Chess960 Enumbering Scheme
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[edit] Chess960 Enumbering Scheme
The Chess960 Enumbering Scheme could be shown in the form of a simple two tables representation. Also a direct derivation of starting arrays exits for any given number from 1 to 960. This mapping of starting arrays and numbers stems from Reinhard Scharnagl and is now worldwide used for Chess960. 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.
[edit] Two Tables Representation
This both tables will serve for a quick mapping of an arbitrary Chess960 starting position (short: SP) at White's base row to a drawn number between 1 and 960 (rsp. 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 place both Bishops at the first base row, then the six pieces in the sequence of the found row of the King's Table upon the six free places left over. Finally the black pieces will be placed symmertically to White's base row.
Example: look at the SP-518. In the King's Table we will find No. 512 "RNQKNR". For the remainder 6 we will find "--B--B--" in the Bishop's Table at No. 6. Altogether by that for the SP-518 = 512+6 this will result in the well known white starting array "RNBQKBNR" from traditional Chess.
[edit] King's Table
| Max. | Positioning Sequence of the other Pieces | ||||||||||||||||||||||
| 0 | Q | N | N | R | K | R | 336 | N | R | K | Q | R | N | 672 | Q | R | K | N | N | R | |||
| 16 | N | Q | N | R | K | R | 352 | N | R | K | R | Q | N | 688 | R | Q | K | N | N | R | |||
| 32 | N | N | Q | R | K | R | 368 | N | R | K | R | N | Q | 704 | R | K | Q | N | N | R | |||
| 48 | N | N | R | Q | K | R | 384 | Q | R | N | N | K | R | 720 | R | K | N | Q | N | R | |||
| 64 | N | N | R | K | Q | R | 400 | R | Q | N | N | K | R | 736 | R | K | N | N | Q | R | |||
| 80 | N | N | R | K | R | Q | 416 | R | N | Q | N | K | R | 752 | R | K | N | N | R | Q | |||
| 96 | Q | N | R | N | K | R | 432 | R | N | N | Q | K | R | 768 | Q | R | K | N | R | N | |||
| 112 | N | Q | R | N | K | R | 448 | R | N | N | K | Q | R | 784 | R | Q | K | N | R | N | |||
| 128 | N | R | Q | N | K | R | 464 | R | N | N | K | R | Q | 800 | R | K | Q | N | R | N | |||
| 144 | N | R | N | Q | K | R | 480 | Q | R | N | K | N | R | 816 | R | K | N | Q | R | N | |||
| 160 | N | R | N | K | Q | R | 496 | R | Q | N | K | N | R | 832 | R | K | N | R | Q | N | |||
| 176 | N | R | N | K | R | Q | 512 | R | N | Q | K | N | R | 848 | R | K | N | R | N | Q | |||
| 192 | Q | N | R | K | N | R | 528 | R | N | K | Q | N | R | 864 | Q | R | K | R | N | N | |||
| 208 | N | Q | R | K | N | R | 544 | R | N | K | N | Q | R | 880 | R | Q | K | R | N | N | |||
| 224 | N | R | Q | K | N | R | 560 | R | N | K | N | R | Q | 896 | R | K | Q | R | N | N | |||
| 240 | N | R | K | Q | N | R | 576 | Q | R | N | K | R | N | 912 | R | K | R | Q | N | N | |||
| 256 | N | R | K | N | Q | R | 592 | R | Q | N | K | R | N | 928 | R | K | R | N | Q | N | |||
| 272 | N | R | K | N | R | Q | 608 | R | N | Q | K | R | N | 944 | R | K | R | N | N | Q | |||
| 288 | Q | N | R | K | R | N | 624 | R | N | K | Q | R | N | 960 | Q | N | N | R | K | R | |||
| 304 | N | Q | R | K | R | N | 640 | R | N | K | R | Q | N | R. Scharnagl | |||||||||
| 320 | N | R | Q | K | R | N | 656 | R | N | K | R | N | Q | ||||||||||
[edit] Bishop's Table
| Remainder | Bishops' Positioning | |||||||
| a | b | c | d | e | f | g | h | |
| 0 | B | B | - | - | - | - | - | - |
| 1 | B | - | - | B | - | - | - | - |
| 2 | B | - | - | - | - | B | - | - |
| 3 | B | - | - | - | - | - | - | B |
| 4 | - | B | B | - | - | - | - | - |
| 5 | - | - | B | B | - | - | - | - |
| 6 | - | - | B | - | - | B | - | - |
| 7 | - | - | B | - | - | - | - | B |
| 8 | - | B | - | - | B | - | - | - |
| 9 | - | - | - | B | B | - | - | - |
| 10 | - | - | - | - | B | B | - | - |
| 11 | - | - | - | - | B | - | - | B |
| 12 | - | B | - | - | - | - | B | - |
| 13 | - | - | - | B | - | - | B | - |
| 14 | - | - | - | - | - | B | B | - |
| 15 | - | - | - | - | - | - | B | B |
[edit] Direct Derivation
The accurate sequence of White's Chess960 starting array could be derived from its number as follows:
a) Divide the number by 960, determine the remainder (0 ... 959) and use that number thereafter.
b) Divide the number by 4, determine the remainder (0 ... 3) and correspondingly place a Bishop upon the matching bright square (b, d, f, h).
c) Divide the number by 4, determine the remainder (0 ... 3) and correspondingly place a Bishop upon the matching dark square (a, c, e, g).
d) Divide the number by 6, determine the remainder (0 ... 5) und correspondingly place the Queen upon the matching of the six free squares.
e) Now only one digit (0 ... 9) is left on hand; place the both Knights upon the remaining five free squares according to following scheme:
| Digit | Knights' Positioning | ||||
| 0 | N | N | - | - | - |
| 1 | N | - | N | - | - |
| 2 | N | - | - | N | - |
| 3 | N | - | - | - | N |
| 4 | - | N | N | - | - |
| 5 | - | N | - | N | - |
| 6 | - | N | - | - | N |
| 7 | - | - | N | N | - |
| 8 | - | - | N | - | N |
| 9 | - | - | - | N | N |
f) The now still remaining three free squares will be filled in the following sequence: Rook, King, Rook.
[edit] External links
- Reinhard Scharnagl's ChessBox (English/German)
