<p>I would say that the role of luck depends on your merit level. If you’re insane, like my friend who got a perfect on USA(J)MO + has an insane amount of extracurriculars, then luck probably won’t matter, since you’ll get accepted anyways (and he did). If you’re more borderline (i.e. maybe near-perfect test scores, insane extracurriculars, but maybe not too many major awards), then luck will probably matter much more. If you’re completely unqualified… well, you might get lucky? lol</p>