And finally solved it.
If you're unfamiliar with the premise, here is the quick and dirty from the website:
The name of the game is Petals Around the Rose. The name of the game is important. The computer will roll five dice and ask you to guess the score for the roll. The score will always be zero or an even number. Your mission is to work out how the computer calculates the score and become a Potentate of the Rose.
Warning: it's addictive. Second warning: the website played some Casio keyboard/midi music file when loaded with IE -- it did not with Mozilla's Firefox. A separate, music-free applet can be found on this page.
One odd synchronicity: the first site's author set up a guestbook for new potentates to proclaim their majesty and all that the title confers. Two places ahead of my entry (#4957), another Jason from Roswell, GA, logged in his success on the same day. WTF?!?
Enjoy -- but if you figure it out PLEASE DO NOT POST THE ANSWER HERE! Thank you.