Should I have tried to get more value out of these or was I right to play somewhat cautiously with the Ace on the board? Really wanted to bet River but figured I'd only get called by an Ace so.....

Also, about the 4bet pre....figured his squeeze range was kind of wide and had seen him/her 3bet ATs before.

PokerStars - $0.05 NL (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

UTG: 68.8 BB (VPIP: 23.08, PFR: 8.97, 3Bet Preflop: 6.25, Hands: 82)
Hero (MP): 177.4 BB
CO: 110.4 BB (VPIP: 30.77, PFR: 25.64, 3Bet Preflop: 11.11, Hands: 40)
BTN: 144 BB (VPIP: 25.17, PFR: 21.77, 3Bet Preflop: 10.71, Hands: 152)
SB: 76 BB (VPIP: 14.29, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 15)
BB: 164.2 BB (VPIP: 28.83, PFR: 23.46, 3Bet Preflop: 6.56, Hands: 168)

SB posts SB 0.4 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.4 BB) Hero has Q Q

fold, Hero raises to 2.6 BB, fold, fold, SB calls 2.2 BB, BB raises to 12 BB, Hero raises to 29 BB, fold, BB calls 17 BB

Flop: (60.6 BB, 2 players) T A 7
BB checks, Hero checks

Turn: (60.6 BB, 2 players) 8
BB checks, Hero bets 30 BB, BB calls 30 BB

River: (120.6 BB, 2 players) T
BB checks, Hero checks

Im not sure we even have a value bet OTT lol std 4b calling range will be QQ+ and AK so youre only really getting called by better ever. If he has JJ he really shouldnt be calling anything on this board, and is v unlikely to call a 2nd bet imo

I flat pre but im sure 4b is perfectly fine though it might be a little on the large side, but dont hold me to that.

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You wouldn't expect villain to ever be calling a 4bet with 88-TT or suited connectors? I mean, I wouldn't be calling a 4bet with those hands, but feel like its not that uncommon.

Could be calling flop with a club draw.

Also, didn't mention in my original post but I was 3betting like 13% during this session so feel like people are likely to call me pretty light.

But probably your right, should have just check called through to River.

SCs and medium PPs are much less likely to be squeezing an MP open in the first place because they play better MW especially from BB. Theyre much less likely to call a 4b OOP than IP too imo. Even if they do call with these pre, theyre not what youre targeting to call a 2nd bet. Thats literally just JJ.

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I quite like taking the flop IP, can't see him 5b jamming worst and you have position so don't really have much need.

88 is flat99 close TT squeeze.

OTT you get value from 99 and Jj exclusively. Everything else that you beat leads turn or c/raises and makes you fold.

So yeah I'm just checking down, and then river may bet small