What is the game of Hex?

Hex is a two-player strategy board game played on a rhombus-shaped grid of hexagonal cells. Each player owns two opposite edges of the board. Players alternate placing stones of their color on empty cells, aiming to form an unbroken chain of their stones connecting their two sides. The game cannot end in a draw.

Hex was independently invented by mathematician Piet Hein in 1942 and Nobel laureate John Nash in 1948. Nash proved that the first player has a winning strategy on any board size, though finding it is computationally difficult for large boards.

Can Hex end in a draw?

No. It is mathematically proven that every completed Hex game has a winner. Once all cells are filled, exactly one player will have a connecting chain. This property (known as the Hex theorem) is equivalent to the Brouwer fixed-point theorem in topology.

What board sizes are available?

Five sizes: 7×7, 9×9, 11×11, 13×13, and 14×14. The standard tournament size is 11×11, which offers the best balance of depth and game length.

What is the swap rule in Hex?

The swap rule (also called the pie rule) compensates for first-player advantage. After the first player places a stone, the second player can choose to swap colors — taking the first player's stone and side. This discourages the first player from making an obviously strong opening move.

Play Hex Online

Connect your two sides of the board with an unbroken chain of stones before your opponent does. A timeless strategy game with no possibility of a draw.

Turn

Red

Moves

Time

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Red connects top ↔ bottom • Blue connects left ↔ right

Hex strategy game — connect your sides of the board with a chain of stones

What Is Hex?

Hex is a two-player abstract strategy game played on a rhombus-shaped board of hexagonal cells. It was independently invented by Danish mathematician Piet Hein in 1942 and by John Nash (the Nobel-prize-winning mathematician portrayed in A Beautiful Mind) in 1948. Despite its simple rules, Hex has deep strategic complexity and has been studied extensively in combinatorial game theory.

Rules of Hex

The board: A rhombus (diamond) of hexagonal cells. Standard tournament size is 11×11, but this version offers 7×7 through 14×14.
Sides: Each player owns two opposite edges of the board. Red connects top and bottom; Blue connects left and right.
Turns: Players alternate placing one stone of their colour on any empty cell.
Winning: The first player to form an unbroken chain of their stones connecting their two sides wins.
No draws: It is mathematically impossible for a Hex game to end in a draw — every completed board has a winner.

The Swap Rule

Because the first player has a theoretical advantage, tournament Hex uses the swap rule (also called the pie rule). After the first player places a stone, the second player may choose to swap colours, taking ownership of that stone and side. This forces the first player to choose a balanced opening move rather than an obviously powerful one. The swap rule is available in this version for human vs AI games.

Strategy Tips

1. Think in Connections, Not Territory

Unlike Go, Hex is about connectivity, not surrounding area. A single chain connecting your two sides wins — even if your opponent controls most of the board. Focus on building a bridge between your edges.

2. Use Bridge Connections

A bridge is a pair of stones separated by one empty hex, where both shared neighbours are empty. Bridges are virtually connected: if your opponent blocks one path, you can complete the other. Chains of bridges are a powerful way to reach across the board.

3. Play in the Centre

The centre of the board is strategically valuable because stones placed there radiate influence in all directions. Edge cells connect to fewer neighbours and are generally weaker unless they directly anchor a bridge to your side.

4. Block Efficiently

When blocking your opponent, try to place stones that simultaneously threaten your own connection. A purely defensive move wastes a tempo — the best moves attack and defend at the same time.

5. Learn the Ladder

A ladder is a forcing sequence where one player must keep blocking in a diagonal line. Ladders in Hex work similarly to Go: if the ladder reaches the edge, the attacking player connects; if a blocking stone is already in the path, the defender succeeds. Recognising ladders early saves many moves.

Board Sizes

7×7: Fast games, great for learning. Tactics dominate.
9×9: A good intermediate size with room for strategy.
11×11: The standard tournament size. Rich strategic play.
13×13: Deep, complex games for experienced players.
14×14: The largest board — marathon-length battles.

Mathematical Significance

Hex holds a special place in mathematics. John Nash’s non-constructive strategy-stealing argument proves the first player has a winning strategy, but does not reveal what that strategy is. The theorem that every Hex game must have a winner is equivalent to the Brouwer fixed-point theorem, a foundational result in topology. Hex has also been used to study computational complexity — determining the winner of a Hex position is PSPACE-complete.

Frequently Asked Questions

Hex is a two-player strategy game on a rhombus-shaped board of hexagonal cells. Players take turns placing stones, aiming to form an unbroken chain connecting their two opposite sides. It cannot end in a draw.

Hex was independently invented by Piet Hein in 1942 and John Nash in 1948. Nash proved that the first player always has a winning strategy.

No. Every completed Hex board has exactly one winner. This “no-draw” property is mathematically proven and is equivalent to the Brouwer fixed-point theorem.

After the first move, the second player may choose to swap colours instead of placing a stone. This compensates for first-player advantage and encourages balanced opening moves.

11×11 is the standard tournament size and offers the best balance of depth and game length. Beginners may prefer 7×7 or 9×9 for faster games.

More Strategy Games

Enjoy Hex? Try these other free games:

Go

The ancient game of territory on a 9×9 to 19×19 board.

Gomoku

Get five in a row on a 15×15 grid.