Before I begin, I did a search through math.stackexchange and came across two previous attempts to get people to solve probability problems involving bingo. Neither produced a response.
So what makes me think I'll be any luckier? Maybe some new guy/gal has some insight.
The game of bingo is played with a bingo card having 25 squares, arranged in 5 columns of 5 squares. The first column has numbers between 1-15, the 2nd column has numbers between 16-30, and so on (the 5th column (!) has numbers between 61-75). Someone randomly draws a number from 1-75 and announces it. To make things a little interesting, the middle square is labeled "free". If a number called matches one on your card, you mark it. The goal is to have a complete row, column, or diagonal of 5 marked off first.
Here's my question: what is the expected number of random draws when there is a winner among $N$ players? I was thinking about this because I got involved in such a game this evening with my kids, and it seemed to take an awfully long time for a winner to surface.
My thoughts: this seems to me to be an extremely tough problem. I consider myself better than average in computing expected values, yet I found myself completely stuck on even how to approach the problem. I suppose I could have searched the literature, but I figured I needed to pose a decent question here; I owe it to the users who have posed so many interesting questions here for me to answer.
I'll look for any insight that might move the discussion forward; I do not expect a complete answer for you to post.