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Shatranj. The widely played Arabian predecessor of modern chess. (8x8, Cells: 64) (Recognized!)[All Comments] [Add Comment or Rating]
George Duke wrote on Wed, Aug 5, 2009 04:51 PM UTC:
It tends not to be noticed that C960 castling is a 2/3 reduction, because of the other accompanying reduction for Bishop-same-colour. Instead of every King placement, C960 permits only 56 of the 168 respecting the two Rooks' positioning. (In general, on 8x8 fixed castling is better, and by 8x10 free castling is better -- but that's an educated value judgment.) Since ShatranjShuffle2880 has no castling, it has 3 times the arrays available over C960, wherewith Rooks to King placements are not mattering. Hence the exact times 3, what we were trying to understand.
(1) Incidentally with mirrors 168x2 = 336, and that number 336  keeps recurring, chiefly just because it is 8x7x6, such as at Man & Beasts 04,
http://www.chessvariants.org/index/displaycomment.php?commentid=23281.
(2) Technically 960/40320 = 0.0238 = 1/42, the fraction being exact. So C960 uses only 1/42 of pure (8 factorial), representing every possible permutation, and most of the 960 are still ugly as a bulldog.