Connect6
A traditional board for the game (here showing a game of Go) is wooden, with the lines painted on. The stones are flattened spheroids and fit closely together when placed on adjacent points.
Players	2
Age range	any, but be aware that infants might swallow the spheroids
Setup time	No setup needed
Playing time	10 min-60 min,
Random chance	None
Skills required	Strategy, Observation

Connect6 (Chinese: 六子棋; Pinyin: liùzǐqí; Japanese: 六目並べ; Korean: 육목) introduced by Professor I-Chen Wu at Department of Computer Science and Information Engineering, National Chiao Tung University, is a fair and highly complex game. Photograph of Go board, taken by myself File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Go is a strategic board game for two players. ... An abstract strategy game is a board game with perfect information, no chance, and (usually) two players. ... It has been suggested that Pinyin method be merged into this article or section. ... I-Chen Wu is a Professor at Department of Computer Science, National Chiao Tung University. ... National Chiao Tung University (Traditional Chinese: ; Hanyu Pinyin: Gúolì Jiāotōng Dàxúe; Tongyong Pinyin: Gúolì Jiaotong Dàsyúe; abbreviated as NCTU) is a top-tier research university located in Hsinchu, Taiwan, ROC. It was established by former Chiao Tung University faculty members and alumni...

Two players, Black and White, alternately place two stones of their own colour, black and white respectively, on empty intersections of a Go-like board, except for that Black (the first player) places one stone only for the first move. The one who gets six or more stones in a row (horizontally, vertically or diagonally) first wins the game. Go is a strategic, two-player board game originating in ancient China between 2000 BC and 200 BC. Go is a popular game in East Asia. ...

Game Rules

The rules of Connect6 are very simple and similar to the traditional Gomoku game: Gomoku, go-moku, or gobang (Japanese: 五目並べ, Gomoku Narabe, five points) is an abstract strategy board game. ...

• Players and stones: There are two players. Black plays first, and White second. Each player plays with an appropriate color of stones, as in Go and Gomoku.

• Game board: Connect6 is played on a square board made up of orthogonal lines, with each intersection capable of holding one stone. In theory, the game board can be any finite size from 1×1 up (integers only), or it could be of infinite size. However, boards that are too small may lack strategy (boards smaller than 6×6 are automatic draws), and extremely large or infinite boards are of little practical use. 19×19 Go boards might be the most convenient. For a longer and more challenging game, another suggested size is 59×59, or nine Go boards tiled in a larger square (using the join lines between the boards as additional grid lines).

• Game moves: Black plays first, putting one black stone on one intersection. Subsequently, White and Black take turns, placing two stones on two different unoccupied spaces each turn.

• Winner: The player who is the first to get six or more stones in a row (horizontally, vertically, or diagonally) wins. (This is a departure from Gomoku, where it must be exactly five in a row.)

According to Professor Wu, the handicap of black's only being able to play one stone on the first turn means that the game is comparatively fair; unlike similar games such as Gomoku and Connect Four, which have been proven to give the first player a large advantage, possibly no additional compensation is necessary to make the game fair. Gomoku, go-moku, or gobang (Japanese: 五目並べ, Gomoku Narabe, five points) is an abstract strategy board game. ... Gomoku, go-moku, or gobang (Japanese: 五目並べ, Gomoku Narabe, five points) is an abstract strategy board game. ... Connect Four (also known as Plot Four) is a two-player board game in which the objective is to be the first to get four of ones own discs in a line. ...

Fairness

In principle, even some complex games are not fair: either the first or second player has an advantage. (Games such as Gomoku have been mathematically proven to give an advantage to one player or another; complex games such as chess are generally too complicated to analyze fully.) Herik, Uiterwijk, and Rijswijck give an informal definition of fairness (Herik, Uiterwijk, and Rijswijck, 2002) as follows: A game is considered a fair game if it is a draw and both players have roughly equal opportunities for making mistakes. From this, it is argued that Connect6 is fair in the following senses: Chess is a recreational and competitive sport for two players. ...

• Each player always has one more stone than the other after making each move.

• For about one thousand opening templates, Professor Wu let the AI program written by his team play against itself, and the result seemed to show that the game does not favor either one for these templates. Note that the AI program can beat most casual players, but this does not necessarily imply that its strategy is strictly optimal.

• The initial breakaway (where White plays far away from the initial black stone) does not apparently favor White, according to Professor Wu. If the initial breakaway did not get penalty, the game would favor White for the following reason: Black must go back to defend the two white stones and then the situation is good for White since the game becomes to let White place two stones initially.

However, this evidence is not conclusive. Hondas humanoid robot AI redirects here. ...

Complexity

If Connect6 uses an infinite board, both state-space and game-tree complexities are infinite as well. Instead, assume that a Go board is used. The game-tree complexities for it are still much higher than those in Gomoku and Renju, since many more moves are possible placing two stones than one—specifically n(n−1)/2 moves are possible, where n is the number of unoccupied spaces before a move. However, the state-space complexity is largely unchanged, since any legal position in one game will also be legal in the other. Based on the standard in Herik, Huntjens, and Rijswijck, the state space complexity of Connect(19,19,6,2,1) is 10¹⁷², the same as that in Go or Gomoku. If a larger board is used, the complexity is much higher, since the number of moves increases exponentially with board size; it should still be the same as the other two games on the same size board. In game theory, game complexity is a measure of the complexity of a game. ... In game theory, game complexity is a measure of the complexity of a game. ... Renju (Japanese: 連珠) is the professional variant of Gomoku, a Japanese board game. ... In computer science, a state space is a description of a configuration of states used as a simple model of machines. ...

Now, let us investigate the game tree complexity. Assume that the averaged game length is still 30, the same as the estimation for Gomoku (Allis 1994). Then, the number of grids chosen to put one stone is about 300, and the number of choices of one move is about or 45,000. Thus, the game-tree complexity is about ≈ 10¹⁴⁰, much higher than that for Gomoku. Again, if a larger board is used, this complexity becomes much higher. In game theory, a game tree is a directed graph whose nodes are positions in a game and whose edges are moves. ...

History

One day in the summer of 2003, Professor I-Chen Wu came up with this game when playing with his daughter. He started considering the potential of the game to be popular, and began to investigate it. To be popular, he reasoned, his game must be fair and complex, so his first plan was to have a computer program play the game to see how fair and complex it is. 2003 (MMIII) was a common year starting on Wednesday of the Gregorian calendar. ...

In spring 2004, a master student of Professor Wu, Dei-Yen Huang, joined Wu's project as his master thesis. In the first quarter of 2005, they completed the first Connect6 AI program, which already can beat most players. Then Wu's team allowed his AI program to play itself. 2004 (MMIV) was a leap year starting on Thursday of the Gregorian calendar. ... A masters degree is an academic degree usually awarded for completion of a postgraduate (or graduate) course of one to three years in duration. ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ...

In 2005, Wu's team wrote a paper, presented in the 11th Advances in Computer Games Conference (ACG11), held in Taipei, Taiwan, 2005. Nickname: the City of Azaleas (杜鵑花之城) Coordinates: Country Republic of China Region Northern Taiwan Capital Xinyi Dist (信義區) Mayor Hau Lung-bin Area    - City 271. ...

In September 2005, ThinkNewIdea Limited built the first Connect6 game server. 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ...

On September 20–September 21, 2005, the game was covered by many news media in Taiwan. September 20 is the 263rd day of the year (264th in leap years). ... September 21 is the 264th day of the year (265th in leap years). ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ...

In 2005, interested people started discussing the organization of a Connect6 website at http://www.connect6.org and supporting a forum for discussion.

In March 2006, the game was added to http://www.littlegolem.net.

The program NCTU6, rewritten by Professor Wu, won gold in the Connect6 tournament at the 11th Computer Olympiad. The 11th Computer Olympiad was held in Turin, Italy between May 25 and June 4, 2006 in conjunction with the 14th World Computer Chess Championship and the 5th Computer and Games conference (CG 2006). ...

The First Annual NCTU Cup Connect6 Open Tournament was sponsored by National Chiao Tung University (NCTU) and held in Hsinchu, Taiwan, on July 16th, 2006.

See also

• Game complexity
• Renju
• Go (board game)
• Chess
• Games played with Go equipment

In combinatorial game theory, game complexity is a measure of the complexity of a game. ... Renju (Japanese: 連珠) is the professional variant of Gomoku, a Japanese board game. ... Go is a strategic board game for two players. ... Chess is a recreational and competitive sport for two players. ... Many games can be played with go equipment: a supply of white and black stones and a board with 19×19 intersections, and many more can be played with minor modification. ...

External links

• The organization for Connect6

Internet servers

• pente.org Play Connect6 and other similar games at Dweebo's Stone Games (pente.org).
• BrainKing Play Connect6 and many other games on BrainKing.
• Little Golem Play Connect6 and many other games at Little Golem.
• Ludoteka Play Connect6 and many other games at Ludoteka.