I don't think mathematics is the issue here, rather problem definition. OP wants "Shuffle my playlist into a random order and then play it through" You are th

I don't think mathematics is the issue here, rather problem definition. OP wants "Shuffle my playlist into a random order and then play it through" You are thinking closer to "After this song is done, choose a new song at random among ALL available." Spotify's is a mixture, while good offline clients tend to go to the first.