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Hex is a connection game , and can be classified as a Maker-Breaker game , a particular type of positional game. The game can never end in a draw tie , in other words, Hex is also a " determined game ".

Hex is a finite, perfect information game, and an abstract strategy game that belongs to the general category of connection games.

When played on a generalized graph, it is equivalent to the Shannon switching game. As a product, Hex is a board game ; it may also be played with paper and pencil.

Although Hein called it Con-tac-tix, [1] it became known in Denmark under the name Polygon due to an article by Hein in the 26 December edition of the Danish newspaper Politiken , the first published description of the game, in which he used that name.

The game was independently re-invented in by the mathematician John Nash at Princeton University. They called their version "Hex" and the name stuck.

About , American mathematician and electrical engineer Claude Shannon and E. Moore constructed an analog Hex playing machine, which was essentially a resistance network with resistors for edges and lightbulbs for vertices.

The machine played a reasonably good game of Hex. Later, researchers attempting to solve the game and develop hex-playing computer algorithms emulated Shannon's network to make strong automatons.

In John Nash expounded an existence proof that on symmetrical boards, the first player has a winning strategy. In , mathematician Alfred Lehman showed that Hex cannot be represented as a binary matroid , so a determinate winning strategy like that for the Shannon switching game on a regular rectangular grid was unavailable.

Until , humans remained better than computers at least on big boards such as 19x19, but on Oct 30, the program Mootwo won against the human player with the best ELO rank on LittleGolem, also winner of various tournaments the game is available here.

This program was based on Polygames [6] an open-source project, initially developed by Facebook Artificial Intelligence Research and several universities [7] using a mix of: [8].

In the early s Dolphin Microware published Hexmaster , an implementation for Atari 8-bit computers. The first implementations used evaluation functions that emulated Shannon and Moore's electrical circuit model embedded in an alpha-beta search framework with hand-crafted knowledge-based patterns.

Starting about , Monte Carlo tree search methods borrowed from successful computer implementations of Go were introduced and soon dominated the field.

Later, hand crafted patterns were supplemented by machine learning methods for pattern discovery.

These programs are now competitive against skilled human players. Elo based ratings have been assigned to the various programs and can be used to measure technical progress as well as assess playing strength against Elo-rated humans.

Each player has an allocated color, conventionally Red and Blue or White and Black. Once placed, stones are not moved, captured or removed from the board.

The goal for each player is to form a connected path of their own stones linking the opposing sides of the board marked by their colors, before their opponent connects his or her sides in a similar fashion.

The first player to complete his or her connection wins the game. The four corner hexagons each belong to both adjacent sides.

This is somewhat analogous to chess games ending long before checkmate - the game usually ends with one player or the other resigning.

Since the first player to move in Hex has a distinct advantage, the pie rule is generally implemented for fairness. This rule allows the second player to choose whether to switch positions with the first player after the first player makes the first move.

From the proof of a winning strategy for the first player, it is known that the hex board must have a complex type of connectivity which has never been solved.

Play consists of creating small patterns which have a simpler type of connectivity called "safely connected", and joining them into sequences that form a "path".

Eventually, one of the players will succeed in forming a safely connected path of stones and spaces between his sides of the board and win.

The final stage of the game, if necessary, consists of filling in the empty spaces in the path. A "safely connected" pattern is composed of stones of the player's color and open spaces which can be joined into a chain, an unbroken sequence of edge-wise adjacent stones, no matter how the opponent plays.

There are also safely connected patterns which connect stones to edges. Patterns and paths can be disrupted by the opponent before they are complete, so the configuration of the board during an actual game often looks like a patchwork rather than something planned or designed.

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