Preflop: Hero is SB with Q A
MP folds, CO raises to $0.06, BTN raises to $0.20, Hero calls $0.19, BB folds, CO calls $0.14
Flop: ($0.62) T Q A (3 players)
Hero checks, CO checks, BTN bets $0.48, Hero raises to $1.89 and is all-in, CO raises to $3.81 and is all-in, BTN calls $3.33
Turn: ($10.13) 3 (3 players, 2 are all-in) River: ($10.13) 5 (3 players, 2 are all-in)
Spoiler:
Results: $10.13 pot ($0.30 rake)
Final Board: T Q A 3 5
CO showed A Q and lost (-$4.01 net)
BTN showed K J and won $9.83 ($5.82 net)
Hero showed Q A and lost (-$2.09 net)
Did I goof here? Should I have 4-betted this flop with AQo against BTN?
Against a 3better and a overcaller, in hindsight I think might have jumped the gun a little bit going all in there. With that 3/4 pot bet immediately on me, I felt it was either fold or shove with a Villain behind me: Calling to be reraised behind me would have been even grosser. And in the unknown, there was some possible fold equity if either Villain ended post-flop with JJ or AJ.
I highly doubt either Villain would have called PF with either AA-KK or AK. So what remains are other two pairs, sets, or made straight here.
Would I be correct to calculate my pot equity as such?
Total pot = 6,27$
Shove = 1,89$
Pot equity = 30.14%