I’m not entirely sure that admissions at Famous Universities are independent, although that’s just me. (There’s not entirely good reason to expect this, save for my friends, who should have had something like 30% of getting in, if you did the math, and none of them did.)
I also think that the strategy of applying multiple times is fairly unrealistic. It’s ~$1000 each time, so your strategy suggests two years and ~$2000 spent all on admission to a Famous University. That seems rather…extreme?
My goal here isn’t to try and get in to a Famous University, or propose a way to do so more effectively, but to point out the sort of inherent problems that come with the quiet social acceptance of prestige in schools. I think it’s very much about this and less about students simply not optimizing for the admissions process in the first place.