I ask this in a partly recreational, and partly research-related spirit, and I realize my problem might be ill-posed, so any suggestions for clarification might go a long way.
Succinctly, my problem can be stated as
Find the period of a "black box" pseudorandom number generator
but I suppose the following formulation might be more attractive:
Most programs for playing MP3 files (and MP3-playing devices as well) possess a "shuffle" feature that allows the player to play a list of songs in essentially "random" order.
If you run a music player set to shuffle long enough, you will note that sometimes the time interval between the instances your favorite song in the playlist can be short, or can be long.
Now, for a number of reasons, you can't take a look at what pseudorandom number generator your music player is using; you are however interested in how frequently your favorite song in the playlist would be played.
So, one now asks,
Can you determine how often your favorite song in the playlist would be played based on the time intervals between the different instances your song is played?
How long should your playlist be? Obviously, you can't conclude much if you only have two songs in your playlist...
How long should you leave your music player playing to answer question number 1?
I should probably make the drastic assumption that all the songs in the playlist have the same length, e.g. 3 minutes or so.