When playing Spotify playlists in shuffle mode (currently the only available mode for free accounts, while as a paying premium customer I can play in the original playlist order or in a pseudo-randomized shuffle mode), the tracks don't seem to be selected by an actual random function but rather by an algorithm that favors popular songs and misses out on seldom played songs, thus making me miss about 20% to 30% of the songs in my playlist. At least, this behavior seems plausible after reading experiments and reverse engineering by other users that matches my experience.
Is it possible to tweak the algorithm to favor the seldom played songs instead? If so, how? Do I need an alternative spotify client? Are there any such clients?