Wythoff's game with two queens

Extend Wythoff's game to two queens racing to the corner, each moving west, south, or south-west; the player who cannot move loses. With two pieces a position is a pair of coordinates, and the reachable positions form a tree: each node branches into the available moves, and leaves are positions with no move.

Labelling the tree backwards from the end marks each position winning or losing: a position is losing if every move leads to a winning position for the opponent, and winning if some move leads to a losing one. The cold (losing) positions again reveal a pattern you can tabulate.