So, what deck does Rau run?

Hmm. Thats a nice question.

Nice and layed out for you.
Yes, Rau runs an equal 12 Tribute monsters and 12 non tribute monsters. Its Syncro Vanity. Feel free to netdeck. Because this one work, and not some variant with Psycho Commander/Devil Sanctuary/only 4 Monarchs.

Side:

And Extra:
Yes Rau's extra is very expensive. No Brionac though. Its overrated. And sucks in this deck.

Strategy?
1: Use Kuriboh Flute
2: Drop Monarch
3: Nuke Feild
4: Attack
5: E.Tele for Krebons
6: Swing
7: Syncro
8: Pot of Avarice.