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 back rank.
At first, the act of castling might seem strange, but really the result is the same as ever: 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" refers to the number of legal starting positions for this variant, where there is a rook on each side of the king and the bishops are each on a different-colored square.
To start a 960 game, go here: https://www.chess.com/daily
..and under Advanced Options choose Type: Chess960.
Here's a short video from IM Danny Rensch to help start a live game, including Live 960 games:
For more info: http://en.wikipedia.org/wiki/Chess960
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