Gaming article "Sim - Gustavus Simmons' game"
Sim is an interesting logic game, and you'll need only two pencils of different colors and a sheet of paper to play it. The game is played in graph consisting of multiple dots (vertices). The graph displays a few dots connected to each other with a line (edge). In our version of the game, the graph has seven dots. Players move in turn, connecting vertices that are not already connected using their designated colors. The first player uses red, and the second player uses blue. Each player should avoid the creation of a triangle made solely of their color; the player who completes such a triangle loses immediately.
This game was invented by Gustavus Simmons - a graph theory specialist; which explains the name of the game. We will use red and blue colors, where Player 1 is red, and Player 2 is blue.
The first thing you should be questioning is whether a triangle of one color will ever be formed when all of the dots are connected. The answer is yes. It turns out that this situation will occur if the graph consists of six or more points. And it is not difficult to prove.
I have calculated this game using seven vertices on my computer, and found out that the second player has the winning strategy. However, in my opinion nobody really knows the best strategy. Maybe you will find it!
It is definite that the second player has an advantage in this game but to realize it he/she must be very attentive. The second player should move in a way that takes moves away from his/her opponent. Look at Fig.1, the first player has connected 1 to 2 and 1 to 7. Note that he/she cannot join 2 to 7. The second player shouldn't make the move from 2 to 7 either, as this move does not decrease the number of Player 1's moves. But sometimes players have to make moves that reduce their own freedom. But when such a situation appears, you are better off connecting 3 to 7, as Blue had done in Fig. 1. Though Blue has left himself without a move from 2 to 7, Red still cannot join these points, as it would create a triangle (illegal formation). That's about all of the basics of this game. After you play several times and work out different strategies, you may discover some advanced "laws" of the game.
In the Figures 2-4 Red can win, and in Figures 5 and 6, Blue can win. The program has found the positions with the only move which lead to a win. Train your intuition!