way ahead, way behind

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To complicate the strategy a little: let's say your opponent is a very aggressive player who likes to bluff and is very likely to try to use that A to push you off a hand (assuming the play of the hand up till now has led him to believe you're on a pocket pair).
Against such an opponent, you should bet knowing full well that he's likely to checkraise and you will call down.
This of course is more risky than simply checking behind because he may accidentally happen to have an A. But if your opponent's tendency is to play too loose and aggressively, you have to take that risk sometimes to let him hang himself.

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This is an excellent point, and playing this way can be a very profitable strategy against the right opponent. This is a great example of how knowing your opponent can make you extra money.