VT wrote:non zero, positive n less than 1. Sorry.
I'll wager its MUCH less than one. Keep in mind that the waitlist program is managed by people with extensive training in math. The point of a waitlist is cover the department's rear in case of an unusually high non-acceptance rate. Professors need those RA's to do work, the department administration will prefer they move from TA to RA after no less than 3 semesters. The school needs a certain number of nimble minds, too few students and problems will show up down the road. So the waitlist may happen to benefit some lucky student but the purpose isn't to give false hope, thats just a side effect.
On the other hand, my safety school is pretty small and they can't afford even one extra acceptance so they only ever have out the exact number of offers they can fund. This means they DO draw pretty extensively from their waitlist. A fellow student at my school is bugging me to withdraw my app cause he thinks he's close to the top. I heard informally from graduate students at this school that this practice has burned them in the past since come late April they are making offers to marginal students.