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gwern comments on Harry Potter and the Methods of Rationality discussion thread - Less Wrong
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Really, you should use it to try to discover a more powerful luck potion, then take the more powerful luck potion to try to discover a more powerful luck potion still, until eventually you get a hard-takeoff scenario where ever-more-powerful luck potions are falling from the sky into your hands by pure chance every second.
After the luck-ularity, Harry can just throw a random rock up in the air, and it will hit Lord Voldemort right between the eyes, killing him instantly at the same time the Pioneer probe crashes into an asteroid.
That's already taken care of; if it's luckier to discover a luckier luck potion than the Philosopher's Stone, then that's what I would discover. And of course, by induction, then subsequent consumption will result in even luckier potions (since luck presumably compounds so any subsequent improvements will still be luckier than a PS's discovery).
If there is no luckier potion or the Luckularity would hit a plateau, then I would be better off with the PS and hence the luck and preference would line up. So seeking the PS is the dominant strategy.