Hey guys,
The correct play is to push flop, to maximize our fold equity
I'd bet $0.7 on the flop.
After the call you should play c/f.
That's what basic strategy suggests, but its not optimal.
Your hand is really strong against his limp/calling range.
Not only you have 2 overcards (in the spot, where Ace high might be good sometimes), but you also have hidden out, because of the paired board.
For example, if he has 22-44 or 56, any 7+ card on turn, will give you 3 additional outs
5TT turn J
now you have 3 J outs, because your Ace will win against his small pockets
Besides, you should realize how wide is his calling range here. By c/f after he calls, you will give up a better hand fairly often. Not mentioning how committed you are against his range.
Bet/call is even better then bet/fold, but in this case you sacrifice descent amount of fold equity that determines your EV in this spot.
Therefore, push flop is a very correct play here.
as played, push turn