Chess960 numbering scheme

Chess960 is a chess variant with 960 possible arrangements of the pieces on each side's starting row, often called the back rank. The International Chess Federation, known as FIDE, requires the king to stand between the two rooks, the bishops to start on opposite-colored squares, and Black's pieces to mirror White's. The Scharnagl scheme assigns each arrangement a unique identifier from 0 to 959.

The mapping is fixed: the same number always produces the same order, and the same order returns the same number. The calculation combines the available choices for placing the two bishops, then the queen and two knights. Once those five pieces are fixed, the remaining squares can only be filled rook, king, rook in that order to keep the king between the rooks.

The sequence RNBQKBNR, using the English initials for rook, knight, bishop, queen, king, bishop, knight, and rook, represents the traditional starting position and has identifier 518. The number lets people communicate, generate, or verify the initial setup without listing eight pieces every time. It does not describe a later game position, the side to move, castling rights, or the strategic difficulty of that arrangement.