Harry Potter and the Half-Blood Prince
The potion's greatest power is in showing us that our innate abilities are as powerful as magic. When Harry tricks Ron by pretending to pour the potion into his pumpkin juice before a Quidditch game, Ron believes that nothing can go wrong because he is under the influence of a potion. As a result, he plays better than he has ever played before and he wins the game for Gryffindor. When Harry reveals that no luck potion was ever involved, Ron realizes that he was capable of greatness all along. These wizards and witches of Hogwarts must learn both how to use magic and how to get along without it by trusting themselves. Magic is often not the most powerful tool in the shed.
Interestingly, the good luck potion also helps Harry secure the much-needed Horcrux memory from Slughorn. The fact that Harry is only able to retrieve this memory via magic reveals the extent to which humans will go to prevent others from discovering secrets, from having their real selves revealed. Slughorn's self-hatred is so huge that he will stop at nothing to make sure his memory is kept secret. In this case, magic helps undo the damage of human guilt.