I've gotta ask a question about the pre-flop action:
If we're out of position on the flop, it means we were in position before the flop. So: did the villain limp in and then call the raise, or did they raise then call a re-raise?
In the first instance villain could have just about anything. In the second, it polarises their range slightly more towards strong hands - though we're heads up, so it doesn't necessarily mean any kind of monster. I figure any pair, any ace, any two paint, connectors, and possibly even some paint-rag action.
In either case, our check on the flop after being the pre-flop aggressor makes it look like we're scared of the ace. If I were the villain, I'd be putting you on pretty much any pair that hasn't hit a set, a couple of high cards or even connectors, and sometimes complete garbage, and bet at the pot almost 100% of the time regardless of the cards I'm holding.
Which means I rarely (hardly ever, actually) flat call this.
What's our plan if we flat call? Keep calling to the river? Check-fold on the turn? Hope a miracle J comes? Down that path lies confusion, difficult decisions, questionable value calls and poor odds
I either raise this or I throw it away, with the action very much skewed towards the raising end. If villain is even halfway decent, they'll be betting this with air more often than not. They don't have to have an ace to call us, nor do they have to have one to bet here. In fact, if they had an ace they might even be inclined to slow-play it a little: there can't be many cards on the turn that will scare them greatly, unless you've already got them beat with a better ace.
If we get raised back, we can probably give villain credit for the ace and get away from the hand.
If we get flat called... then we're in a tricky spot. It could be a weak ace, or it could be something screwy that's hit a lower pair than ours and doesn't believe that we have an ace either. I suspect a flat call of a check-raise will result in the rest of the hand being played very
carefully unless someone catches good, however, and we'll still likely get a cheap showdown - which I'd be inclined to take.