Trying to figure out if my play was +EV or plain stupid

Hi all,

I am sure you guys can help me with this one. This was my second hand at that table; so I had no read on anyone. Based solely on the preflop action, I put the button on JJ+,AQs+,AKo. On the flop, with villain's range (plus 44 added), my equity is

equity (%) win (%) tie (%)
Hand 1: 76.0490 % 74.20% 01.85% { AcAs }
Hand 2: 23.9510 % 22.10% 01.85% { JJ+, 44, AQs+, AKo }

That makes my bet on the flop +EV regardless of what villain actually holds. Am I right or is my logic totally flawed and my bet was stupid? (Villain had QQ).

Ultimate Bet
No Limit Holdem Ring game
Blinds: $0.01./$0.02.
9 players
Converter

Button is at seat 0 with $2.32.
Hero is at seat 1 with $1.98.
BB is at seat 3 with $1.19.
UTG is at seat 4 with $2.63.
UTG+1 is at seat 5 with $1.88.
MP1 is at seat 6 with $1.17.
MP2is at seat 7 with $4.65.
CO+1 is at seat 8 with $3.89.
CO is at seat 9 with $.63.
The button is at seat 0.

Pre-flop: (9 players) Hero is SB with A A
UTG folds, UTG+1 calls, MP1 calls, MP2 calls, 2 folds, Button raises to $0.13, Hero raises to $0.54, 4 folds, Button calls.

Flop: 4 4 Q ($1.16, 2 players)
Hero is all-in $1.44, Button calls.

Turn: 9 ($4.04, 1 player + 1 all-in - Main pot: $4.04)


River: 8 ($4.04, 1 player + 1 all-in - Main pot: $4.04)


Results:
Final pot: $4.04

Its fine. With 1.5 times potsize left you arent EVER folding. Youll get called by KK,QQ,AQ (if he has it),AhKh (if he has it)

even just taking his range as KK,QQ,AA you are ahead since he has KK more often than QQ (because one of the Qs is out). Also any other hand that he might have is behind you.

Having said that it might be better to bet say $0.70 and then push the river. This is really opponent dependent though and purely depends on which you think hes most likely to call with JJ.