NL5 HJ v UTG 4B Pot

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NL5 HJ v UTG 4B Pot

Blinds: $0.02/$0.05 (6 Players) BN: $5.00
SB: $7.54
BB: $4.55
UTG: $5.96
MP: $10.23
CO: $7.85 (Hero)
Preflop ($0.07) Hero is CO with Q Q
UTG folds, MP raises to $0.15, Hero raises to $0.45, 2 folds, BB calls $0.40, MP raises to $1.95, Hero calls $1.50, BB folds
Unknown villain, when he squeezes like this, giving him QQ+, AK, and maybe some AQo, KQo as bluffs? Assuming population is not balanced here, and very likely value heavy. Our hand, QQ has something like 49% equity vs. this range, so I think we have to call. My question is, do we ever have a 5-bet shoving range here?
Flop ($4.37) 9 9 6
MP checks, Hero bets $1.51, MP raises to $8.28 and is all in, Hero calls $4.39 and is all in
Decent board for our hand, overall better for his range. Opt to bet small after villain checks, my thinking is I don't want to give AK a free card. PIO thinks this is OK when you have a diamond but checks all its QQ without one. Feel like I punted after calling his shove. Need 23% equity to call this off. If villain has only AA, KK, and AKs of diamonds, then QQ with a diamond has 18% equity. Is the range I put him on realistic though? I don't know how wide people are shoving in this spot.
Turn ($18.55) 9 9 6 2
River ($18.55) 9 9 6 2 9
Final Pot MP lost and shows three of a kind, Nines.
CO wins and shows a full house, Nines full of Queens.
CO wins $15.50
Rake is $0.67

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