There is an element of chance in getting into any top school, but only among the applicants who meet all the other qualifications. That is, between two students with 4.0 GPA, great SAT scores, and a wide selection of extracurricular activities and community service, it's a toss up. But a student with poor grades has no chance. It doesn't matter how many times the student with bad grades sends his application, he isn't getting in just by random chance. When it comes to Harvard, I would guess that 80-90% of applicants can be dropped immediately due to grades, SAT scores or lack of activities. Out of the remaining pool, for those without extenuating circumstances such as athleticism or family connections, is where such as race and "personality" might become a factor, and who ends up getting picked has an element of randomness.