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SIM as a Game of Chance

The game of SIM [2] is played by two persons on the six vertices of a regular hexagon using two colored pencils. Each player in turn fills in one of the 15 possible lines connecting a pair of points. The player who is first to form a complete triangle of his color loses (only those triangles with vertices on the six starting points are considered). The object of the game then is not to form such a triangle yourself and to force your opponent to do so. The game’s inventor,