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Hi, Gary. A good part of our difference is merely a semantic debate. I,
too, agree with the ideas you express: 'My point was simply that large
boards are a good home for long-range pieces and more types of pieces.'
That's 100% accurate, and I agree with you. My problem here is how you
define 'large', and if greater numbers, longer ranges, and more
different pieces are required by larger (not 'large') boards. The point
about Go is that a 19x19 board is small enough that 2 players merely
putting unmoving stones on the board one at a time in alternating turns is
a good game. And it isn't even chess. My 16x16 4D game uses only a
standard FIDE piece set, with close to FIDE moves, and starts with a piece
density of 12.5% My 9x21 game starts with a piece density of 19%. Grand
Chess, as well as 2 of my large shatranj variants, all start with a 40%
piece density on a 10x10 board. Maybe my argument here is one of
aesthetics. Larger boards do not require larger numbers of pieces. Elegant
simplicity is a valuable goal in game design, for it increases the
playability of the game. And 10x10, or 20x20, is not 'large' - for
square, even-numbered boards, 8x8 is about the smallest size that gives a
decent game - clearly 2x2 and 4x4 are useless, and 6x6 is 'the easy game
for the ladies and children' and early computers, so 8x8 is the bottom.
For odd numbered boards, 5x5 is useless, and 7x7 is Navia Dratp. Still not
much room below 8x8, and 7x7's can have their bishop setup problems.
Please, define your terms. ;-)
On piece 'powers' - this is where I was tongue-in-cheek, in describing
pieces with diminishing *linear* ranges. On a 4x4x4x4 board*, you can only
possibly go 3 at most from your starting position in any one direction, but
you have a lot of directions in which to go. A simple rook, moving
linearly, can reach 12 positions on this board. A knight, in the middle,
can reach 23, using only its 'L-shaped' move. Even from a corner, it
reaches 12. *Of course, the board is actually physically 16x16, divided
into 4x4 sections, and movement rules simulate the 4x4x4x4 board, but you
could use Great Shatranj pieces, none of which move more than 2 squares,
quite successfully on that board. 
I am not arguing against any position as much as I'm arguing for mine. If
you say 10x10 is big, and requires at least 25 pieces per side to maintain
the 50% starting density, and we need amazons at least, then I'm arguing
against you. ;-) Enjoy. Joe (and I know I left a lot out, but next time)