# Hex (board game)

Hex is a strategy board game that was invented by Piet Hein, a Danish poet and mathematician.

## History

Hein introduced the game in 1942 under the name " polygon " in front at the Niels Bohr Institute. On December 26, 1942, the Danish newspaper Politiken published the game, and it was thus popular in Denmark.

John F. Nash in 1947 at Princeton University invented independently by Piet Hein same game based on game-theoretic considerations. Even today, it is played in Princeton, while often referred to as " John " or " Nash ".

1952 Parker Brothers published the game under the name " Hex", the most famous name of the game today. Piet Hein drove the game as a "con -tac- tix ".

## Description

It is played on a diamond-shaped board with eg 11 times 11 hexagonal segments. In Nash 's biography "A Beautiful Mind " is presented that John Nash 14 x 14 holds for the best size. Two opposing side lines are red, the other two blue. The corner squares are one of two colors. A player wins if he joins the sides of its color with its tiles. Hex is closely related to other connection games like TwixT or Y.

## Game rules

- You play on a diamond-shaped board made of n by n hexagonal fields ( picture). Piet Hein recommended for a 11x11 board, John Nash 14x14 it. Other common sizes are 13x13, 17x17 and 19x19. A field is adjacent to the six surrounding fields (a field at the edge of the board has four and a corner square two or three neighbors).
- The parties ( red and blue) take turns placing a stone of their color on each one still unoccupied space, Red begins.
- In each case two opposite sides of the board are marked with the same color. Each player needs to connect the sides of his color with a chain of its stones to win. A chain consists of the same colored stones, all of which are directly or indirectly adjacent to each other.
- To compensate for the advantage of the first move, one usually uses an exchange rule, according to the blue after the first red train can swap the colors. That is, blue takes over the opening gambit of red and plays with the red stones on. Red on the other hand gets the blue stones and have to play against his opening gambit. Red should thus set his first stone as possible so that neither red nor blue have a distinct advantage because blue can always opt for the side that has the advantage.

## Properties

- A cycle ( repetition of position ) can not occur because the number of stones on the board grows with every train.
- A draw is excluded, because the only way to block the opponent, it is to build a winning chain itself. When all fields are filled, there is always exactly one player has a winning chain.
- It is a finite game with perfect information. If both sides play optimally, the winner from the outset is fixed. On the board sizes used in practice (from about 9 × 9) but it is not yet able to fully analyze the winning strategy and optimal play.
- Without exchange normally red has a winning strategy, as can be shown by a proof by contradiction: If Blue has a winning strategy, then you could Rot him this "steal" by first making any train and then follows the winning strategy. Red would thereby an additional stone on the originally occupied space, which can be a disadvantage for red. That blue can not rely on this field, is only an advantage for red. If the strategy it specifies that red puts on this field, then makes red instead any other train, which additionally occupied box is moved, so to speak.
- With ex usually blue theoretically has a winning strategy, because it can always select the page for which there is a winning position.
- Without the exchange usually has red and in practice the interaction between human players a great advantage. When using the exchange rule, however, the odds of winning on a not too small board are almost the same.
- If the board is not the same in both directions ( m × n fields with m ≠ n ), then the player who has to join the sides close set, a winning strategy known.

## Online play

- Little Golem is a server that offers next Hex also some other games. The playing time is here more planned for several days ( English).
- Board Space offers the possibility hex games (and some other games) to play at a time. Here it is uncommon during a party to leave (English).