[cwxuageb] Chess is mostly local, and keep it that way

To see if a piece is attacked, first look for attackers in its local neighborhood.  5x5 is enough to detect King, Pawn, or Knight attacks.  Then, check for ranged attacks coming from 8 possible directions (Queen, Rook, Bishop).

Subjectively, most of the piece interactions come from nearby, with a small number of possibilities for long-range interactions.  This balance between short-range and long-range makes chess a beautiful game.  People generally like locality; it's easy to reason about.  Too many long-range interactions make a game too complicated to be enjoyable, but too few make it boring.

Incidentally, this design also shows up in go 囲碁: fights are local, except for ladders which can extend a long distance.

Do games invented and developed by humans tend to evolve to have this balance?

Vague idea: the different ranges might align with strategy versus tactics.  Maybe long versus short range in time.

A principle of keeping things mostly local suggests a way to extend chess to higher dimensions.  In d dimensions, let the rook (small rook) move orthogonally, in 2*d possible directions.  And then, rook movement should be it for ranged movement: there should be no other permitted ranged movement.  There should be no ranged diagonal movement: the number of possible diagonal movements in higher dimensions grows exponentially with dimension, somewhere between 2^d (space diagonals only) to 3^d-1 (generalized queen).  We judge anything exponential to be too many possible long range interactions, so we eliminate bishops and queens in higher dimensional chess.

On an empty board, a rook requires d moves to travel to an arbitrary point in d dimensions.  That might be a lot of moves in high dimensions, but let's just say positioning rooks becomes part of game strategy (in contrast to tactics which dominate local fights).

Maybe also provide a piece that moves like a rook but is a transport vehicle, able to carry multiple other pieces with it.  Or, in general, we can have other ranged pieces, but the only type of long range movement is that of the rook.  For example, we might have hybrid pieces combining rook movement and some short-range movement.

Maybe provide limited possibilities for teleportation to deal with the rook taking so long to get anywhere.  So long as there isn't much teleportation, the game remains mostly local.  We could have drops like shogi.

Previously similar.

In higher dimensional chess, there can be, perhaps should be, a lot of variety, richness, in short-range pieces.  Somewhat inspired by the gold and silver generals in shogi.  A wide variety could automatically happen through the exponential number of possibilities of short-range diagonal movement.

The area (a.k.a. volume, hypervolume, measure) of the local neighborhood around a piece does grow exponentially, e.g., 5^d, possibly making the local part of the game too complicated to be enjoyable: too many possible short range attacks.  However, it still remains local.

Furthermore, a neighborhood of area 7^d is not unreasonable either on a large board, allowing nice range-limited ranged pieces.  We can use previous ideas for higher dimensional chess piece types, except limit the range of ranged pieces to 3 squares.  The goal is to increase the possibilities for pins and forks, the bread and butter of chess tactics, while still keeping things (mostly) local.

Another way to prevent the number of possibilities of movement (both short-range and long-range) from growing exponentially is to restrict movement to only within an orthogonal plane: no space diagonals or generalized knights.  There are O(d^2) axis-aligned planes through a point: quadratic, not exponential.  We can bring back all 2D chess movement and its balance between short and long range.