What is the name of the potion that makes the drinker lucky?

The name of the potion that makes the drinker lucky is Felix Felicis. Also known as Liquid Luck, it temporarily improves the drinker’s luck, making successful outcomes more likely while the potion remains active.

Felix Felicis is difficult and time-consuming to brew, and a mistake during preparation can make it poisonous. Because of its powerful effects, the potion is controlled at Hogwarts: students are not allowed to use it in examinations, elections or sporting competitions. Excessive consumption can also produce recklessness, dizziness and overconfidence.

In Harry Potter and the Half-Blood Prince, Professor Slughorn gives Harry a small bottle after Harry appears to have brewed a perfect Draught of Living Death. Harry later uses the potion to create the impression that he has taken it, persuading Ron to act confidently during a Quidditch match. He eventually drinks it to encourage himself to obtain an important memory from Slughorn.

Felix Felicis does not guarantee that every desire will come true. Its effect is better understood as heightened instinct and unusually favourable timing. It is therefore different from Veritaserum, which compels truth-telling, Amortentia, which creates powerful infatuation, and Polyjuice Potion, which changes appearance.