What potion gives the drinker unusually good luck in the Harry Potter books?

Felix Felicis is the potion that gives its drinker unusually good luck in the Harry Potter books.

Felix Felicis is also called “Liquid Luck.” In Harry Potter and the Half-Blood Prince, Professor Slughorn awards Harry a small quantity after Harry performs exceptionally well in a Potions lesson. Harry later uses it as part of a plan involving Professor Slughorn and the memory of Tom Riddle.

The potion does not simply make every possible outcome happen automatically. It gives the drinker the sense that the best course of action is clear, although reckless or excessive use can cause harmful effects. The books also establish that it is banned in organized competitions and examinations.

Amortentia is the world’s strongest love potion, Polyjuice Potion changes appearance, and Veritaserum compels truthfulness. None of those is the series’ luck potion.