In Chinese number culture the lucky numbers are 6, 8 and 9, and the number to work around is 4. Each of them is a pun. 八 bā, eight, sits close to 發 fā, to prosper. 六 liù, six, carries the sense of things running without obstruction. 九 jiǔ, nine, is an exact homophone of 久 jiǔ, long-lasting. 四 sì, four, is one tone away from 死 sǐ, death. The whole system runs on sound rather than on symbolism, which is why it does not travel intact into other languages.
How tight each pun is depends on which Chinese you are speaking. In Cantonese the eight and prosper pair is much closer than in Mandarin: 八 is baat and 發 is faat, a single consonant apart, which is one reason the enthusiasm for eight runs hottest in Hong Kong and Guangdong and spread outward with Cantonese-speaking emigrants. Four works the other way. 四 and 死 are near-identical across Mandarin, Cantonese, Hokkien and Wu alike, so avoiding it is the one part every Chinese-speaking community recognises.
Belief is not quite the right word for most of it. A developer who prices the eighth floor higher is answering demand rather than acting on conviction, and buyers who pay the premium tend to explain it as resale logic. Skipping four is the sturdier half, because leaving a number off a lift panel costs nobody anything, so it survives in places where no one involved would call themselves superstitious. Plenty of people in China observe the whole thing in public and ignore it entirely at home.