menloparkmom your lottery logic is a bit flawed. Lotteries are 100% random and have 0 basis on skill or luck. To compare college admissions to a lottery might seem like an amusing hyperbole to use, because it really does seem like a crapshoot, like a “lottery,” when this is in fact not the case. Admission to one school is not independent of admission to another school, because an admissible student is a good student in each of the adcom tables.
But also, your logic is wrong in a second sense because if you purchased lottery tickets in 11 different states, your odds of winning a lottery WOULD in fact go up. Because you now have 11 chances of winning a lottery, rather than 1. In fact, purchasing 11 lottery tickets in the same lottery vs purchasing 11 separate tickets in separate lotteries would be roughly the same probability of winning (in both cases greater than purchasing 1), provided that we say that each lottery has a roughly equal likelihood of winning.