Hex (board Game) - Strategy

Strategy

The game can never end in a tie, a fact proved by John Nash: the only way to prevent your opponent from forming a connecting path is to form a path yourself. In other words, Hex is a determined game.

When the sides of the grid are equal, the game favors the first player. A standard non-constructive strategy-stealing argument proves that the first player has a winning strategy as follows:

Since Hex is a finite, perfect information game that cannot end in a tie, either the first or second player must possess a winning strategy. Note that an extra move for either player in any position can only improve that player's position. 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. If the strategy ever called for moving on the square already chosen, the first player can then make another arbitrary move. This ensures a first player win.

One might attempt to compensate for the second player's disadvantage by making the second player's sides closer together, playing on a parallelogram rather than a rhombus. However, using a simple pairing strategy, this has been proven to result in an easy win for the second player.