Now that I think more about it, Action Points seems not the right way to simulate luck.
Maybe you could houserule a new ability score: luck (in addition to Str, Dex, etc.). That would emphasize that some people are lucky and others are not. A pickpocket for instance would attempt to rob the character with the lowest score. Then, if they really need luck (like having someone come out of nowhere save them from inescapable death), they could spend an Action Point plus make a Luck check. If the check is successful, something lucky happens.
Well, this houserule needs to be more thought out, but my point is to say that some people are lucky and others unlucky (at least in a fantasy setting), then that something like Conan's fate points is more apropriate.