John Lawson wrote on Fri, Sep 13, 2002 12:56 AM UTC:
The measurement that was used by Gabriel Vincente Maura to justify the
design of his variant, Modern Chess (Ajedrez Moderno),
http://www.chessvariants.com/large.dir/modern.html
is kind of interesting. This is taken from the booklet that came with my
Modern Chess set, 'Mathematical Thesis of Modern Chess', 50 p., 2nd
English Edition Revised, 1974.
He defines the maximum mobility of each piece as the number of squares it
can move to from its best position on the board, that is:
K=8, Q=27, B=13, N=8, R=14, P=2
The maximum relatve mobility for the total of each player's pieces is the
sum of the maximum mobilities of all the pieces, divided by two, because
there are two players. Thus:
(K+Q+2B+2N+2R+8P)/2 = (8+27+26+16+28+16)2 = 60.5
He defines the maximum mobility that the chessboard offers simply as the
number of squares. He wants the maximum relative mobility of the pieces
(60.5) to be equal to the maximum mobility offered by the chess board
(64). Since the numbers aren't equal, he declares FIDE Chess to be
defective. Needless to say, for Modern Chess, with the addition of the
Marshall, both numbers work out to 81.
Some example calculations for other variants:
'mobility' board
Grand Chess 98 100
Timur's Chess 86 112
Xiang Qi 59.5 90
Shogi(unpromoted) 45.5 81
Shogi(promoted) 75 81
I believe that this is little better than numerology, but it's still fun
to play with.
The measurement that was used by Gabriel Vincente Maura to justify the design of his variant, Modern Chess (Ajedrez Moderno), http://www.chessvariants.com/large.dir/modern.html is kind of interesting. This is taken from the booklet that came with my Modern Chess set, 'Mathematical Thesis of Modern Chess', 50 p., 2nd English Edition Revised, 1974. He defines the maximum mobility of each piece as the number of squares it can move to from its best position on the board, that is: K=8, Q=27, B=13, N=8, R=14, P=2 The maximum relatve mobility for the total of each player's pieces is the sum of the maximum mobilities of all the pieces, divided by two, because there are two players. Thus: (K+Q+2B+2N+2R+8P)/2 = (8+27+26+16+28+16)2 = 60.5 He defines the maximum mobility that the chessboard offers simply as the number of squares. He wants the maximum relative mobility of the pieces (60.5) to be equal to the maximum mobility offered by the chess board (64). Since the numbers aren't equal, he declares FIDE Chess to be defective. Needless to say, for Modern Chess, with the addition of the Marshall, both numbers work out to 81. Some example calculations for other variants: 'mobility' board Grand Chess 98 100 Timur's Chess 86 112 Xiang Qi 59.5 90 Shogi(unpromoted) 45.5 81 Shogi(promoted) 75 81 I believe that this is little better than numerology, but it's still fun to play with.