Fischer random chess numbering scheme: Difference between revisions

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{{Short description|Naming a Fischer Random board using numbers}}

{{Refimprove|date=August 2012}}

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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 brightlight 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).

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'''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. Ignoring '''Bishops''' and '''Queen''', find the positions of two '''Knights''' within the remaining five spaces. Place the '''Knights''' according to its value by consulting the following '''N5N''' table:

{| class=wikitable cellpadding="4" cellspacing="0"

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For any SP, after ignoring the bishops, attention is given first to the knights (rather than to the queen). After taking account of the arrangement of the two knights in six squares (skipping over bishops), the queen is left with four possibilities: 0,1,2,3 (counting from the a-side of the board and skipping over bishops and knights). The queen's position is the number of hyphens to the left of the "Q" in the NQ-skeleton for the SP.

{| class=wikitable cellpadding="4" cellspacing="0"

|- style="background:#eeeeee;" align="center"

| Digit

| colspan="6" | Knight positioning

|- align="center"

| '''0''' || N || N || - || - || - || -

|- align="center"

| '''1''' || N || - || N || - || - || -

|- align="center"

| '''2''' || N || - || - || N || - || -

|- align="center"

| '''3''' || N || - || - || - || N || -

|- align="center"

| '''4''' || N || - || - || - || - || N

|- align="center"

| '''5''' || - || N || N || - || - || -

|- align="center"

| '''6''' || - || N || - || N || - || -

|- align="center"

| '''7''' || - || N || - || - || N || -

|- align="center"

| '''8''' || - || N || - || - || - || N

|- align="center"

| '''9''' || - || - || N || N || - || -

|- align="center"

| '''10''' || - || - || N || - || N || -

|- align="center"

| '''11''' || - || - || N || - || - || N

|- align="center"

| '''12''' || - || - || - || N || N || -

|- align="center"

| '''13''' || - || - || - || N || - || N

|- align="center"

| '''14''' || - || - || - || - || N || N

|}

Given an SP, extract the bishop's code, the NQ-skeleton and its queen's position. Then, locate, in the appropriate column, the NQ-skeleton at hand, say at No. M. The Fritz9 idn = (bishop's code) + M. For the standard SP, we extract 6 RNQKNR and 1 and get Fritz9 idn = 6 + 353 = 359.

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{{DEFAULTSORT:Fischer Random Chess Numbering Scheme}}

[[Category:Fischer random chessChess960|numbering scheme]]