AQo defending SB

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AQo defending SB

Blinds: $0.01/$0.02 (3 Players) BB: $3.95
BN: $2.11
SB: $2.00 (Hero)
Preflop ($0.03) Hero is SB with A Q
BN raises to $0.07, Hero raises to $0.20, BB folds, BN calls $0.13
I think SB should almost always be raising with a tight range. AQo is good enough and I think bet sizing is fine?
Flop ($0.42) 2 4 8
Hero bets $0.22, BN calls $0.22
Not sure who has range advantage here, but I think ranges are close. Maybe its better for villain since he could have 88,78,89?
Since I 3bet I think I can represent an overpair plus I have equity if I hit A or Q.
Flop is dryish so i think half pot is enough?
Turn ($0.86) 2 4 8 K
Hero checks, BN bets $0.42, Hero folds
BU calling range is now tighter plus they can have Kx in their range, So I think c/f is best
Final Pot BN wins $0.83
Rake is $0.03

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