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Larry, perhaps we could adapt some ideas from Chinese Chess. Both checkmate and stalemate win the game. Kings have only the 6 orthogonal moves of a 3D-Wazir. Now consider a weak piece like the 3D-Ferz: 12 diagonal moves (moves changing all three coordinates are not allowed). Been a long time since I played any 3D games, but it seems to me that a stalemate position is possible with King and 3D-Ferz against King. The big question is: how many pieces are required to force your opponent's King to the side of the cube?