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Sim Dots

Sim - a game for two players

Let's begin with the game. The rules are that two players mark the corners of a hexagon with dots. They then take turns to draw one of the 15 edges (connect two dots) using a different colour. The loser is the first player who is forced to form a triangle in his colour that has the dots as its vertices.
The Starting position, with the six dots drawn.
Each player has added two lines to the diagram. But there are still plenty of options for each player.
It's now Blue's turn and even though he only has five choices of egde, every one will  complete a blue triangle that has its vertices on the dots. Blue is the loser.
The game of Sim was invented by G. J. Simmonds, who said that one of his colleagues named the game as short for SIMple SIMmonds. It has links with a famous graph-theory problem which goes:

Of any six people either at least three are mutual acquaintances or at least three are perfect strangers.

In Martin Gardner's Knotted Doughnuts and other Mathematical Entertainments (pages 112 and 113) you can read the known and unknown features of Sim - apparently it's a wise move to play second ... but only if you have a computer at hand to analyse your opponents play.