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What is Chess960?
Chess960 (also called FischerRandom) is just like regular chess... except that the starting position is shuffled to include 960 different possible positions! So you can throw out your opening book, but keep your opening principles. You play the same, but you just have different placement of pieces on the starting row.
The only change in rules is that castling is funky - when you castle, the king/rook end up in the same position as when they castle in regular chess (king on g-file and rook on f-file for kingside, king on c-file and rook on d-file for queenside).
The 960 comes from the number of different possible starting positions where there is a rook on each side of the king and where there are bishops of opposite color.
(For more info, read here: http://en.wikipedia.org/wiki/Chess960 )