don't want to flat and likely go 3 ways with the worst position. Folds back to Hero who 4 bets to $100. With no reads and a big stack I like 4 bet / fold here Vs big stack arriving at the table. I think my sizing was too large though with only one caller in between. I think $80-$90 was probably better. There have been no 4 bets in the entire 8 our session but this is a new player. At 1/2 Vs an unknown who covers us 300 BB deep I'm ok with folding to the 5 bet OOP. First caller folds and V calls way too quickly though so we've probably stepped in it. Ranging him here with mostly KK+, AK as well. I think QQ, AQs hands would have to think before flatting or folding. I expect AQ and JJ- to fold but an unknown could always have a spaz combo or two.

Flop (~$210): Q 6 3
Bingo! Hero $75, V calls fairly quickly but with a sense of caution. Was hoping to induce a raise here from KK+ and AK with diamonds while still getting value from his entire perceived pre flop calling range ( we don't want to blast AK no diamond out of the pot by sizing too large right?).

Turn ($360): Q 6 3 A
Seems pretty gross as the only cards we didn't really want to see were the A or the K. I feel like x/c is best here since we may get KK to fold to the barrel and AK will want to bet a lot, AA may x back allowing us not to get stacked when we are behind. We x, V x.

River ($360): Q 6 3 A A
Ok, now there's only 1 combo of AA that beats us, we x'd turn which may lead V to believe his AK is nutty and V may also think it's less likely we have an Ace if he holds KK. Even if we give him both the combos of AQo here we are only behind 3 combos. So how much do we bet here? We have $425 behind and V covers. I wouldn't mind a jam at 2/5 but at 1/2 I think it scares people away too much. We settle on $250 after quite a bit of thought (20 secs?) and V goes into the tank. After about 2 minutes he finds a call.

Thoughts?

You think he's strong when he 3b then why 4b? 4betting QQ from UTG 300bb deep is fine in theory but in practice vs an old guy is an overrep. I could be wrong and he's might be messing around but we know older guys squeezing is going to usually be strong.

Flop looks ok, could go bigger as exploit.

Turn I don't expect AK to bet all that often, he doesn't want to get felted by QQ, AQ, AA, and won't be afraid of KK. Those hands basically sum up your entire range. I'd bet small again to get the rest of the stack in on river.

As played I think river bet should be a shove but I don't fault a smaller size too much if you want to ensure a call from a not so strong ace or suspicious KK.

I often do flat the 3 bet here in this spot. I chose to get out of my comfort zone and 4b this time for a few reasons.
1 - I thought it was at least equally as likely that V auto 3 bets TT+,AQ+ here and doesn't understand sizing as V having the top of his range and inviting it to go 3 ways in position with KK+, AK.
2 - As mentioned I'd rather get it to heads up then have to worry about additional V that can call quite a bit of Ax, Pocket pairs, and suited Broadways that can come back to bite us.
3 - It's less likely I'll get 5 bet and have to fold my equity since 5 bets are so incredibly rare in this game.

I think I do like your small turn bet line better as the AA could still raise us while AK may be more content to flat.

FWIW I don't mind a 4b and I don't think the old V is always strong here with this tiny 3b. He's either 1) nitty omc who doesnt understand sizing and has a big hand or 2) weird button clicker who is trying to build a pot deep in position with a wider range. If (2) is more likely then it's a slam dunk 4b.

We should bet this turn. Sizing is debatable. Mdelore makes a good argument for small sizing. But I'm disinclined to give FDs and JTs the right implied price to draw. So I'm probably going 1/2 psb recognizing this doesn't leave much behind for the river, but we're not betting diamond or most broadways anyway.

Grunch: I like it. I wouldn’t hate a smallish bet OTR but repoing I’d here isn’t the worst thing.

I'm fine with pre, but would go a little bigger on the flop. I would also bet turn, because an A is a likely holding and I want more money in the pot. This is where I might choose to down-bet, although it's not a play I make often.

As played, river is fine.