Hex (board game)

Hex is a two-player abstract strategy board game played on a rhombus-shaped board composed of hexagonal cells. The game was invented independently by Piet Hein in 1942 and John Nash in 1948.

Objective: The objective of the game is for each player to create a connected chain of their own pieces linking the two opposite sides of the board marked for their color. One player must connect the two sides colored white, while the other player must connect the two sides colored black (or sometimes red and blue).

Gameplay: Players alternate turns placing one of their pieces on any empty cell. The first player typically has a slight advantage, which can be mitigated by the "swap rule" (see below).

Rules:

• The board is a rhombus made up of hexagonal spaces. Common board sizes are 11x11, 13x13, and 14x14.
• Two players take turns placing stones of their color on empty hexagons.
• There is no limit to the number of stones a player can place.
• Once a stone is placed, it cannot be moved or removed.
• A player wins by creating a connected chain of their stones linking the two opposite sides of the board assigned to them. A chain can be formed horizontally, vertically, or diagonally, but must connect directly between the two designated sides.
• The game cannot end in a draw; one player must win.

Swap Rule (Pie Rule): To mitigate the first-player advantage, the "swap rule" is often employed. After the first player makes their first move, the second player has the option to "swap" colors with the first player, effectively taking the first player's position and stone placement. This ensures that the first player's initial move is not overly advantageous.

Strategy: Hex requires strategic thinking and tactical planning. Key elements of Hex strategy include:

• Creating Connected Paths: Players must focus on building connected pathways across the board.
• Blocking Opponent's Paths: Preventing the opponent from forming a complete chain is equally crucial.
• Bridging: Creating multiple connections between pieces to improve path resilience.
• Forcing Moves: Placing stones that force the opponent into disadvantageous positions.
• Tempo: Maintaining the initiative and forcing the opponent to react to your moves.

Mathematical Properties: Hex is a mathematically deep game with several interesting properties. One of the most notable is that it is a "determined" game, meaning that given perfect play, one player or the other can always force a win. However, finding the optimal strategy for even moderate-sized boards remains computationally challenging. It has been proven that determining the winner of Hex on an arbitrary board is PSPACE-complete. This complexity has made Hex a popular subject of study in artificial intelligence research.

Variants: Various Hex variants exist, including different board sizes and rule modifications.

See Also:

• Y (board game)
• Bridg-It