Native “playlist” shortcode random playing… How?

I’m using the beautiful shortcode “playlist” in my site but I want the random playing of my audio files.

What I use is this:

How to make random playing, maybe also with dad jQuery?

I removed all that duplicated and unnecessary stuff, take a look at otto’s or kaiser’s answers for the very simple solution.

• Trac ticket: #29629.
• Codex entry for Playlist Shortcode.