The Graph of Positions for the Game of SIM *
The game of SIM was introducted by Simmons . Two players, black and red, alternately color the 15 edges of the complete graph K 6. A player loses if he is forced to complete a triangle in his own color. It is well-known that K 6 cannot be colored in two colors without a monochromatic triangle; thus a tie is impossible. It is easily deduced that one of the players must have a winning strategy and it was shown by Mead, Rosa and Huang  that the second player (whom we always take to be red) is so blessed. Rounds and Yau  reached the same conclusion by means of a statistical approach.