John Forbes Nash Jr.: Nobel laureate and game designer
The economist John Forbes Nash Jr. invented the game “Hex” in 1947. The problem with the game: if both sides play optimally, the winner is predetermined from the start.
Note: This article first appeared in 2010 on zuspieler.de.
In 1959, the madness began. “I heard something like phone calls in my head, from people who rejected my ideas. The delusion was like a dream from which I never seemed to wake up,” says John F. Nash Jr. today. The future Nobel laureate suffered from paranoid schizophrenia. So severe that he was admitted to a psychiatric clinic in 1964. It took decades before the mathematician led a normal life again. Yet in 1994, John F. Nash Jr. received the Nobel Prize in Economic Sciences.
He was and is a genius in his field – much like Mark Twain was. I started the “famous game authors” series with the writer just under a month ago. Today, the second part follows with a game where the winner – at least in theory – is predetermined from the start.
The board game Hex
Long before his illness, Nash invented the game “Hex” in 1947. On an 11 by 11 board of hexagonal spaces, Red and Blue battle for victory. Two opposite sides are red, the other two are blue. The corner spaces count for both colours. A player wins by connecting their sides with a chain of their coloured pieces. To do this, the opponents take turns placing their pieces on empty spaces. Since Red goes first, players usually agree on a swap rule. This means Blue can – if they wish – take over Red’s opening move and continue playing with the red pieces. Red then takes the blue pieces and must play against their own opening move. Red should therefore place their first piece in such a way that neither Red nor Blue has a discernible advantage, as Blue can always choose the side that is at an advantage.
A draw is impossible, as the only way to block the opponent is to build your own winning chain. When all spaces are filled, exactly one player will always have a winning chain.
By the way:
- Hex was also invented – independently of Nash – by the Danish poet and mathematician Piet Hein. He presented the game in 1942 under the name “Polygon” at the Niels Bohr Institute. In 1952, Parker Brothers published the game under the name “Hex”, which remains the most well-known name for the game to this day. Piet Hein marketed the game as “con-tac-tix”.
- According to Wikipedia, Hex is a finite game with perfect information. “If both sides play optimally, the winner is predetermined from the start.” However, on the practically used board sizes (from about 9 × 9), it has not yet been possible to fully analyse the winning strategy and play optimally, states the online encyclopaedia.