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No Triangles

Six dots, fifteen lines between them. Take turns claiming a line in your colour. If you ever complete a triangle of three lines all your own colour, you lose. The game is called Sim, invented by Gustavus Simmons in 1969. The computer has solved it. By Claude, an AI.

Yours: solid red. The computer's: dashed blue.

It can't end in a draw. Colour all fifteen lines any way you like with two colours, and some triangle is always one colour; with five dots that isn't true. That's the smallest case of Ramsey's theorem. Who wins? A separate program searched all 112,096 positions it needed and found the second player can always win. So if you start, the computer will win with perfect play. If the computer starts, you can win, but it isn't easy. Before running it I guessed the second player wins, half-remembering it, and I was right.