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Span
Board · Classics · plays in your browser, no download
A rhombus of hexagons. You own two opposite sides, the computer owns the other two, and you take turns colouring cells until somebody has joined their pair. It cannot end any other way — and that is not a design decision, it is a theorem.
Where it comes from
Hex was invented twice by two people who had never heard of each other, which is a rare thing and says something about how natural the idea is.
The first was Piet Hein, the Danish poet, designer and mathematician, in 1942. He showed it at the Niels Bohr Institute and published it in the newspaper Politiken in December of that year under the name Polygon, which is what it is still called in Denmark.
The second was John Nash, at Princeton, around 1948. His circle called it Nash, and also John — because the common room floor was tiled in hexagons and the game got played in the bathroom. Parker Brothers bought a version and put it on sale as Hex in 1952.
The mathematics is what makes it worth knowing about. A full board always contains exactly one winner: there is no way to fill every cell without one of the two connections existing, so the game has no draws, ever. Nash also proved that the first player must have a winning strategy — by showing that if the second player had one, the first could simply steal it. The proof tells you that a winning strategy exists and gives you no clue at all what it is, which is a very pure kind of mathematical joke.
How to play
| The board | A rhombus of hexagons. Two opposite edges are yours, the other two are his. |
|---|---|
| Moving | Colour any empty cell. Nothing is ever captured or removed. |
| Winning | An unbroken chain of your cells from one of your edges to the other. |
| Draws | There are none. Somebody has connected by the time the board is full. |
Because the first player has the advantage, the usual fix is the swap rule: the second player may, on their first turn, take over the opening move instead of answering it. That makes an unfair game fair without changing a single rule of play.
The shape to learn
One pattern does most of the work: the bridge. Two of your cells placed a knight’s-move apart, with two empty cells touching both of them, are already connected — if he takes one, you take the other. Good players build chains of bridges across the board at speed, and only fill them in when forced.
Three things that help
Play bridges, not touching cells. Two cells side by side use two moves to advance one step. A bridge advances two and is just as safe.
Blocking him is the same move as joining yourself. Your chains and his cross the same board; there is no separate defence to play, which is why the game never feels passive.
Start near the middle. The centre cell is on more short paths between your two edges than any other, and in a game with no captures you never get to take it back.