HEX — Nash's AI Strategy Game

Game Mode

Choose Your Side

🎯

Objective

Form an unbroken chain of your pieces connecting your two assigned edges. No draws exist — someone always wins (John Nash, 1942).

⬡

Teal — Left → Right

Connect the Left edge to the Right edge. Choose this side in vs AI mode using the Side Selector above.

⬡

Gold — Top → Bottom

Connect the Top edge to the Bottom edge. In 2-Player mode pass the device to Player 2 on their turn.

👆

How to Place

Tap or click any empty hexagon to place your piece. Players alternate turns automatically. Each hex touches 6 neighbours.

🧠

Strategy Tips

Control the centre — it connects the most paths. Block your opponent's chain early. Every move both attacks and defends. Use Undo to take back a move.

👥

2-Player Mode

Both players share one device. Screen shows whose turn it is clearly. Player 1 = Teal (Left→Right). Player 2 = Gold (Top→Bottom).

Minimax Search

Shannon (1950) — Philosophical Magazine

AI explores all possible moves to a fixed depth, alternating between maximising its own score and minimising yours. Guarantees the best possible move. Complexity: O(b^d).

α-β

Alpha-Beta Pruning

Knuth & Moore (1975) — Artificial Intelligence Journal

Cuts branches that cannot affect the final result. α = best MAX found; β = best MIN found. Prune when β ≤ α. Reduces complexity from O(b^d) to O(b^(d/2)) — searches twice as deep in the same time.

Union-Find (Win Detection)

Tarjan (1975) — Journal of the ACM

Detects winning connections in O(α(n)) ≈ O(1) amortized time using Disjoint Sets. Two virtual edge-nodes per player — a win is detected the instant they merge into the same component.

Dijkstra Heuristic

Dijkstra (1959) — Numerische Mathematik

Board evaluation inside Minimax. Computes minimum "cost" path to win (friendly=0, empty=1, enemy=∞). Score = player cost − AI cost, giving the AI a sense of who is closer to winning.

⬡ Gold — Top → Bottom

Teal ←→

⬡ Gold — Top → Bottom

You (Teal) — Left → Right

AI (Gold) — Top → Bottom

Tap any hex to place your piece

AI Brain — Live

⟳ Thinking…

AlgorithmMinimax + α-β

Search Depth—

Nodes Evaluated—

Branches Pruned—

Board Score—

AI Last Move—

MOVE —

TOTAL NODES —

DEPTH —

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Move History

No moves yet.