An Increasing Preference Distribution

Suppose your music player contained songs and you set it to shuffle songs, giving increasing preference to a song each time it was played. That is, initially, all songs are equally likely to be chosen but every time a song is played, its probability of being selected for the next play goes up in such a way that the probability of it being selected is proportional to the number of times it has been played. What would happen over a large number of plays? Would all your songs remain about equally likely or would a few dominant favorites emerge? Investigate this using this Demonstration.