By framing the problem like this you are making the assumption the variables are independent which is very much not the case. Your work can influence your luck, and even how much effect said luck has.

Luck indeed finds you hard at work. But also, if you’re not sitting at the table, you’re on the menu.

That hasn't really been my experience, but ymmv. But it's also why we should fight so much against centralization in the economy even if it brings efficiency gains. Ideally you'd want to have as large of a table as possible.