The game was invented in 1969 by Gustavus J. Simmons, a mathematician at the Sandia Corporation laboratories in Albuquerque, and was described in Gardner, Martin. Knotted Doughnuts and other Mathematical Entertainments. New York: W. H. Freeman and Company, 1986. 111-113.
Using Ramsey theory it can be proved that any two-coloring of the complete graph on 6 vertices (K6) must contain a monochromatic triangle, and hence a draw is impossible.
Computer search has verified that the second player can win Sim with perfect play, but there is not known to be a simple strategy for winning.