Say you have ten playlists. Say the first song in your root playlist (all playlists) is from alternative rock. The chances of the next song being from alternative rock are 1 in 10 (assuming you have same-sized playlist). So the chances of no songs from the same playlist playing back to back is very small.

Yes, but it my case, I have 2,200 songs and at least 75 playlists (probably a lot more). Now, I admit that some playlists are much bigger than others. So, let's take something like my Tenacious D playlist. I've seen tracks from this come back-to-back before (or within a few songs). There are about 20 tracks in the playlist. That means the chance of getting one of those tracks at any time would be 20/2200 or 1 in 110.

Now, the chance of one of those songs coming up as the next song is still approx. 1 in 110 because it's independent odds.

But (and correct me if I'm wrong), the probability of the two coming back to back would be 1/110*1/110, which is significantly smaller chance.