Abstract: A chess game is provided having a hexagonal board having alternate sides constituting bases for respective of three participants. Polygonal fields are provided on the board in the form of triangles, quadrilaterals or hexagons. These fields extend between the three bases and occupy at least substantially all of the board. Three like sets of men correspond to the bases, and include a king, queen, two bishops, two castles, two knights, a plurality of pawns and a cardinal, which is still movable after the corresponding king is checkmated. There may be provided an extra pawn in each set, and there may also be provided an identifying field or ring to place under or encircle a checkmated king. The cardinal and queen are entitled to similar moves. The cardinal may not conquer men from sets of other participants. The cardinal has social-political characteristics, and it is arranged that this man can be conquered only under difficult circumstances or not at all.