Here is a great little puzzle demonstrating some of the more bizarre situations Chess960 symmetry can throw up:
SP366 Black to play (castling all sides permitted):
Why can't black copy white's play and come out materially equal?
Answer bottom left corner
Answer: because black's queen ends up undefended!
With best play:
3.Bxb8..Bxb1,
4.Bxc7! Bxc2
5.Bxd8! Bxd1
6.Bxe7! Bxe2??
7.Bxf8
3.Bxb8
7.Bxf8