Not really a genetic lottery, though some places in the world make it a lot easier to succeed and become rich. Being born or move to any of the western nations will greatly increase your chances. But the person also has to have a will to do so too.
But the person also has to have a will to do so too.
Unless they inherit wealth or connections. My understanding is it’s about a 50:50 split between make or inherit worldwide depending on what you call weath.