Chess960 numbering scheme
integer between 0 and 959 that ndicates a valid starting position for Chess960
The game Chess960 (also called Fischer random chess), played with conventional chess pieces and rules, starts with a random selection of one of 960 positions for the pieces. Arrangements of the pieces are restricted so that the king is between the rooks and the bishops are on different colored squares. In order to both select a valid arrangement and to then concisely discuss which randomly selected arrangement a particular game used, the Chess960 numbering scheme is used: a number between 0 and 959 indicates a valid arrangement and given an arrangement the number can be determined.
The numbering scheme can be shown in the form of a simple two-tables representation. Also a direct derivation of starting arrays exists for any given number from 0 to 959. This mapping of starting arrays and numbers stems from Reinhard Scharnagl and is now used worldwide for Fischer random chess. The enumeration has been published first in the internet and then 2004 in his (German language) book "Fischer-Random-Schach (FRC / Chess960) - Die revolutionäre Zukunft des Schachspiels (inkl. Computerschach)", ISBN 3-8334-1322-0.
Counting the 960 starting positions
The 960 legal starting positions in Chess960 can be derived in several equivalent ways:
Method (a): Step-by-step with knights last
Choose squares for the bishops on opposite colors: 4 light-square choices for one bishop and 4 dark-square choices for the other.
Place the queen on one of the remaining 6 squares.
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