Hex

👥 2 players 📍 Indoor📍 Anywhere ⚡ Calm 🧩 Moderate ⏱ 15-30 minutes 🎂 Ages 6+

Quick Pitch

Hex is an elegant connection game where two players alternately place stones (or mark hexagons) on a hexagonal grid, trying to create a continuous path from one side of the board to the opposite side.

Equipment Needed

  • Sheet of paper
  • Pencil or pen (two different colors recommended)
  • Ruler (helpful for drawing hexagonal grid)

Setup

  1. Create Hexagonal Grid:

    • Standard: 11×11 hexagons (can use 7×7, 9×9, or 13×13)
    • Arrange hexagons in rows offset to create the pattern

  2. Label Sides:

    • Two opposite sides: Player 1's goal (e.g., "Red")
    • Other two opposite sides: Player 2's goal (e.g., "Blue")

Example of small 3×3 hex board (simplified):

    Red Goal
   / — \ — /
  /  1  \  2
 / — \ — / — \
/  3  \  4  \  5
\ — / — \ — /
 \  6  \  7  /
  \ — / — /
    Blue Goal

In a real board, all hexagons touch, creating a honeycomb pattern.

  1. Decide Turn Order: Random or Player 1 goes first

Rules

Objective

Create a continuous path of your color hexagons connecting your two opposite sides of the board. Adjacent hexagons (sharing an edge) form a continuous path.

Gameplay

  1. Players alternate turns
  2. On each turn, a player marks one empty hexagon with their color/symbol
  3. A hexagon connects to adjacent hexagons (sharing an edge, not diagonals)
  4. A player's path must connect their starting side to their ending side
    • Player 1 connects from left side to right side (or top to bottom)
    • Player 2 connects from top to bottom (or left to right)

Winning

The first player to create a continuous path of their color from one side to the opposite side wins immediately.

Path Requirements

  • Path must consist of adjacent hexagons of the same color
  • Diagonals don't count (only edge-to-edge adjacency)
  • Path must touch both goal sides (not just reach them)

Expert Player

Tips

Opening Play:

  • Center board positions are often valuable as they participate in many potential paths
  • Controlling the middle allows flexibility in later play
  • Corner and edge positions are less flexible

Path vs. Blocking:

  • Balance building your own path with blocking opponent's
  • Sometimes blocking is more crucial than advancing your own position
  • Anticipate where opponent might connect next

Bridge Concept:

  • Two stones with one empty hexagon between them form a "bridge"
  • Bridges are powerful because opponent must block both sides
  • Create chains of bridges to force opponent to waste moves blocking

Connection Complexity:

  • Once you have multiple path branches, opponent cannot block all
  • Early branching gives you redundancy later
  • Opponent cannot block everything; eventually you'll find a path

Strategic Importance:

  • In 11×11 hex, positions are rarely lost until very late game
  • The player who builds better bridges and creates more flexibility usually wins
  • Some positions have mathematically determined winners

Computer Analysis:

  • Hex has been partially analyzed by computers
  • On 7×7 boards, first player (moving first) has a winning strategy
  • On 11×11, the advantage of moving first is small but exists

Variations

  • Different Board Sizes: 7×7 (quick), 13×13 (long, deep strategy)
  • Swap Rule: After opponent's first move, current player can either take the position or pass and let opponent move again (equalizes first-player advantage)
  • Three-Player Hex: Three colors, three sides — requires modified rules
  • Reverse Hex: Be blocked from reaching your sides (opposite goal)
  • Weighted Hexagons: Some hexagons worth more points/harder to use
  • Misère Hex: Last to move loses instead of wins
Learn More — History & Origins

History & Origins

Hex was invented independently by Danish mathematician Piet Hein in 1942 and American mathematician John Nash (who later won the Nobel Prize) in 1948. Hein called it "Polygon," while Nash called it "Hex." The game gained prominence after Nash's work, which proved that games on certain board sizes always have a winning strategy. Hex has been extensively studied in combinatorial game theory. The board is often played on an 11×11 hexagonal grid in standard play.

Cultural Context

Hex is beloved by mathematicians for its elegant simplicity and deep strategic implications. John Nash's work on Hex contributed to game theory and helped establish his reputation in mathematics. The game appears in numerous recreational mathematics texts and is studied in university courses on combinatorial games.

The "Hex Theorem" — that there are no drawn Hex games (one player must always have a winning strategy) — is a fundamental result in combinatorial game theory. This proves that Hex is a "determined" game, unlike some others where draws are inevitable with optimal play.

Hex demonstrates how beautiful mathematical games can emerge from simple rules. The game remains popular among mathematicians, computer scientists, and game enthusiasts worldwide.

See Also