Claudio, yes, the 1, 2, 3, 4 are absolute [small, whole] numbers. These
distances are forced by the nature of the pieces - any chesslike piece
must move at least 1 square; if it leaps it must move at least 2 squares;
if it both slides and leaps, it may move 3 squares [though it could move
less]; and if you have a double leaper, it may move up to 4 squares. These
numbers are totally independent of the boards on which they are placed. And
yes, their power varies with board size; specifically it goes up more and
more as the boards get smaller. Technically, an n/2 piece is scalable,
getting its maximum movement range from board size and not as an intrinsic
part of the piece itself. And it could have, on an 8x10 board, a
back-and-forth movement of 4 and a side-to-side movement of 5. This is not
something I had thought of until just now answering your question. The
scalable R/2, B/2 or whatever could be interesting [if gimmicky] pieces.
Anyway, that's why I listed 3 somewhat different ways to look at
shortrange pieces instead of just 1 definition of 'the' shortrange
piece.
Greg, I'd enjoy playing Grand Shatranj against you [or any of my other
shortrange variants], but I don't feel I should compete for a 'World
Championship' with only 1 other person. If several players, including,
say, John Vehre, were to compete, then I would be more willing to play,
but wouldn't have a prayer of winning. I'd be happy to play a friendly
game with you.
Sam, Gary, I agree that shogi-style drops certainly unbalance a situation,
and should therefor more easily lead to a conclusion; but I am, frankly,
terrified of games that use drops as I have almost no familiarity with
them and far too easily get lost in the maze of potential positions -
another reason why I only discuss Western chess development in the
article.
Christine does have a nice little add, but I can't tell and spoil the
surprise. I will note that while it's easy to tell our writing apart,
people will find it much harder to tell our designs apart, as we fall into
the category of designers exemplified by Fighting Kings and Royal Pawn
Chess. And since we discuss games and look at each other's work, it's
sometimes hard for us to tell just who did what. [Now if we could only
understand each other...]