Gomoku Family

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Introduction, Game Names and Rules

Here we survey a collection of associated games variously known as the Connect-Five, Go-Moku or Renju family.

Connect Five

The object of this two-player game is to create a line of 5 stones of the player�s colour on a square grid. Black starts first and stones are laid down alternately, and permanently, on the grid. The game is a draw if the board is filled and no horizontal, vertical or diagonal line of 5 stones has been created.

Connect Five is known as Ameba (Hungary, Poland), Caro (Vietnam), Cross-Circles on a Non-Margin Board (Russia), Freestyle Go-Moku (van den Herik, Uiterwijk and van Rijswijck, 2002), Gobang (Germany), Go-moku (Japan), Lufarchak (Sweden), Morpion (France), Omok (Korea), Piskvorky (Chehia, Slovakia), WuZiQi (China), and Go-Moku or Five In A Row elsewhere.

The game is a 'big brother' version of Tic-Tac-Toe or Noughts and Crosses which requires only a 3x3 grid and aims to create a line of 3 stones. Pencil and squared paper may conveniently be used instead of stones on a board, making the game very accessible worldwide.

Both Tic-Tac-Toe and Connect Five are examples of m-n-k games where the objective is to create a line of k stones on an m x n board. Tic-Tac-Toe is 3-3-3, whereas Connect Five is 19-19-5 on a Go board (as played in countries that know Go), 15-15-5 or 13-13-5 on smaller boards, and �-�-5 on an unrestricted board.

Since 1936, the Japanese have believed that Connect Five was a first-player win, and had produced an extended, though partial, proof to their satisfaction. The information in that proof was used as opening book theory in the earliest computer-codes for this game.

Victor Allis proved by a complete computer-search that it was a first-player win and thereby weakly-solved the game.

Because of the first-player bias, a variety of games have been derived from the basic Connect Five to make the game fairer for the 2nd player. These use various rules which constrain either Black, White, or both players.

This introduction to the Renju family mentions some of these games.

Go-moku

This is Connect Five on a 19x19, 15x15 or 13x13 board with this rule:

  • Rbw1: an Overline is not a win for either side.

It is popular all over the world and the Computer Olympiads of 1989-1992 had 15x15 tournaments for computers. It is also called Standard Go-moku (van den Herik, Uiterwijk and van Rijswijck, 2002).

The game was regarded as a 1st-player win by Japanese players, and was also weakly solved for a 15x15 (or larger) board as a 1st-player by Victor Allis. Go Moku on a 13x13 board is also a 1st-player win but requires a solution other than for the 15x15 board.

Japanese Go-moku (Go-moku-narabe)

This is played on a 19x19 board with these rules:

  • Rbw1: an Overline is not a win for either side
  • Rb1: the 1st player (Black) puts the first stone on the center of the board (j10, assuming an a-s, 1-19 board)
  • Rw1: the 2nd-player (White) must play move 2 in the central 3x3 square (i9-k11)
  • Rb2: Black is not allowed to create a 3x3 fork

Korean O-muk

This is played on a 19x19 board with these rules:

  • Rbw1: an Overline is not a win for either side
  • Rb1: the 1st player (Black) puts the first stone on the center of the board (j10, assuming an a-s, 1-19 board)
  • Rw2: the 2nd-player (White) must play move 2 in the central 5x5 square (h8-l12)
  • Rb3: Black is not allowed to create a 3x3 or 4x4 fork

Pro-Go-Moku (Five in a Row with the prohibited central square)

This is played on a 15x15 board with these rules:

  • Rbw1: an Overline is not a win for either side
  • Rb4: move 3 (i.e. Black's 2nd) must be outside the central 5x5 square (i.e. outside f6-j10)

The game is sometimes known as Free Renju in Russia and the Ukraine. The first player has a big advantage with 90-95% wins at a high level of play.

Renju

This is played on a 15x15 board with these rules:

  • Rb5: Black is not allowed to create an overline, a 3x3 fork or a 4x4 fork: such moves win for White.

Rules about opening play vary according to the standard of the players:

  1. Beginners: any opening is allowed
  2. Intermediate Players: White Option Opening Rule. White places:
    1. 1st Black stone on central square h8, 1st White stone in the central 3x3 square g7-i9,
    2. 2nd Black stone in one of 12 places in the central 5x5 square f6-j10.
  3. Masters:
    1. Black places the 1st Black stone on h8, and the 1st White stone in the central 3x3 square g7-i9.
    2. Black places the 2nd Black stone in the central 5x4 square f6-j10.
    3. White may then choose to swap colours and play Black if it wishes.
    4. The side now White plays a 4th move.
    5. The side now Black gives two options for the 5th move, and White picks one of these.

These are the Renju International Federation Rules as used for the human World Renju Championships.

Computer Renju World Championships were held in 1991, 1998 and 2000: there are over-the-board tournaments and problem-solving competitions. The strongest Tournament program strength is above 3-4 Dan (Candidate of Master).

Important links

Pente

This game is played on a 19x19 board with these rules:

  • Rb4: the 3rd move (Black's 2nd) is made outside the central 5x5 square
  • Rbw2: if a player can close 2 opponent's stones on both ends, this 'pair' is removed as a 'capture'
  • Rbw3: five 'captures' is one way of winning

This is popular in the USA, and is a simplified variant of Japanese Ninuki-renju. The first player's advantage is probably too high at 70-80%. There have been Pente tournaments in USA, Sweden and Russia, and a match between two Pente programs was won by Mark Mammel's Program. The programs cannot beat the strongest players yet.

Important links

Keryo-Pentei

This game is played on a 19x19 board with these rules:

  • Rb4: the 3rd move (Black's 2nd) is made outside the central 5x5 square
  • Rbw4: if a player can close 3 opponent's stones on both ends, this 'three' is removed as a 'capture'
  • Rbw3: five 'captures' is one way of winning

This game is popular in the USA and Japan, but not as popular as Pente.

Ninuki-Renju

This game is played on a 19x19 board with these rules:

  • Rbw1: an Overline is not a win for either side
  • Rb2: Black is not allowed to create a 3x3 fork
  • Rbw2: if a player can close 2 opponent's stones on both ends, this 'pair' is removed as a 'capture'
  • Rbw3: five 'captures' is one way of winning
  • Rbw5: only perfect five win the game. (Perfect five such five which can not be captured by next move)

It was played before the 2nd World War but is not popular in Japan now.

Boku

This game can be played on a hexagonal board invented by Rob Nelson. It has these rules:

  • Rbw6: if a player can close two opponent-stones on both ends, they can choose which to remove
  • Rbw7: the next move cannot be done at the place where a stone is removed (the Go rule of Ko)

Of course, it is possible to play this game on a 19x19 or other-sized board.

Link: http://www.londongame.com/boku.html

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