Amazons

Rules

Board. A rectangular board. Each square is either empty, dead, or contains a single amazon. Each amazon is coloured either black or white (not both).

Left moves. Pick a black amazon and move it over a positive number of empty squares in any of the 8 straight-line directions (orthogonally or diagonally), landing on an empty square. Then shoot an arrow from the landing square, which must also move over a positive number of empty squares in a straight line; it must land on an empty square, which becomes dead.

Right moves. Pick a white amazon and move it over a positive number of empty squares in any of the 8 straight-line directions (orthogonally or diagonally), landing on an empty square. Then shoot an arrow from the landing square, which must also move over a positive number of empty squares in a straight line; it must land on an empty square, which becomes dead.

Convention. Classical (normal or misère play).

Notes

Amazons move like Chess queens, but note that there are no captures in this ruleset.

This is a short partizan ruleset. It is partizan because only Left can move the black pieces (and only Right can move the white pieces). To see why it is short, consider the following:

• finite: the board is finite, and each cell is in one of four states (empty, dead, black amazon, or white amazon), so the number of subpositions is always finite.
• loop-free: since an empty square becomes dead after each move, the number of empty squares is reduced by 1 each turn. (So, in fact, the birthday of a position is bounded above by the number of empty squares.)