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Square Off is a territory game based on configurations of squares. It is played on a Chess board divided in four quadrants, as displayed in the diagrams. There are two players, Black and White. Both have 32 men in their color.
The game starts on an empty board, with a swap option for the second player: the first player puts a white man on the board after which the second player decides whether he accepts that move as his first, and thus plays white, or rejects it, in which case it is his turn and he plays black.

 RulesObject The game ends by one player's resignation or when the board is full. The winner is now the player with the most territory, that is: the highest number of 'marked men' on the board.

 Play After the swap, players move in turn to put one man on a vacant square. In White's case there is one possible addition to this, see Symmetric positions. If a man thus placed completes one or more 'squares' of 4 men of that color, either within one quadrant or with one man in each quadrant, then all unmarked men involved, including the one just placed, are 'marked'. The diagram shows a legal white and a legal black 'square', and a small white one on the brink of completion, where a man placed on the cell marked with the transparent man would complete a square.

 Symmetric positions By the nature of the move protocol, only Black can establish a symmertic position with regard to the horizontal or vertical axis, or with regard to the center point. White, if faced with any such position, has the option of replacing Blacks last placed man by his own, and transferring the removed man to a vacant square elsewhere on the board. White can postpone the option without losing the right to use it in a subsequent symmetric position, should one arise. In the diagram black has created a point symmetric position on his first move. The other two highlighted cells show where he could have created line symmetry.

 Swap The swap rule is based on the fact that cells of a quadrant participate in different numbers of possible 'squares'. The first player can choose a '9-squares' cell, but then the second will certainly accept it as his first move, or he can choose a '4-squares' cell, in which case the second player might consider playing black and starting with a '9-squares' cell himself. How I invented ... Square Off Square Off © MindSports