# Hex

Hex is a deceptively simple game first invented by Danish mathematician Piet Hein in 1942, who called it "CON-TAC-TIX." (or Polygon) It was later independently re-invented by famous mathematician John Nash? (subject of A Beautiful Mind) when he was a graduate student at Princeton in 1948. It was called Nash, or sometimes John (because it was sometimes played on bathroom tiles.) In 1952 Parker Brothers marketed it under the name of Hex, and the name stuck.

## Board sizes

Hex is played on a rhombus of hexagons, where both players pick two opposite sides each take turns putting stones down on the board to try to form a solid connected bridge to opposite sides. The size of the board varies, according to circumstances:

• 5x5 and 7x7 are often used for educational purposes.
• 10x10 is popular on some sites, particularly for blitz tournaments.
• 11x11 is the most popular size, and the one used by Piet Hein in his newspaper puzzles.
• 12x12 is an uncommon size, but Hein's boards were this size.
• 13x13 is the common tournament size.
• 14x14 is used at some sites, and was the one recommended by John Nash. (see a beautiful mind)
• 15x15 and 19x19 games are offered on some sites, but are not often played. They are time-consuming, and at this size the openings become very "airy", i.e. very hard to tell if a move is good or not.

Having the first move confers an important advantage. Hex players typically use the Swap Rule, sometimes called the Pie Rule, to make the game more even.

## The invention of Hex

(according to Thomas Maarup)

Piet Hein tried to set up strict conditions for recognizing games of real value. This amounts to a list of six conditions; a game must be:

1. Fair
2. Progressive
3. Finite
4. Clear
5. Strategic
6. Decisive

Piet Hein describes how the complete game of Hex ocurred to him one morning by the combination of the list above with the Four-Colour Theorem:

Suddenly in the half-light of dawn a game awoke, demanding to be born. Today it is ready for release into the world [...] The game builds on the simple geometrical property of a planar surface that two lines within a square each connecting a pair of opposite sides must intersect.

Hein describes how he was working with the Four-Colour Conjecture when having the idea for Hex. He considered four areas in a ring, realising that only one pair of opposite areas can connect to each other across the middle. [...] This idea leads him to a game in which the players must try to create the connection, a condition that only one of them will be able to achieve.

## Property

The only way to block your opponent from connecting his two sides is to do it yourself. Hex thus has the unusual property that winning the game is exactly the same as not losing it. Because of this, there is an unclear distinction between offense and defense in Hex.

## Hex compared to Go

• Go and Hex have similar branching factors at similar sized boards, but Hex games are usually shorter, especially at lower levels.
• Both games have territorial and connection aspects, but in opposite amounts.
• Both games have immobile pieces, which is thought to give humans an advantage over computers. However, since Hex pieces are never removed, Hex positions are easier to analyse logically. The strongest Hex programs exploits this, using an approach similar to theorem provers.
• In Hex, it is always better to have a stone of your colour on a point than nothing. This is not the case in Go, and makes Go harder to analyse.
• Because of the connection aspect of Go, the games have many similar tactical concepts such as ladders, ladder breakers (called ladder escapes in Hex), and joseki.
• Because pieces are never removed, Hex is a finite game without ko or superko rule.
• Hex does not have an official handicap system. A common informal handicap is to not use the swap rule, and let the weaker player go first.
• Hex, like Go, is considered a hard game for computers. Also like Go, the strongest programs use Monte-Carlo playouts rather than evaluation functions.
• Moves in Hex often have high non-local impact, as in Go, but maybe slightly more so due to the frequency of ladders.

## Computer Hex players

• http://six.retes.hu/ Six, a Hex playing program for Linux/Un*x systems running KDE. It is the strongest publicly available program.

Hex has been exhaustively solved by analysis for size 8 and below. There exist applets that can play perfectly on 7x7.

## Hex online playing (turn-based/realtime)

• Little Golem features turn-based (i.e correspondence) Hex games over the web. Most of the world's strongest players play here.
• http://havannah.vying.org originally Havannah server, Hex was added also (real-time playing with Java Applet) (as of october 2015, unfortunately a dead link)

Many other sites feature Hex, but as of today, the first two seem most popular.

## Wiki for the game Hex

Hex has it's own wiki at https://www.hexwiki.net (Hex Wiki).

Unfortunately, it has been offline since quite some time now (february 2014). The Hex Wiki (.net) is up and the same as the mirror below (october 2019)

Try this link as of 2016: http://hexwiki.amecy.com.

RBerenguel: There's a (read-only) mirror here( http://www.trmph.com/hexwiki/)