So I just discovered that everytime I play a Genius playlist it plays in the same order. My guess is that everybody else already knew that.
Today, however, I discovered that if you place a Genius playlist inside a Playlist Folder and then select the Playlist Folder, set it to shuffle, and then play, the songs play shuffled. That is, the tracks play in a different random order each time the Playlist Folder containing the Genius playlist is played.
When I told Kirk McElhearn about this he imagined that one could create several Genius Playlists based on the same Artist seed in order to maximize variety. So I tried that. And here's what's cool:
My presumption was that two (or more) Genius Playlists based on a similar seed each might contain duplicate tracks which would therefore be duplicated in the Playlist Folder that I put them in. But they are not. While the two Genius Playlists show 100 songs each, the total of tracks for the Playlist Folder is 174; the duplicate tracks don't "register" in the Playlist Folder context.
I like this because I can maintain the Genius playlists longer without having to refresh or recreate them.