Are there any Chess960 positions where Black has the advantage? I've heard it said that some Chess960 positions have a significant advantage for White, usually involving fast attacks against undefended pawns. However, since zugzwang positions do exist, it's theoretically possible that Black could have an advantage in some opening setups. Which leads to the question: are there any where he does? If not, are there any that give White less of an advantage than he has in normal chess?
It happens that someone tried to evaluate all 960 positions with an engine. Several positions got a score of 0.00, but none of them offered any advantage for black. 

Of course, those conclusions are only the evaluations of Stockfish at 40 plies depth. It is a strong hint, but no definite proof, that Black is fine  in the huge majority of 960-chess starting positions, but not better in any of them.

This result matches with the intuition that in a symmetric, non-developed position, with all pawns on the 2d and 7th rank, there is always something useful to do if you are on move: in other words, there cannot be mutual zugzwang.