Exact Weighted Lottery

In my previous post, I described the lottery for the Western States Endurance Run, which uses a weighted lottery to allocate \(m\) identical prizes among \(n\) participants. Each participant \(i\) has \(t_i\) tickets, and tickets are drawn in a uniformly random order until \(m\) distinct participants have been selected. The point of the previous post was that it’s not so easy to calculate the…