Learn Swedish: Han har mycket pengar, men inte mycket tur. - He has a lot of money, but not much luck.

Good catch! Yes, pengar is grammatically plural in Swedish (the singular is en peng, meaning "a coin"). However, it's a famous exception. When talking about money in general, Swedish treats it as an uncountable mass, just like English does. Because of this, you must use mycket (much/a lot of) instead of många (many).

Why is it mycket tur and not många tur?

Tur means "luck", which is an abstract, uncountable concept—you can't count "one luck, two lucks". Because it is uncountable, we use mycket (much), whereas många (many) is only used for things you can count individually.

I've seen mycket translated as "very" before. How do I know when it means "very" vs "a lot of"?

Mycket does double duty! When you place it in front of an adjective, it means "very" (like mycket bra = very good). But when you place it in front of a noun, as in this sentence with pengar and tur, it means "much" or "a lot of".

I thought tur meant a "trip" or "tour". Does it also mean "luck"?