Capablanca84000 like Fischer Random Chess (chess960), but 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 can similarly begin on one of 5 files (a,c,e,g,i).
the archbishop may 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.
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
the most popular current Capablanca84000 combination is rook-knight-bishop-queen-chancellor-king-archbishop-bishop-knight-rook.
to calculate the corresponding 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.
45533 is currently the most popular combination played in Capablanca84000.
Capablanca84000 and its calculating system should be public domain and may be used or modified by any person, or hosted for free on any website. the reason for designing Capablanca84000 was to give something to the world of chess. no third party may charge or be charged for using Capablanca84000. I claim no design ownership whatsoever for Capablanca84000. I wish for it to be public domain.