The Connect6 game, first introduced by Dr. I-Chen Wu, is a fair and highly complex game with simple rules. The game is a kind of 6-in-a-row game. However, each player can place two stones for each move, except for the first player's first move. The game is intuitively fair in the sense that one player always has one more stone than the other after making each move. Here are the frequently asked questions (FAQs) of Connect6.
If you have more questions, please send to us at firstname.lastname@example.org。
Thank you very much.
Connect6 Working Group
Currently supported by
Internet Application Technology Laboratory
Department of Computer Science and Information Engineering
National Chiao Tung University
Q1: What are the rules of Connect6?
Answer: Each player can place two stones for each move, except for the first player's first move. The one who first connects up to six consecutive stones horizontally, vertically, and diagonally wins. As for board size, see Q3. When the board is filled up, the game draws.
Q2: Does Connect6 has prohibited moves like Renju?
Answer: No. Since the fairness is not a problem for Connect6, no prohibited moves are required.
Q3: What is the board size of Connect6?
Answer: In theory, since the game seems fair, the board size can be infinite. However, practically, it is hard to support such a game board. Therefore, our proposal is to play on 19x19 Go boards. Currently, most players use this board size. Using a larger board size is to be discussed in Q3-1.
Q3-1: Will the rule of Connect6 be changed or extended later?
Answer: Yes, it is possible to extend some rules. Most current Connect6 professionals play on 19x19 Go boards. However, many of them believe that Connect6 is a draw game. After studying in one or two years, we may need to extend the rules. Two proposals are given.
You are welcome to discuss this issue in the forum. It is expected that the rule extension will be changed no more.
Q4: Are there any Connect6 Tsumegos or Josekis like Renju or Go?
Answer: Currently, the forum in http://connect6.csie.nctu.edu.tw/contest-result.html and http://groups.msn.com/connect6 has some Tsumegos and Josekis. Since the game Connect6 is still young, you are welcome to study and develop new ones.
Q5: Are there any Live-3 and Dead4 terms in Connect6?
Answer: Yes, they are mentioned in Professor Wu's paper.
Q6: Where to find articles about Connect6?
Answer: http://www.connect6.org/k-in-a-row.pdf and http://www.connect6.org/connect6.pdf.
Q7: Where is the homepage of Connect6
Answer: The homepage of Connect6 is at http://www.connect6.org/ or http://connect6.csie.nctu.edu.tw/ 。
Q8: Where are Connect6 forums to discuss?
Answer: The current Connect6 forums are listed as follows:
Q9: How was Connect6 named?
Answer: Originally, the team of Professor Wu named it Ren6, like a variation of Renju with six. Although this hints a professional game, this also hints that the game also has some prohibition rules. Therefore, the name is changed to Connect6.
Q10: Where can we play Connect6?
Answer: An online game site is at http://www.cycgame.com/ in Chinese. Some offline game sites are at www.littlegolem.net (English), pente.org (English), www.ludoteka.com (Spanish), BrainKing.com (multi-lingual).
Q11: Are there some computer programs to play Connect6?
Answer: There are already three computer programs, NCTU6, X6 and AVG, attending the Connect6 tournament of the 11th Computer Olympiad. There are more soon.
Q12: Are there any Connect6 organizations?
Answer: Currently, it is being organized at http://www.connect6.org/ 。
Q13: Are there any Connect6 open tournament for human players?
Answer: Yes, the first Annual NCTU-Cup Connect6 open tournament (The first Connect6 open tournament for human players in the world) was held in Taiwan on July 16, 2006. See the Chinese page or the English page for the results.
Q14: How can a game be considered a fair game?
Answer: Herik, Uiterwijk, and Rijswijck gave a good 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 a roughly equal probability on making a mistake.
Q15: Then, can we prove that a game is fair?
Answer: Practically, it is hard to have a perfect model for calculating the probability of making a mistake as mentioned in Q14, since some undiscovered strategies such as making breakaway moves, as described in Subsection 2.3, may result in different probabilities. On the contrary, it is relatively easy and possible to show when a game is unfair. Therefore, Professor Wu provides the following three distinct definitions for unfair games.
Then, Professor Wu defined that a game is considered potentially fair, if it has not yet been shown or claimed to be definitely unfair, monotonically unfair, or empirically unfair. This definition indicates that a potentially fair game for the time being may not remain potentially fair in the future. However, if a game remains potentially fair any longer, it could have a higher chance to be fair.
Q16: Is the game Connect6 fair?
Answer: Connect6 games are intuitively fair, in the sense that one player always has one more stone than the other after making each move. Besides, Connect6 is, at least, potentially fair for the time being. Surely, we expect to see more evidences, either fair or unfair, or more experiences in the future.
Q17: Is the game Go-Moku or Renju fair? Is it still deserved to play?
Answer: We need to investigate different variation of Go-Moku.
Go-Moku in the free style (without any restriction on Black) is known to favor Black over White when played in the free style. After each move made by Black, Black has one more stone than White, while White only has the same number of stones as Black after his move.
In order to reduce this unfairness, the Japanese Professional Renju Association (1903) imposed some new rules to restrict the play of Black for professionals. For example, Black is forbidden from playing double three and double four. Experiences of professionals indicate that the game with these restrictions, known as Renju, still favors Black. Theoretically, Black has been proved to win in the free style by Allis (1994) and Allis, Van den Herik and Huntjens (1996), and under Renju restrictions by Wágner and Virág (2001).
The Renju International Federation (RIF) (1998) attempted to increase the fairness of the game by imposing new rules for the first five moves. The RIF (2003) called again for new opening rules and listed the requirements for new rules, indicating that the current rules still need to be improved for this game.
The game under RIF rules is potentially fair. However, adding more rules also increases the difficulty of learning the game. Besides, the fairness problem for Go-Moku or Renju has an important side effect of reducing the board size. Sakata and Ikawa (1981) mentioned that increasing the board size raised Black advantage. Hence, the standard board size was set to 15 × 15. Indeed, a smaller board lowers the complexity of the game and thus makes it easier to solve the game.
For the second question, actually, it is harder to define "deserve to play". It really depends on players. One might think it is more fun to play a game which can always break tie. For Renju, many enjoy playing the strategy of four-three.
Q17-1: Who first proved that Black wins in the free style and under the prohibition rules?
Answer: As far as we know, many Japan professional Renju professionals claimed to prove them. In academic society, it is said that Black has been proved to win in the free style by Allis (1994) and Allis, Van den Herik and Huntjens (1996), and under Renju restrictions by Wágner and Virág (2001).
This often caused misunderstanding between Renju players and academic people. The key difference is as follows. Academic people need to prove it clearly for all variations, while Renju professionals (similarly for Go professionals) normally would not elaborate the details. We quote a paragraph (the second paragraph in Section 5.1) from the Thesis by Allis (1994).
In Japan professional renju players (renju being a complicated variant of go-moku) have studied go-moku in detail and have stated that the player to move first (black) has an assured win (Sakata and Ikawa, 1981). These statements are sometimes accompanied by a list of main variations, such as the 32-page analysis in Sakata and Ikawa (1981). Close examination of these analyses reveals that in each position only a small number of white moves are analyzed. For example, after black's first move at the center of a 15x15 board, white has 35 distinct moves, of which 2 are adjacent to black's first move, ignoring symmetrically equivalent moves. In Sakata and Ikawa (1981) only the variations after 2 moves adjacent to black's first move are discussed. As far as we know, prior to this work no complete proof of black's win in go-moku has been published.
Allis, L. V. (1994). Searching for solutions in games and artificial intelligence, Ph.D. Thesis, University of Limburg, Maastricht.
L.V. Allis, H.J. van den Herik, M.P.H. Huntjens, Go-Moku solved by new search techniques, Comput. Intelligence: An Internat. J. 12 (1) (1995) 7–24.
Sakata, G. and Ikawa, W. (1981). Five-In-A-Row. Renju. The Ishi Press, Inc., Tokyo, Japan.
Wágner, J., Virág, I. (2001) Solving Renju, ICGA Journal, Vol. 24 (1) 30–34.
Q18: What is called breakaway?
Answer: A breakaway move means to place stones far away from the major battle field, where most stones have been placed. White's first move (after Black's first move) is called an initial breakaway move, if it is also a breakaway move.
Most importantly, Wu and Huang (2005) proved that White loses if making an initial breakaway move. Due to this result, Connect6 cannot be shown to be monotonically unfair by breakaway moves.
Q19: According to the articles, the game complexity is close to Go's. Is it possible?
Answer: The estimation simply follows the definitions of game-tree complexity and state-space complexity defined by Herik, Huntjens, and Rijswijck, (2002).
Q20: Who first invented Connect6?
Answer: Not available and not important. Since the game rule is too simple, it is quite possible for someone to play such games sometimes. A few players in Taiwan, China, Eastern Europe, and Japan also claimed to play this game before. However, so far, these claims are via vocal or BBS, not officially. The first official paper introducing this game should be Wu and Huang (2005). Anyway, you are welcome to send us more information about this.
Q21: Did Professor Wu et al. patent this game?
Answer: No. They never did this. On the contrary, they hope to promote this game, so they never thought to patent, even if it can be patented.
Q22: Is Connect6 in the tournament of Computer Olympiad?
Answer: Yes, it is. The 11th Computer Olympiad started to include Connect6 as a contest game. The result of this year is here.