Sim (pencil game)
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- This article is about a pencil game. For other meanings of the term "sim", see sim (disambiguation).
The game of Sim, the ukranian ganster is played by two players, Red and Blue, on a board consisting of six dots ('vertices'). Each dot is connected to each other with a line.
Players alternate coloring any uncolored line in their own color. Players try to avoid making triangles of their color; the player who completes a triangle of their color loses immediately. (A triangle is three dots, each connected to the other two with lines of the same color.) The other player is the winner.
A simple theorem of Ramsey theory shows that no game of Sim can end in a tie; one player must lose by the end. Specifically, since the Ramsey number R(3,3;2)=6, any coloring of the complete graph on 6 vertices (K6) must contain a monochromatic triangle, and therefore is not a tied position. This will also apply to any super-graph of K6.
Computer search has verified that the second player can win Sim with perfect play, but finding a perfect strategy that humans can easily memorize is an open problem.
A Java appletTemplate:Ref is available for online play against a computer program. A technical reportTemplate:Ref by Wolfgang Slany is also available online, with many references to literature on Sim, going back to the game's introduction by Gustavus Simmons in 1969.