In theory the swap rule ensures that the second player has a winning strategy, but in practice the first player can choose a hex for which no winning strategy is known.Ĭameron Browne wrote a book entitled Hex Strategy: Making the Right Connections, which covers Hex strategy at a greater level of detail than any preceding work. Nowadays, in most online sites, the swap rule is the default, with the swap made after only one move.

However, using a simple pairing strategy, this has been proven to result in a win for the second player.Ī fairer way is to use the pie rule, by which the second player has the option of swapping colors after the first player makes the first move, or first three moves, thus encouraging the first player to even out the game. One way is to make the second player's sides closer together, playing on a parallelogram rather than a rhombus. There are two ways to make the game fairer.

If the strategy ever called for moving on the square already chosen, the first player makes another random move. Therefore, if the second player has a winning strategy, the first player could steal it by making an irrelevant move and then follow the second player's strategy. Note that an extra move for either player in any position can only improve that player's position. It is obvious that since hex is a finite, perfect information game which cannot end in a tie, either the first or second player has a winning strategy. A standard non-constructive strategy-stealing argument proves that the first player has a winning strategy. When the sides of the grid are equal, the game favors the first player. The game can never end in a tie, a fact found by Nash: the only way to prevent your opponent from forming a connecting path is to form a path yourself.

In the image on left, Red moved first in this game and won. Red's goal is to form a red path connecting the top and bottom sides of the parallelogram, and Blue's goal is to form a path connecting the left and right sides. (Of course, the colors are merely a convention and the actual colors vary from board to board and from version to version.) They alternate turns placing a piece of their color inside a hexagon, filling in that hexagon with their color. Players have two colors, say 'Red' and 'Blue'.

Java hexagonal game