In the movie A Beautiful Mind, around the 9th minute, what is the name of the game they play?
Why is Nash so surprised at losing this game?
2 Answers
It is a Go board. However, the game played is Hex
Hex is a strategy board game for two players played on a hexagonal grid, theoretically of any size and several possible shapes, but traditionally as an 11×11 rhombus. Players alternate placing markers or stones (Go stones make ideal playing pieces) on unoccupied spaces in an attempt to link their opposite sides of the board in an unbroken chain. One player must win; there are no draws. The game has deep strategy, sharp tactics and a profound mathematical underpinning related to the Brouwer fixed point theorem. It was invented in the 1940s independently by two mathematicians. The game was first marketed as a board game in Denmark under the name Con-tac-tix, and Parker Brothers marketed a version of it in 1952 called Hex; they are no longer in production. Hex can also be played with paper and pencil on hexagonally ruled graph paper.
Recall that in the movie, Mr. Nash looked amazed at losing. "But...I had the first move. And I played perfectly!" This is because the game Hex is "solved." With perfect play on a symmetric board, the first player will ALWAYS win. Nash himself proved this in 1952, so this scene was another reference to Nash's mathematical work.
However, proving the existence of a solution does not necessarily mean you can execute it perfectly every time (the proof in this case was not even a constructive one, Nash doesn't have an algorithm for winning, just proof that such a solution exist!).
Go boards are frequently used for Hex games, and many people have confused the two while watching the movie. Go is also both more popular and more complicated game than Hex, lending to the confusion.
Nash is also credited with inventing a game, eventually marketed by Parker Brothers as a board game called Hex. This game, played on a parallelogram-shaped field of hexagonal cells, was discovered independently in Denmark around the same time. In Princeton it was called Nash, after its creator, or John, a double entendre involving the fact that it was played on the tiles in the mathematics department’s men’s room floor. There are two players, each of whom has tokens of a single color (red and blue, say). The object is to form an unbroken path from one side of the board to the other before one’s opponent does the same in the opposite direction.
There are online versions of the game. The first player always has a winning strategy; that is, the player who makes the first move can always win, provided he executes the proper sequence of moves.
Clip - A Beautiful Mind - "The Challenge" - A Game of Go:Youtube
-
16Sorry, according to the description you provide Hex is played "on a hexagonal grid". Go board is not "a hexagonal grid", not even close. What gives? Mar 16, 2017 at 9:37
-
5Are you sure it wasn't Go? The clip you link to starts with someone saying "I've played enough Go for one day". Perhaps Nash's annoyance is shown in the movie as a precursor to his creating Hex, precisely because he considered Go "flawed" since he lost despite "playing perfectly".– terdonMar 16, 2017 at 10:00
-
11The picture you give of the game in progress looks like a typical Go position. It looks nothing like a Hex position. There seems to be no evidence for your claim other than a statement on Quora (itself unevidenced). It is also true that Hex is a first player win, but the strategy is unknown for a board that big so Nash cannot have known he played perfectly (though the same would be true of Go). Mar 16, 2017 at 11:47
-
24This answer is wrong. You can tell whether Go or Hex is being played by looking at the position of the stones; the final positions in the two games look nothing alike. The game in that first picture is unequivocally Go. They even said so in the movie... Mar 16, 2017 at 14:21
-
6I have to agree with the other comments. While them playing Hex would be a beautiful bit of historical reference, it just doesn't hold up to studying how they are playing when watching the scene in question. No matter how I look at it, it does seem like they really are playing Go.– Abion47Mar 16, 2017 at 14:50
Actually, according to the script, that's Go, not Hex:
All right, who's next?
No, I've played enough "Go" for one day, thank you.
Come on. I- I hate this game. Cowards, all of you! None of you rise to meet my challenge? Come on, Bender. Whoever wins,Sol does his laundry all semester.
You can hear the conversation and that they clearly mention Go in the clip linked to in Mary's answer.
Since they claim it's Go, right there in the movie, I don't see how it could be anything else.
-
2The move makes sense (white captures a large black group) - what doesn't make sense is that Nash and the bystanders wouldn't have seen it coming until it actually happened. Mar 16, 2017 at 14:31
-
@BlueRaja-DannyPflughoeft ah, as I said, I don't know Go :) Thanks for the correction.– terdonMar 16, 2017 at 15:26
-
@BlueRaja-DannyPflughoeft It's possible that a combination of them playing quickly and simultaneously talking about something (mostly) unrelated was a sufficient distraction.– Abion47Mar 16, 2017 at 16:28
Go: It's said that it's one of the more complicated game (much more than chess), and that Artificial Intelligences wouldn't be able to beat best players until some years (happened in fact last year with Alphago of Google Deepmind). That game, which is complicated reflects a lot the intelligence behind the man in the movie.