For many people, that luck already happened based on who their parents are and what sort of upbringing they had. Someone born to middle-class American parents has a whole lot better shot at being a billionaire than someone born in the inner-city ghetto, or, for that matter, in rural China.
Much of the remaining "luck" comes from our choices. Think of it this way: how many people choose to work a steady job for all of their life. They will never be a billionaire, regardless of how lucky they get, and so their contribution to the average is zero. Actually, I suspect this invalidates your math: more than 1 in 2 people have probability zero of being a billionaire simply by virtue of not taking the chance of being one, and therefore of the people who take the chance, the odds are significantly better than 0.0001%.
Much of the remaining "luck" comes from our choices. Think of it this way: how many people choose to work a steady job for all of their life. They will never be a billionaire, regardless of how lucky they get, and so their contribution to the average is zero. Actually, I suspect this invalidates your math: more than 1 in 2 people have probability zero of being a billionaire simply by virtue of not taking the chance of being one, and therefore of the people who take the chance, the odds are significantly better than 0.0001%.