Wikipedia

Fischer random chess numbering scheme: Difference between revisions

Browse history interactively
← Previous edit
Content deleted Content added
VisualWikitext
→Example: better explanation, with diagram
m →Direct derivation: In chess we refer to light squares and dark squares
Tags: Mobile edit Mobile app edit Android app edit App section source
 
(25 intermediate revisions by 9 users not shown)
Line 1:
{{Short description|Naming a Fischer Random board using numbers}}
{{Refimprove|date=August 2012}}
 
Line 5 ⟶ 6:
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)",'' {{ISBN|3-8334-1322-0}}.
 
== Two-tablesDirect representationderivation ==
White's starting array can be derived from its number N (0 ... 959) as follows:
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 random 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 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 symmetrically to White's base row.
 
'''a)''' Divide N by 4, yielding quotient N2 and remainder B1. Place a '''Bishop''' upon the light square corresponding to B1 (0=b, 1=d, 2=f, 3=h).
=== Example ===
{{Chess diagram small
|tright
|
|rd|nd|bd|qd|kd|bd|nd|rd
|pd|pd|pd|pd|pd|pd|pd|pd
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
|pl|pl|pl|pl|pl|pl|pl|pl
|rl|nl|bl|ql|kl|bl|nl|rl
}}
Consider the SP-518 arrangement. The largest multiple of 16 less than 518 is 512, so we search for 512 in the King's table and the remainder, 6, in the Bishop's table. In the King's table, number 512 is "RNQKNR". In the Bishop's table, "--B--B--" is at number 6. We insert the pieces from the King's table into these gaps to get the starting array "RNBQKBNR", which is the starting order in traditional chess.
 
'''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).
=== King's table ===
 
{|border="1" cellpadding="4" cellspacing="0"
'''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"
|- style="background:#eeeeee;" align="center"
| Max.Digit
| colspan="235" | PositioningKnight Sequence of the other Piecespositioning
|- align="center"
| '''0''' ||Q|| N || N ||R - ||K - ||R -
| rowspan="21" |   || '''336''' ||N||R||K||Q||R||N
| rowspan="21" |   || '''672''' ||Q||R||K||N||N||R
|- align="center"
| '''161''' || N||Q||N||R||K||R || '''352'''- || N||R||K||R||Q||N || '''688'''- ||R||Q||K||N||N||R -
|- align="center"
| '''322''' || N||N||Q||R||K||R || '''368'''- ||N||R||K||R||N||Q|| '''704'''- ||R||K||Q|| N ||N||R -
|- align="center"
| '''483''' || N ||N||R||Q||K||R - || '''384'''- ||Q||R||N||N||K||R|| '''720'''- ||R||K|| N||Q||N||R
|- align="center"
| '''644''' ||N||N||R||K||Q||R|| '''400'''- ||R||Q|| N || N||K||R || '''736'''- ||R||K||N||N||Q||R -
|- align="center"
| '''805''' ||N||N||R||K||R||Q|| '''416'''- ||R|| N||Q||N||K||R || '''752'''- ||R||K|| N ||N||R||Q -
|- align="center"
| '''966''' ||Q - || N||R||N||K||R || '''432'''- ||R||N||N||Q||K||R|| '''768'''- ||Q||R||K||N||R|| N
|- align="center"
| '''1127''' ||N||Q||R||N||K||R - || '''448'''- ||R|| N || N||K||Q||R || '''784''' ||R||Q||K||N||R||N-
|- align="center"
| '''1288''' ||N||R||Q||N||K||R - || '''464'''- ||R|| N||N||K||R||Q || '''800'''- ||R||K||Q||N||R|| N
|- align="center"
| '''1449''' ||N||R||N||Q||K||R - || '''480'''- ||Q||R||N||K||N||R|| '''816'''- ||R||K|| N ||Q||R|| N
|}
|- align="center"
 
| '''160''' ||N||R||N||K||Q||R|| '''496''' ||R||Q||N||K||N||R|| '''832''' ||R||K||N||R||Q||N
'''e)''' There are three blank squares remaining; place a '''Rook''' in each of the outer two and the '''King''' in the middle one.
|- align="center"
 
| '''176''' ||N||R||N||K||R||Q|| '''512''' ||R||N||Q||K||N||R|| '''848''' ||R||K||N||R||N||Q
== Two-tables representation ==
|- align="center"
 
| '''192''' ||Q||N||R||K||N||R|| '''528''' ||R||N||K||Q||N||R|| '''864''' ||Q||R||K||R||N||N
=== King's table ===
|- align="center"
 
| '''208''' ||N||Q||R||K||N||R|| '''544''' ||R||N||K||N||Q||R|| '''880''' ||R||Q||K||R||N||N
{|- align="'center' border=1 style="margin-left: 10px" class=wikitable
|+Scharnagl's NQ-skeleton Table
| '''224''' ||N||R||Q||K||N||R|| '''560''' ||R||N||K||N||R||Q|| '''896''' ||R||K||Q||R||N||N
|-
|- align="center"
| 0||<code>QNNRKR</code>|| 192||<code> QNRKNR </code>|| 384||<code> QRNNKR </code>|| 576||<code> QRNKRN </code>|| 768||<code> QRKNRN </code>
| '''240''' ||N||R||K||Q||N||R|| '''576''' ||Q||R||N||K||R||N|| '''912''' ||R||K||R||Q||N||N
|-
|- align="center"
| 16||<code>NQNRKR</code>|| 208||<code> NQRKNR </code>|| 400||<code> RQNNKR </code>|| 592||<code> RQNKRN </code>|| 784||<code> RQKNRN </code>
| '''256''' ||N||R||K||N||Q||R|| '''592''' ||R||Q||N||K||R||N|| '''928''' ||R||K||R||N||Q||N
|-
|- align="center"
| 32||<code>NNQRKR</code>|| 224||<code> NRQKNR </code>|| 416||<code> RNQNKR </code>|| 608||<code> RNQKRN </code>|| 800||<code> RKQNRN </code>
| '''272''' ||N||R||K||N||R||Q|| '''608''' ||R||N||Q||K||R||N|| '''944''' ||R||K||R||N||N||Q
|-
|- align="center"
| 48||<code>NNRQKR</code>|| 240||<code> NRKQNR </code>|| 432||<code> RNNQKR </code>|| 624||<code> RNKQRN </code>|| 816||<code> RKNQRN </code>
| '''288''' ||Q||N||R||K||R||N|| '''624''' ||R||N||K||Q||R||N
|-
| style="background:#eeeeee;" colspan="7" rowspan="3"| R. Scharnagl
| 64||<code>NNRKQR</code>|| 256||<code> NRKNQR </code>|| 448||<code> RNNKQR </code>|| 640||<code> RNKRQN </code>|| 832||<code> RKNRQN </code>
|- align="center"
|-
| '''304''' ||N||Q||R||K||R||N|| '''640''' ||R||N||K||R||Q||N
| 80||<code>NNRKRQ</code>|| 272||<code> NRKNRQ </code>|| 464||<code> RNNKRQ </code>|| 656||<code> RNKRNQ </code>|| 848||<code> RKNRNQ </code>
|- align="center"
|-
| '''320''' ||N||R||Q||K||R||N|| '''656''' ||R||N||K||R||N||Q
| 96||<code>QNRNKR</code>|| 288||<code> QNRKRN </code>|| 480||<code> QRNKNR </code>|| 672||<code> QRKNNR </code>|| 864||<code> QRKRNN </code>
|-
|112||<code>NQRNKR</code>|| 304||<code> NQRKRN </code>|| 496||<code> RQNKNR </code>|| 688||<code> RQKNNR </code>|| 880||<code> RQKRNN </code>
|-
|128||<code>NRQNKR</code>|| 320||<code> NRQKRN </code>|| 512||<code> RNQKNR </code>|| 704||<code> RKQNNR </code>|| 896||<code> RKQRNN </code>
|-
|144||<code>NRNQKR</code>|| 336||<code> NRKQRN </code>|| 528||<code> RNKQNR </code>|| 720||<code> RKNQNR </code>|| 912||<code> RKRQNN </code>
|-
|160||<code>NRNKQR</code>|| 352||<code> NRKRQN </code>|| 544||<code> RNKNQR </code>|| 736||<code> RKNNQR </code>|| 928||<code> RKRNQN </code>
|-
|176||<code>NRNKRQ</code>|| 368||<code> NRKRNQ </code>|| 560||<code> RNKNRQ </code>|| 752||<code> RKNNRQ </code>|| 944||<code> RKRNNQ </code>
|}
 
=== Bishop's table ===
 
{|border="1" cellpadding="4" cellspacing="0"
{| class=wikitable cellpadding="4" cellspacing="0"
|- style="background:#eeeeee;" align="center"
| rowspan="2" | Remainder
| colspan="8" | Bishop positioning
|- style="background:#eeeeee;" align="center"
| a || b || c || d || e || f || g || h
|- align="center"
| '''0''' || B || B || - || - || - || - || - || -
Line 116 ⟶ 119:
|}
 
{{Chess diagram small
== Direct derivation ==
|tright
White's starting array can be derived from its number N (0 ... 959) as follows:
|
|rd|nd|bd|qd|kd|bd|nd|rd
|pd|pd|pd|pd|pd|pd|pd|pd
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
|pl|pl|pl|pl|pl|pl|pl|pl
|rl|nl|bl|ql|kl|bl|nl|rl
|The standard starting position for chess is denoted by SP-518.
}}
 
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 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 symmetrically to White's base row.
'''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).
 
Consider the SP-518 arrangement. The largest multiple of 16 less than 518 is 512, so we search for 512 in the King's table and the remainder, 6, in the Bishop's table. In the King's table, number 512 is "RNQKNR". In the Bishop's table, "--B--B--" is at number 6. We insert the pieces from the King's table into these gaps to get the starting array "RNBQKBNR", which is the starting order in traditional chess.
'''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).
 
===Scharnagl's methods===
'''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 table:
 
{|border="1" cellpadding="4" cellspacing="0"
|- style="background:#eeeeee;" align="center"
| Digit
| colspan="5" | 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
|}
 
'''e)''' There are three blank squares remaining; place a '''Rook''' in each of the outer two and the '''King''' in the middle one.
 
== Starting position IDs in Fischer random chess ==
 
For years, Reinhard Scharnagl has championed the desirability of giving each of the starting positions (SP) a unique identification number (idn) in the range 0-959 or, perhaps, 1-960. He has presented his methods on the internet and in books. See the external references. As an application, a random number generator could make one probe into the range at hand for a random number, and produce a random SP. Late in 2005, the program Fritz9 became available. It has a Fischer random chess option, but, for some unexplained reason, it assigns idns to SPs in a different way. Rather than requiring a giant table with 960 entries, both methods can use some smaller tables and some arithmetic.
 
===Preliminaries===
 
Both methods take account of the positions of the bishops first, and ignore the distinction between the king and rooks. Once the positions of the bishops, knights and queen are known, there is only one possibility for the remaining three squares. In the places where division of whole numbers is done, it is always done giving a quotient (designated q1,q2,..) and a remainder (designated r1,r2 ..).
 
There are 16 ways to put two bishops on opposite colored squares. These are shown and numbered in the small table below. The entries actually can be calculated using simple arithmetic, but the table method seems less error prone. For the standard SP the bishop's code is 6.
 
Scharnagl's Bishop's Table
-
0 BB------ 4 -BB----- 8 -B--B--- 12 -B----B-
1 B--B---- 5 --BB---- 9 ---BB--- 13 ---B--B-
2 B----B-- 6 --B--B-- 10 ----BB-- 14 -----BB-
3 B------B 7 --B----B 11 ----B--B 15 ------BB
 
In any SP, when looking at the arrangement of the other pieces around the bishops, it is helpful to write down the NQ-skeleton for that SP. This is done by ignoring the bishops and replacing the "K" and "R" by a common symbol, say "-". The NQ-skeleton for the standard SP is -NQ-N-. The sections below showing Scharnagl's Methods and the Fritz9 Methods are independent, and may be read in any order.
 
===Scharnagl's methods===
 
The methods described below are appropriate for the idn range 0-959. For the idn range 1-960, he recommends conversion by dividing by 960 and working with the remainder. This has the effect of assigning to idn 0 the SP that was at idn 960, and leaving the other idn SP matchups unchanged. If this calculation is applied in the idn range 0-959, nothing is changed.
 
For any SP, after skipping over the bishop's, the queen may occupy any one of six possible squares, and they are numbered from left to right (from White's perspective) 0,1,2,3,4,5. The two knights, then, can appear in any of the remaining five squares (skipping over bishops and queen) in 10 ways. These are shown and numbered in the N5N table below.
{| align='left' border=1 style="margin-right: 15px" class=wikitable
|+Scharnagl's N5N Table
|-
|0 || <tt>NN---</TT> || 5 ||<tt>-N-N-</tt>
|-
|1 || <tt>N-N--</tt> || 6 ||<tt>-N--N</tt>
|-
|2 || <tt>N--N-</tt> || 7 ||<tt>--NN-</tt>
|-
|3 || <tt>N---N</tt> || 8 ||<tt>--N-N</tt>
|-
|4 || <tt>-NN--</tt> || 9 ||<tt>---NN</tt>
|-
|}
 
{| align='right' border=1 style="margin-left: 10px" class=wikitable
|+Scharnagl's NQ-skeleton Table
|-
| 0||<tt>QNN---</tt>|| 192||<tt> QN--N- </tt>|| 384||<tt> Q-NN-- </tt>|| 576||<tt> Q-N--N </tt>|| 768||<tt> Q--N-N </tt>
|-
| 16||<tt>NQN---</tt>|| 208||<tt> NQ--N- </tt>|| 400||<tt> -QNN-- </tt>|| 592||<tt> -QN—N </tt>|| 784||<tt> -Q-N-N </tt>
|-
| 32||<tt>NNQ---</tt>|| 224||<tt> N-Q-N- </tt>|| 416||<tt> -NQN-- </tt>|| 608||<tt> -NQ—N </tt>|| 800||<tt> --QN-N </tt>
|-
| 48||<tt>NN-Q--</tt>|| 240||<tt> N--QN- </tt>|| 432||<tt> -NNQ-- </tt>|| 624||<tt> -N-Q-N </tt>|| 816||<tt> --NQ-N </tt>
|-
| 64||<tt>NN--Q-</tt>|| 256||<tt> N--NQ- </tt>|| 448||<tt> -NN-Q- </tt>|| 640||<tt> -N--QN </tt>|| 832||<tt> --N-QN </tt>
|-
| 80||<tt>NN---Q</tt>|| 272||<tt> N--N-Q </tt>|| 464||<tt> -NN--Q </tt>|| 656||<tt> -N--NQ </tt>|| 848||<tt> --N-NQ </tt>
|-
| 96||<tt>QN-N--</tt>|| 286||<tt> QN---N </tt>|| 480||<tt> Q-N-N- </tt>|| 672||<tt> Q--NN- </tt>|| 864||<tt> Q---NN </tt>
|-
|112||<tt>NQ-N--</tt>|| 304||<tt> NQ---N </tt>|| 496||<tt> -QN-N- </tt>|| 688||<tt> -Q-NN- </tt>|| 880||<tt> -Q--NN </tt>
|-
|128||<tt>N-QN--</tt>|| 320||<tt> N-Q--N </tt>|| 512||<tt> -NQ-N- </tt>|| 704||<tt> --QNN- </tt>|| 896||<tt> --Q-NN </tt>
|-
|144||<tt>N-NQ--</tt>|| 336||<tt> N--Q-N </tt>|| 528||<tt> -N-QN- </tt>|| 720||<tt> --NQN- </tt>|| 912||<tt> ---QNN </tt>
|-
|160||<tt>N-N-Q-</tt>|| 352||<tt> N---QN </tt>|| 544||<tt> -N-NQ- </tt>|| 736||<tt> --NNQ- </tt>|| 928||<tt> ---NQN </tt>
|-
|176||<tt>N-N--Q</tt>|| 368||<tt> N---NQ </tt>|| 560||<tt> -N-N-Q </tt>|| 752||<tt> --NN-Q </tt>|| 944||<tt> ---NNQ </tt>
|}
 
For any SP, both the queens position and the N5N configuration are immediately available from the NQ-skeleton. The queen's position is the number of characters to the left of the "Q", giving 2 for the standard SP. The N5N configuration is obtained by omitting the "Q", giving -N-N- for the standard SP, so its N5N code is 5. In general
Line 243 ⟶ 166:
 
Going the other way, given an idn, locate, in the table, the largest number, say M, that is less than or equal to idn. Then idn - M gives the bishop's code, and the skeleton at M shows how to fill in the rest of the pieces. Given idn = 518 we locate 512, with NQ-skeleton -NQ-N-, in the table, and get bishops code = 518 - 512 = 6.
 
===Preliminaries===
 
Both methods take account of the positions of the bishops first, and ignore the distinction between the king and rooks. Once the positions of the bishops, knights and queen are known, there is only one possibility for the remaining three squares. In the places where division of whole numbers is done, it is always done giving a quotient (designated q1,q2,..) and a remainder (designated r1,r2 ..).
 
There are 16 ways to put two bishops on opposite colored squares. These are shown and numbered in the table above. The entries actually can be calculated using simple arithmetic, but the table method seems less error prone. For the standard SP the bishop's code is 6.
 
In any SP, when looking at the arrangement of the other pieces around the bishops, it is helpful to write down the NQ-skeleton for that SP. This is done by ignoring the bishops and replacing the "K" and "R" by a common symbol, say "-". The NQ-skeleton for the standard SP is -NQ-N-. The sections below showing Scharnagl's Methods and the Fritz9 Methods are independent, and may be read in any order.
 
===Fritz9 methods===
Line 250 ⟶ 181:
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"
In the table below, the columns correspond to the queen's position, and, in each column, the ordering is alphabetic with "-" last.
|- 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 -NQ-N-RNQKNR and 1 and get Fritz9 idn = 6 + 353 = 359.
 
'''Fritz9 NQ-skeleton Table'''
 
-
{| class=wikitable
1 NNQ--- 241 NN-Q-- 481 NN—Q- 721 NN---Q
|-
17 NQN--- 257 N-NQ—497 N-N-Q- 737 N-N--Q
| 1 || NNQRKR || 241 || NNRQKR || 481 || NNRKQR || 721 || NNRKRQ
33 NQ-N-- 273 N-QN—513 N--NQ- 753 N--N-Q
|-
49 NQ—N- 289 N-Q-N- 529 N--QN- 769 N---NQ
| 17 || NQNRKR || 257 || NRNQKR || 497 || NRNKQR || 737 || NRNKRQ
65 NQ---N 305 N-Q--N 545 N--Q-N 785 N---QN
|-
81 QNN--- 321 -NNQ—561 -NN-Q- 801 -NN—Q
| 33 || NQRNKR || 273 || NRQNKR || 513 || NRKNQR || 753 || NRKNRQ
97 QN-N-- 337 -NQN—577 -N-NQ- 817 -N-N-Q
|-
113 QN—N- 353 -NQ-N- 593 -N-QN- 833 -N--NQ
| 49 || NQRKNR || 289 || NRQKNR || 529 || NRKQNR || 769 || NRKRNQ
129 QN---N 369 -NQ—N 609 -N-Q-N 849 -N--QN
|-
145 Q-NN—385 -QNN—625—NNQ- 865—NN-Q
| 65 || NQRKRN || 305 || NRQKRN || 545 || NRKQRN || 785 || NRKRQN
161 Q-N-N- 401 -QN-N- 641—NQN- 881—N-NQ
|-
177 Q-N--N 417 -QN—N 657—NQ-N 897—N-QN
| 81 || QNNRKR || 321 || RNNQKR || 561 || RNNKQR || 801 || RNNKRQ
193 Q--NN- 433 -Q-NN- 673—QNN- 913 ---NNQ
|-
209 Q--N-N 449 -Q-N-N 689—QN-N 929 ---NQN
| 97 || QNRNKR || 337 || RNQNKR || 577 || RNKNQR || 817 || RNKNRQ
225 Q---NN 465 -Q--NN 705—Q-NN 945 ---QNN
|-
| 113 || QNRKNR || 353 || RNQKNR || 593 || RNKQNR || 833 || RNKRNQ
|-
| 129 || QNRKRN || 369 || RNQKRN || 609 || RNKQRN || 849 || RNKRQN
|-
| 145 || QRNNKR || 385 || RQNNKR || 625 || RKNNQR || 865 || RKNNRQ
|-
| 161 || QRNKNR || 401 || RQNKNR || 641 || RKNQNR || 881 || RKNRNQ
|-
| 177 || QRNKRN || 417 || RQNKRN || 657 || RKNQRN || 897 || RKNRQN
|-
| 193 || QRKNNR || 433 || RQKNNR || 673 || RKQNNR || 913 || RKRNNQ
|-
| 209 || QRKNRN || 449 || RQKNRN || 689 || RKQNRN || 929 || RKRNQN
|-
| 225 || QRKRNN || 465 || RQKRNN || 705 || RKQRNN || 945 || RKRQNN
|}
 
Anyone with Fritz9 can verify this table by entering in the idns. It directly refers to just those SPs with bishop's code 0 i.e. with the bishops on a1 and b1.
Line 282 ⟶ 264:
 
{{DEFAULTSORT:Fischer Random Chess Numbering Scheme}}
[[Category:Fischer random chessChess960|numbering scheme]]
Retrieved from "https://en.wikipedia.org/wiki/Fischer_random_chess_numbering_scheme"