Many prominent social scientists have advocated for random-draw lotteries as a solution to the “problem” of college admissions. They argue that lotteries will be fair and equitable, eliminate corruption, reduce student anxiety, restore democratic ideals, and end debates over race-conscious admissions. In response, we simulate potential lottery effects on student enrollment by race, gender, and income, using robust simulation methods. If we went to a lottery system, what would happen to student diversity? And how would this change the built relationship between students and selective colleges?