![]() ![]() Different stratagems have been devised to minimize this advantage. Thus in the game of Hex, the first player has an advantage. ![]() Impersonating his rival and playing the latter's winning strategy will lead the first player to victory. If, in time, the winning strategy requires placing a chip in a cell occupied by the extra chip, the player puts a chip randomly elsewhere, and thinks of the latter as the (new) extra chip. Note that the extra chip can do no harm to this player. He imagines now being a second player and, as such, playing the winning strategy on the board with an extra chip of his color. To make this work, the first player makes a very first move and, in a sense, forgets about it. We are then going to show that the first player can utilize this same strategy to win the game. Assume there is a winning strategy for the second player. This was shown by John Nash in 1949 by what since became known as the strategy stealing argument. In fact the first player can force a win. The most important fact known about the game is that, unlike some other games, it can't end in a draw. Simple as the game appears, no winning strategy has been discovered for bigger boards. Much is known about the game, even a winning strategy for small - up to 9×9 - boards. The other player pursues a similar goal with regard to the blue color. The goal of the "red chip" player is to connect the two red sides of the board with an uninterrupted chain of red chips. ![]() One player plays with red chips, the other with blue chips. Two players take turns putting chips down, one chip per a cell. ![]() The game is played on a diamond shaped board with hexagonal cells and two pairs of opposite sides painted in two distinct colors, say, red and blue. The game of Hex has been invented in 1942 by Piet Hein, reinvented in 1948 by John Nash, got its name in 1952 from a commercial distribution by Parker Brothers, and has been popularized by Martin Gardner in 1957. ![]()
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