祝你好运(zhù nǐ hǎo yùn) - good luck, all the best, I wish you luck in Mandarin

祝你好运 (zhù nǐ hǎo yùn) is the standard way to say good luck to someone in Mandarin. It is a whole small sentence rather than a single word, which is why it takes the pronoun 你 in the middle: you are literally wishing luck at a particular person.

Swap the pronoun when you are talking to a group and you get 祝你们好运. Drop the pronoun altogether in written notices and you get the shorter 祝好运. The formula also stretches: 祝你生日快乐, 祝你成功, 祝你一路平安 all follow the same 祝 + person + good thing pattern, so learning this one gives you a template rather than a single phrase.

The trap for English speakers is treating it like the bare interjection "good luck!" and cutting it down to 好运. On its own 好运 is the noun, not the wish, and it lands oddly. Keep the 祝 and keep the pronoun.