I'm curious because in most situations (like this one), I would definitely bet the flop. My thought process is that I have top pair and have raised PF so opponent is going to put me on a decent starting hand. When the flop hits and shows an A, opponent should assume I have an A when I bet. If he calls/re-raises, then I can put him on an A too or low-mid PP or the set of 4's (maybe even A4).
If I don't bet the flop, then I won't know where my opponent stands. He could hit just about anything on the turn or river and then I won't know if he's slow playing A's or just hit a crappy pair. I'll probably end up folding even though I have top pair or worse, calling when he has been slowplaying.
So in my mind, I would think betting close to the pot in this case would be a standard move. If I leak the .50c with a pair of A's then so be it. A decent amount of time I will pick up the pot here, at the very least know where I stand.
I could be completely wrong (I'm sure I am), but if this is bad play, can you please elaborate on the strategy you would take?
Check to the showdown if opponent lets me? If he bets pot on turn/river do I call or fold? I am really interested to see how you would play this hand out starting on the flop.
You pose good questions and I think your reasoning is fairly common, so this is probably a good topic to address. Let's make one thing abundantly clear first, though: Opening preflop is totally standard. I don't care who's in the big blind, I'm always opening A9o from the small blind.
Still regardless of who is in the big blind (because we don't know him), we can look at this flop and decide that it's as dry as the Sahara. Some flops hit wide ranges; the only two flops that are dryer than this flop are A-3-3 and A-2-2 rainbow respectively. This is the third dryest flop available, and there are a lot of flops available.
Looking at our hand value, we have top pair with a mediocre kicker. We have no real ways of improving other than spiking a nine or an ace, neither of which constitute outs to the nuts. If we need to improve and do, there's a decent chance that our opponent does too or already has us crushed. Furthermore, the complete lack of draws (barring a very unlikely 5-2, 5-3 and 3-2) makes it so that if WE are the ones who are ahead, then there are very few cards that will improve our opponent's hand. He's drawing to a maximum of 4 outs (gutshot), but more likely 3 (ace with a weaker kicker) or 2 (pocket pair in the hole). In this situation we are said to be "Way Ahead or Way Behind" or "WA/WB."
Now, when I have a decently strong hand but not necessarily one that I'm comfortable getting it all-in with, I like to think like this to help understand why certain lines are better than others for a certain situation:
"If I'm ahead, how many bets can I get out of my opponent?"
What's your answer on this board? Mine is "1". The typical opponent won't put in more than one bet with a worse hand than ours on a board as dry as this one. Some will, sure, there's no denying that. But much as we like to, we can't treat every unknown as a calling station who will stack off with KQo here.
We need to get one bet in, and we have a few ways to do this. One is to bet the flop and give up if he calls/raises. One is to check the flop and bet the turn if he checks back. One is to check/call the flop and check/fold the turn. There are other ways. But of these basic ideas, against an unknown, it's safe to say that checking the flop is the best way to get that one bet in while still ahead. This is because for most opponents
1)
bluffing the flop when checked to is relatively common.
2) Calling the flop with air intending to bluff the turn ("floating") is rare.
3) We are expected to bet this flop, so our bet doesn't necessarily represent the ace. He might well bluff-raise this flop to take it away from us, and we can't really call a raise unless we think that he's wild.
So we check the flop, because it will induce a bluff some of the time, and it will make him look us up a bit lighter on the turn when we bet after he checks back the flop ("Hmm, he can't have an ace, because he would have bet the flop"). Some of the times, he'll draw out on us because we gave him a free card, and that sucks. But, some of the time he'll check back the flop and WE draw out on HIM.
Having said all that, I now turn to a completely different perspective to see if we come up with the same conclusion:
There are three overall reasons to bet any flop:
1) As a bluff (T8o on the above flop, for example)
2) For value; to build a pot (77 on a Q-9-7 flop)
3) To protect our hand (66 on a 2-2-5 flop; we're likely ahead but don't want to give a free card to 6 outs)
... and I don't think either of these three apply in this scenario. I'm struggling with this myself a bit, but my new default move on any flop is to check. I only bet when I have a reason to do it. And here, I can't find one.