That's shuffle, not random. Maybe randomized. With random, every song should have the same chance of being picked, which would technically allow the same song to play twice. If you'd let the player run for a decade, every song should have played about the same number of times.

But this usually leads to people perceiving the feature as not being random enough.

See Spotify for example: https://www.quora.com/Is-Spotifys-shuffle-feature-truly-rand...

Random has a lot of meanings, and you are picking a very specific one. It doesn't have to be uniformly distributed, for example, but relevant here is I don't think there's a problem describing a random shuffle as "random". It is playing a list in a random order.

So... You'd say that my summary gets you 80% of the way there?