The game 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 Fischer random chess numbering scheme is used: a number between 0 and 959 indicates a valid arrangement and given an arrangement the number can be determined. The Fischer random chess 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)", . Direct derivation White's starting array can be derived from its number N (0 ... 959) as follows: a) Divide N by 4, yielding quotient N2 and remainder B1. Place a Bishop upon the bright square corresponding to B1 (0=b, 1=d, 2=f, 3=h). b) Divide N2 by 4 again, yielding quotient N3 and remainder B2. Place a second Bishop upon the dark square corresponding to B2 (0=a, 1=c, 2=e, 3=g). c) Divide N3 by 6, yielding quotient N4 and remainder Q. Place the Queen according to Q, where 0 is the first free square starting from a, 1 is the second, etc. d) N4 will be a single digit, 0 ... 9. Place the Knights according to its value by consulting the following N5N table: e) There are three blank squares remaining; place a Rook in each of the outer two and the King in the middle one. Two-tables representation King's table Bishop's table These two tables will serve for a quick mapping of an arbitrary Fischer random chess starting position (short: SP) at White's base row to a number between 0 and 959. First search for the same or the nearest smaller number from the King's Table. Then determine the difference (0 to 15) to the drawn number and select that matching bishops' positioning from the Bishop's Table. According to this first