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Gates and Zuckerberg were born into wealthy families. So definitely do that if you can.

This. Thank you very much for pointing that out!

We don't know which percentage of said individuals' success was due to sheer luck and which due to outright competence. For all we know, the former may very well be beyond 99%.

That's a bit black and white. I think in reality, if you have this kind of intelligence and will power, you will succeed anyway, eventually. If your luck is worse, perhaps relatively smaller number of people will hear about you, but it does not mean you'll be much worse off.