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Starting
Position ID: 451
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Fischerandom Chess Position Generator
Last Updated 11/18/06
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FRC/Chess960 Starting Positions
About Fischerandom Starting
Position Ids
The product 4 x 4 x 6 x
10 gives you 960, the total number of starting positions. The
first 4 stands for the number of possible squares for the light-square Bishop
(b, d, f & h), and the second 4 for the dark-square Bishop (a, c, e &
g). The 6 stands for the number of squares available for the Queen, and
the 10 for the number of KeRN codes (legal Fischer
combinations of Knights, Rooks and the King). See the KeRN
table below.
KeRN Codes:
0 N N
R K R (Knight, Knight, Rook, King,
Rook)
1 N R N K R (Knight, Rook, Knight, King, Rook)
2 N R K N R (and so on...)
3 N R K R N
4 R N N
K R
5 R N K N R
6 R N K R N
7 R K N N R
8 R K N R N
9 R K R N N
To create a starting position given the id, first
divide the id by 4, giving you a quotient and a remainder. The remainder
locates the light-square Bishop: 0 means file b, 1 means file d, 2 means file
f, and 3 means file h.
Second, take the quotient from the first
division and divide it by 4, producing a new quotient and remainder. The new
remainder locates the dark-square Bishop: 0 means file a, 1 means file c, 2
means file e, and 3 means file g.
Third, take the quotient from the second
division and divide by 6, producing the last quotient and remainder. The last
remainder locates the queen, and identifies the number of the vacant square it
occupies (counting from the left, where 0 is the leftmost square and 5 is the
rightmost square).
The last quotient will be a number between 0 to 9 inclusive. This is the KeRN
code, and from the KeRN codes table above, you will
get the location of the King, Rooks and Knights among the remaining 5 squares.
Alternately, given a board position, it's id can be computed as follows:
id = 1 * light-square
Bishop location (counting leftmost as 0) +
4 *
dark-square Bishop location (counting leftmost as 0) +
16 *
Queen location (leftmost is 0 and skipping Bishops) +
96 *
(KRN code)
Example 1: Find starting position 451 (above
right on this webpage)
1) 451 / 4 = quotient 112 remainder 3
2) 112 / 4 = quotient 28 remainder 0
3) 28 / 6 = quotient 4 remainder 4
The first remainder, 3, places the light-square
Bishop in the h-file (note that for Bishops, 0 stands for the first available
square, 1 for the second, 2 for the third,
and 3 for the last). The second remainder, 0, places the dark-square
Bishop on the a-file. The third remainder, 4, places the Queen on the 5th
available square, the f-file (for the Queen, 0 stands for the first available
square, skiping the Bishops, and 5 for the last). The
KeRN code, the quotient from the last division, also
a 4 in our example, from the KeRN table above (for 4
we get R N N K R) gives us the location of the the remaining pieces among the squares left. In this case
Rook on first available square, then Knight, then
Knight again, then the King, and finally the other Rook on the last available
square.
Example 2: Find id for position in the diagram
above (BRNNKQRB)
id = 1 * 3 (light-square
Bishop is on the last available square, remember 0 is the first) + 4 * 0 (dark-square Bishop is on it's first
available square) + 16 * 4 (Queen is on it's fifth available square minus 1 is
4, remember 0 stands for the first available square) + 96 * 4 (KeRN code for RNNKR)
id = 1*3 + 4*0 + 16*4 +
96*4
id = 3 + 0 + 64 + 384
id = 451
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Read more about Starting Position IDs at Wikipedia
FRCEC’s Fischerandom
Castling Rules page
FRCEC’s Fischerandom Chess
Terms Glossary page
Fischerandom Chess Position Generator