So, as I'm sure many of you here are also, I am a fan of xkcd. However, I've never read all of them. When I get interested and the time, I just click 'random' and read that strip.

A probability problem came to mind while I was doing this- right now, there are 650 comics. If I were to start with a random strip, and after that view a random strip, how many clicks of the random button will it take on average to view them all?

I have honestly no clue how to approach this problem. So I coded up a small C++ program to run trials. When I did 50000 trials and averaged them, I got 4789.12 clicks. If anyone wants the source code I can post it but I think that if you have a C++ compiler on your computer you're likely to have the knowledge to do this program just as quickly.

Is there any way to go about this analytically instead of numerically?