The counterexample is the many people who have succeeded through luck
That's not an example, it's a claim with no evidence to support it. Give me an example of a person who has succeeded with only luck. There are about seven billion candidates so it shouldn't be hard to select one.
Everybody gets lucky sometimes, but they might not get lucky on the really important things
What is really important is subjective.
If you're born to a poor family in Africa, the law of large numbers is not going to make up for this setback.
Time will tell. African people often have different values than non-African people. Their value of success probably isn't the same as your's.
Given what I know if Ayn Rand
It seems like what you know about Ayn Rand comes from textbook propaganda. Nothing you've said has convinced me you've read thousands of pages of what she wrote.
I'm inclined to think that the quote is suggesting that successful people deserve to be successful, so you shouldn't take their money and give it to unsuccessful people.
This isn't an unreasonable assumption. But it's incorrect. Money is just one factor in success. Ayn Rand realized that, which is why her books are still read today and why most authors of her day (all of whom are now dead) don't have books which sell in large numbers.
Give me an example of a person who has succeeded with only luck.
The annual US GDP per capita is $55,036. For Somalia, it's $145. I cannot give you a specific example of someone who succeeded by luck, but I can assure you that successful people are not born in the US by chance.
African people often have different values than non-African people.
As of 2005, there were 2.6 billion people who lived on the equivalent of under $2 per day [source]. What possible values could they have where that could be considered success?
Another month, another rationality quotes thread. The rules are: