Methods, apparatus, and systems that allow random music play, and random selection of other media files, using a non-uniform probability distribution. The likelihood that a particular song, piece, or media file will be played or presented in the future is increased or decreased according to positive and negative user behaviors noted with respect to previous plays of the same media file, such as how long the user listens to or views a song, piece, or file; whether the user manually selects a song, piece, or file for play or presentation; and whether the user “skips” a song while it is being played, or otherwise actively chooses not to listen to a song.