Preflop: Standard.
Flop: Perfect check/raise. You got a rag, rainbow flop that likely missed this villain's range, and he's on the foldy side. I'd honestly be tempted to check/raise this flop with any two cards provided my image is clean, but you have two overcards and a gutshot. IMO, not check/raising and putting pressure on villain here would be a large mistake.
Turn: Ok, this is where you ****ed up. The turn ace is obviously not ideal, but if we put villain on this range:
22+,A2s+,K2s+,Q5s+,J7s+,T7s+,97s+,86s+,75s+,65s,A2 o+,K8o+,Q9o+,J9o+,T8o+,98o
He will still have no pair, no draw 148/419 =
35.3% of the time. There is
4.25BBs in the middle, and you still have outs to beat better hands (including 4 outs to the nuts).
You have a very profitable bluff here if you just bet the turn. Assuming you never hit anything, your bluff only has to work 1/5.25 =
19% of the time, but you will sometimes improve to the best hand so your bluffing odds are actually significantly better.
Plus the best way to exploit villain's wide range IS to bet the turn. The problem with the check/raise bluff here is now you put yourself up against a tighter range (and you're paying more to try to get that tighter range to fold!) When you check, villain may check behind a lot of his garbage, he may even defense check with hands like KK, etc that may've been waiting to pop you on the turn. This is a bad dynamic for you. Bet the turn so villain's whole wide range is exposed.
So to reiterate, villain's flop calling range is usually gonna be much wider than his turn betting range after you check. Utilize this fact and just bet the turn, which is very likely a nice profitable bluff vs this villain.
Notes: