É uma prancha Go. No entanto, o jogo jogado é 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.
Quora :
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 - Uma Mente Brilhante - "O Desafio" - Um Jogo de Aventuras: Youtube