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The following e-mail was received by the editors: 

Great website! You write:
 

	'Fischer Random Chess has 960 legal arrays. This number is determined as
follows: 

	First, place the two Bishops. There are 16 different ways for one bishop
to be on a white square and the other Bishop to be on a black square. 

	That leaves six empty squares. Now, place the King somewhere between the
two Rooks. There are 20 different ways for a King and two Rooks to occupy
six squares with the King in between. 

	That leaves three squares for the two Knights and the Queen. There are
three possible ways to place these pieces. 

	Thus, there are 16 x 20 x 3 (960) legal arrays in Fischer Random
Chess.'

	 

	The most complex step is that 20 in the middle. It can be removed like
this:

		Fischer Random Chess has 960 legal arrays. This number is determined as
follows: 

		First, place the two Bishops. There are 16 (4 x 4) different ways for
one bishop to be on a white square and the other Bishop to be on a black
square. 

		That leaves six empty squares. Now, place the Queen. There are 6
different ways to do this. 

		That leaves five empty squares. Now, place the two Knights. There are 10
different ways to do this. 

		That leaves three empty squares. Lastly, place the two Rooks and the
King. There is only one legal way to do this. 

		Thus, there are 16 x 6 x 10 x 1 (960) legal arrays in Fischer Random
Chess. 

		Regards 

		Peter Ridges

I have expanded Fischer's mathematics system to cater for Capablanca's
chess variations.

Capablanca84000 is a variant of Fischer Random Chess (Chess960), based
on the Capablanca (10x8) variation.
The light (for white. dark squared for black) squared bishop may start
on one of 5 files (b,d,f,h,j). the dark (light for black) squared
bishop may similarly begin on one of 5 files (a,c,e,g,i).
The archbishop may then be placed on any of the remaining 8 files.
The chancellor may then be placed on any of the remaining 7 files.
The queen may then be placed on any of the remaining 6 files.
The two knights may be placed within the remaining 5 files in 10 ways:
1+2, 1+3, 1+4, 1+5, 2+3, 2+4, 2+5, 3+4, 3+5, 4+5.
The remaining 3 files are filled in the order of rook-king-rook to
allow for castling on both sides of the king.
Multiplying the quotients gives the number of combinations: 5 x 5 x 8
x 7 x 6 x 10 = 84,000

By taking the random number, 12345, we can calculate the combination
for white (black is mirrored from white through 4th/5th rank).
Placement of light squared bishop: 12345/5 = 2469 with no remainder.
the light squared bishop goes in it's first possible file, b.
Placement of the dark squared bishop: 2469/5 = 493 with remainder of
4. The dark squared bishop goes in it's last possible file, j.
Placement of the archbishop: 493/8 = 61 with remainder 5. The
archbishop goes into its 6th (note, lowest remainder is 0, not 1)
possible file. b and j are already taken, so the archbishop goes into
file g.
Position of the chancellor: 61/7 = 8 with remainder 5. The chancellor
goes into the 6th available file. b, g and j are taken, so the
chancellor goes into file h.
Placement of the queen: 8/6 = 1 with remainder 2. The queen goes into
the 3rd possible file. b, g, h and j are taken so the queen goes into
file d.
Placement of the two knights: The last integer result, 1, indicates
that the two knights occupy the 2nd possible combination of files,
1+3. b, d, g, h and j are taken, so the knights occupy files a and e.
The remaining three files (c, f and i) are filled by the two rooks and
the king, with the king inbetween the two rooks. Thus, the rooks go
into files c and i. The king goes into file f.
The set up for combination 12345 is:
knight-bishop-rook-queen-knight-king-archbishop-chancellor-rook-bishop.

One of the current most popular chess variants on the market today is
Gothic Chess, 'designed' by Edward Trice. The pieces row in Gothic chess
is as follows (from left(a-file) to right(j-file)):
rook-knight-bishop-queen-chancellor-king-archbishop-bishop-knight-rook on
a 10x8 board.
How to calculate the equivalent Capablanca84000 combination: The light
squared bishop is in the 4th possible file. We use the quotient 3.
The dark squared bishop is in the second possible file. For this we
use the quotient 1.
The archbishop is in the 6th possible file, quotient = 5.
The chancellor is in the 4th available file, quotient = 3.
The queen is in the 3rd available file, quotient = 2.
The knights are in the 6th possible orientation, quotient = 5.
Using these numbers we calculate backwards. The last quotient is 5.
The number 5 is achieved after dividing 30 by 6. 30 + 2 is the
previous number. 32 is achieved After dividing 224 by 7. 224 + 3
should be the previous number. 227 is achieved After dividing 1816 by
8. 1816 + 5 should be the previous number. 1821 is achieved After
dividing 9105 by 5. 9105 +1 should be the previous number. 9106 is
achieved by dividing 45530 by 5. The final calculation is to add the
first quotient, 3, to 45530 to give 45533.

The first Capablanca84000 combination is 00000. The last combination is
83999.

Capablanca84000 and its calculating system are intended to be made the
property of the public domain and may be used or improved by any entity,
or hosted for free on any internet website. The reason for designing
Capablanca84000 was to give something to the world of chess. It took under
an hour to design and I would not feel comfortable for receiving anything
more than acknowledgemnt of contribution, since no novel idea was
employed. I wish that no third party may charge or be charged for using
Capablanca84000. I wish for it to be public domain. I wish that the design
ownership belong to José Raúl Capablanca and Robert James Fischer.
I have 'designed' my own personal combination which I believe is unique
and the best set-up. Currently, I choose to keep this combination secret,
until I am the recognised 'designer' of it.

There is aready my proposal for Capablanca Random Chess. I repeat it here:

CAPABLANCA RANDOM CHESS (2004-Nov-26) Proposal 

This definition of CRC should cover the following goals:

a) creating an interesting drosophila for chess programmers 
b) using Capablancas 10x8 Chess board geometry 
c) using Capablancas piece set (incl. archbishop and chancellor) 
d) applying rules aligned to Fischer Random Chess 
e) avoiding conflicts to any claimed patents 

The CRC rules are: 

a) creating a starting position (one of 48.000): 
 1) the bishops have to be placed upon different colored
  squares; same rule applies to the implicite bishop pieces:
  queen and archbishop (aligned to FRC)
 2) the king always has to be placed somewhere between the 
  rooks to enable castlings (aligned to FRC)
 3) use only such positions without unprotected pawns (Chess)

b) describing a method of generating starting positions on 
   free squares by using a dice or random number generator: 
 1) select queen or the archbishop to be placed first (2x)
 2) place the selected 1st piece upon a bright square (5x)
 3) place the selected 2nd piece upon a dark square (5x)
 4) one bishop has to be placed upon a bright square (4x) 
 5) one bishop has to be placed upon a dark square (4x) 
 6) one chancellor has to be placed upon a free square (6x) 
 7) one knight has to be placed upon a free square (5x) 
 8) one knight has to be placed upon a free square (4x)/2 
 9) set the king upon the center of three free squares left
11) set the rooks upon the both last free squares left 
12) this establishes White's first row, the Black side 
    has to be built up symmetrically to this 
13) place ten pawns similar to traditional chess in a row 
14) skip this position if it has unprotected pawns or not
    at least three positions in line 1 differently filled
    compared to Gothic Chess (patented), this finally gives
    about 21.259 distinct starting arrays.
   
c) nature of (asymmetric Fischer-) castlings:
 1) castlings are (like in traditional chess) only valid
  if neither the affected king or rook has been moved, or
  there would be a need to jump over any third piece, or
  the king would be in chess somewhere from his starting
  position to his target field (both included). Therefore
  all squares between king and its target square (included) 
  have to be free from third pieces, same applies to the
  way the rook has to go to its target square.
 2) the alpha-castling (O-O-O, White's left side):
  like in FRC the king will be placed two rows distant
  from the border (here c-file) and the rook at the next 
  inner neighboured square.
 3) the omega-castling (O-O, White's right side):
  like in FRC the king will be placed one row distant
  from the border (here i-file) and the rook at the next 
  inner neighboured square.

d) performing castlings:
 within a GUI try to move the king upon the related rook
 or at least two squares into that direction; manually:
 1) move the king outside of the board
 2) move the rook to its end position (if need to)
 3) move the king to his end position

e) extended FEN encoding:
 1) the extended FRC-FEN could be used as a base
 2) 'a'/'A' are used to identify archbishops
 3) 'c'/'C' are used to identify chancellors
 4) '9' is used to mark nine empty squares
 5) '10' is used to encode ten empty squares
 6) if a castling enabled rook is not the most outer one
  at that side, the letter of his file has to be placed
  immediately following his castling marker symbol, where
  'q'/'Q' are used for the alpha-, 'k'/'K' for omega-side.
 
f) engine notation rules for castling moves:
 According to UCI convention the castling moves should be
 written by using both coordinates (source and target field)
 of the involved king. But there are castlings, where the 
 king does only one or none simple step. In that cases the 
 castling should be distinguishable by appending a 'k', like
 already practized in promotion moves to make them unique.
 Overmore an engine should accept O-O or O-O-O (no zeroes),
 but only use them, when the GUI would demand for such a
 less precise notation.

Capablanca Random Chess (CRC) and Capablanca84000 were hybridised from
previously existing ideas (by Robert James Fischer and Jose Raul
Capablanca) independantly by their respective authors. Capablanca84000 is
the property of the public domain. I request confirmation as to whether
CRC is also the property of the public domain. The author of
Capablanca84000 supports and acknowledges the work of the author of CRC.
CRC and Capablanca84000 are the fruit of the same idea by two independant
authors. CRC and Capablanca84000 are significantly different to allow the
employment of either mathematical system.
Capablanca84000 is a more direct hybrid of Capablanca Chess using the
Fischer Random Chess (FRC) system. CRC is a modified hybrid of Capablanca
Chess and the FRC system.

As for catering for the possible system result which gives a position
similar or identical to a previously existing 'patented' 'invention',
I would state that generating a random number does not breach any patent.
Further, applying this random number to mathematical system which is the
property of the public domain does not breach any patent. Coincidence does
not breach any patent.

I want to make clear, that I do not intent to patent the idea of CRC.
Everybody who like it, may use it freely. Nevertheless it is not public
domain concerning the idea, because I want to be asked when changes or
improvements should become necessary. In so far I claim my copyright on
that idea. 

As an example currently there is a discussion, how the new pieces should
be represented. Indeed it seems neither being simple nor to be skipped
finding appropriate icons DISTINCT to existing and RELATED to the GAITS of
the represented pieces. The solution Smirf (my program being able to play
FRC and CRC, see: [http://www.chessbox.de/_tmp/SmirfPrototyp.png]) provides
for that problem thus avoids the usage of horse heads or bishop hats. And
for newcomers additionally to those pictures it might be helpful also to
use new and better names, where some already have been introduced here: 

CROSSED SWORDS: A=ARCHANGEL (ger. E=Erzengel, protecting the paradise with
swords) instead of Archbishop or Janus 
ROOK on a HORSESHOE: C=CENTAUR (ger. Z=Zentaur, because of its double
nature, horse part below) instead of Chancellor

See for that at: [http://www.chessbox.de/Compu/schachveri1_e.html]

To Greg Strong: I still want to avoid unnecessary conflicts with Ed Trice.
Nevertheless I agree, that randomly produced starting arrays hardly could
be regarded as trial to break a patent, where chances are 1:21.000. May be
it would help to specify an ERC variant: EUROPEAN RANDOM CHESS without
that GC avoiding rule, because such patents seem not to be valid in Europe,
also reflecting the European history of that extended 10x8 variant.

Reinhard, may i suggest an improvement to CRC? it seems to me that you
wish
to limit the number of credible variations to 'as low a number as
possible', to increase the overall credibility of the system. in
Capablanca84000, i considered deleting 42,000 of the variations since
they
are mirror images of the other 42,000. however, the reason behind
Capablanca84000 was to expose a conman using the traditional Fischer
system and no new formulae of my own (except those required for
Capablanca's archbishop and chancellor). thus, i am happy with the
number
84,000. indeed, i could even introduce more than 84,000 if i wanted to by
not being strict about bishops or rooks.
by introducing my suggestion you can get CRC down to about 10,000
variations [edited]. especially since
Capablanca84000 belongs not to I, but to the public domain. [edited]
my suggestion comes in several forms:
A: king must be to the right of the queen. traditional, includes
'invented' position.
B: king must be to the left of the queen. untraditional, deletes need for
patent skirting.
C: king must be on the right side of the board. see A.
D: king must be on the left side of the board. see B.

What is your goal, taa? Supposing you are intelligent I prosume you could
imagine that I notice that you are anonymously spreading desinformation
and nonsense here. Because the castlings like in Chess960 are not
symmetric, there is no redundance of mirrored positions. And CRC of course
is not trying to get as few as possible starting arrays, but instead to
filter positions, which eventually could be used as polemic arguments
against CRC, and to secure a more harmonic impression of that approach.

you might be right, i based the castling assumption on something else.
something i assumed before i learnt about fischer castling.
take standard chess and its mirror as variations in chess960. castling
would be the only difference between the two, other than
left-hand/right-hand bias. that's a shame.
my goal, is to liberate capablanca chess from the slavery which that
person has put it under, with his incredible patent. (note, contrary to
popular opinion, incredible doesn't mean good, it means 'not credible')

ok, i didn't quite get the distinction, but here is my comment on
cappablanca chess in general: it gives rooks more power, and takes too
much power from the knights. the addition of the 16 extra squares reduces
the board mobility of the knights, a pivitol piece in Chess and Fischer
Random Chess. 

and i also find the two new peices to be just a tad extravagant. i think
if i want new peices, play 'chess with different armies', my new
favorite besides FRC. (my prefference now goes: FRC, CwDA, then chess,
then cappablanca chess.) 

anyway, FRC was invented because of how boring openings have gotten in
Chess, because there are millions of pages written about the openings
alone, and everyone is playing off of memory, not playing chess. 

CRC and Cappablanca 84000 are simply superfluous in this way, because
cappablanca chess itself doesn't yet (and perhaps never will) have the
problem of opening memorizations.  

anyway, this is what i think. mostly just taste, but a little informed
opinion as well.

Does anyone happen to know what year this game was invented?  Amazingly
enough, there is no mention of FRC in Pritchard's encyclopedia.  I would
like to supply such basic information as year of invention for all games
supported by ChessV, so any information would be helpful!

Thanks,
Greg

it was invented in 1996 by Robert Fischer in Argentina.  

http://www.chessbox.de/Compu/fullchess1b_e.html

'Giving history lessons to the people on this web site is very low on my
list of priorities.'
_____________________

If your definitive history lessons must include condescending remarks
toward this entire group, then I am confident we can survive completely
without your input.

The CAPABLANCA-RANDOM-CHESS idea goes back to early 2004. One of the first
publishings of that idea has been made by me at July 1st, 2004 in 

http://www.bauer-schweitzer.de/forum/index.html