TRAFFIC LIGHTS

Copyright (c) 1985 Alan Parr

This game is played on an empty 3x3 or 3x4 square board. There are enough red, yellow and green stones. 

 

TURN - On each turn, each player must do one of the following options: Drop a red stone on an empty cell Replace a red stone with a yellow stone Replace a yellow stone with a green stone GOAL - A player wins by making a 3 in-a-row of the same color.

 

An example in a 3x3 board The next player will lose this game. There is no good move left. If he drops a red stone at a1, the next player replaces it with a yellow to make a 3 in-a-row. If he replaces any red stones, the next player wins by replacing the other red stone. If he replaces any yellow stone, the next player wins with green stones.

The 3x3 board have a forced win to the first player: Drop a red stone at the center, the adversary must replace it (only possible move), then First replace it into a green stone. After that, First just needs to maintain symmetry to win. This game is described here (I wish to thank Lada Urbanova for this link).

Meanwhile, during 2006, Carlos Santos, a chess master Portuguese player, analyzed the 3x4 variant and showed that the second player has a winning strategy.