Genius lists blank, button not working (a fix)

For once, I'm posting answer before posting a question... for the benefit of anybody else looking for the same solution.

I was having this thing where my Genius button stopped working. I would click and then nothing. Blank. The Genius recommendations in the iTunes store worked, but not on my local computer. And "Update Genius" in the Store menu of iTunes didn't fix it either. Also, a list I had before disappeared.

Well, I finally figured it out...

In a surprisingly unintuitive way, the answer was to choose "Update iTunes Match" instead.

Once I did that, all Genius buttons work and all Genius playlists came back.

Hope this helps somebody else!