Gomoku
Encyclopedia
Gomoku is an abstract strategy board game
. Also called Gobang or Five in a Row, it is traditionally played with go
pieces (black and white stones) on a go board (19x19 intersections); however, because once placed, pieces are not moved or removed from the board, gomoku may also be played as a paper and pencil game
. This game is known in several countries under different names.
Black plays first, and players alternate in placing a stone of their color on an empty intersection. The winner is the first player to get an unbroken row of five stones horizontally, vertically, or diagonally.
, in which it is referred to as . Go means five, moku is a counter word for piece
s and narabe means line-up. The game is also popular in Korea, where it is called omok (오목(五目)) which has the same structure and origin as the Japanese name.
In the nineteenth century, the game was introduced to Britain where it was known as Go Bang, said to be a corruption of Japanese goban, said to be adapted from Chinese chee bahn (qí bàn) 'chess-board'.
The opening moves show clearly black's advantage. An open row of three (one that is not blocked by an opponent's stone at either end) has to be blocked immediately, or countered with a threat elsewhere on the board. If not blocked or countered, the open row of three will be extended to an open row of four, which threatens to win in two ways. White has to block open rows of three at moves 10, 14, 16 and 20, but black only has to do so at move 9.
Move 20 is a blunder for white (it should have been played next to black 19). Black can now force a win against any defence by white, starting with move 21.
There are two forcing sequences for black, depending on whether white 22 is played next to black 15 or black 21. The diagram on the right shows the first sequence. All the moves for white are forced. Such long forcing sequences are typical in gomoku, and expert players can read out forcing sequences of 20 to 40 moves rapidly and accurately.
The diagram on the right shows the second forcing sequence. This diagram shows why white 20 was a blunder; if it had been next to black 19 (at the position of move 32 in this diagram) then black 31 would not be a threat and so the forcing sequence would fail.
Generalized
gomoku is PSPACE-complete
.
Board game
A board game is a game which involves counters or pieces being moved on a pre-marked surface or "board", according to a set of rules. Games may be based on pure strategy, chance or a mixture of the two, and usually have a goal which a player aims to achieve...
. Also called Gobang or Five in a Row, it is traditionally played with go
Go (board game)
Go , is an ancient board game for two players that originated in China more than 2,000 years ago...
pieces (black and white stones) on a go board (19x19 intersections); however, because once placed, pieces are not moved or removed from the board, gomoku may also be played as a paper and pencil game
Paper and pencil game
Paper-and-pencil games are games that can be played solely with paper and pencil .In some board games, including some abstract strategy games like Gomoku, a piece once played will not be moved on the board or removed from the board...
. This game is known in several countries under different names.
Black plays first, and players alternate in placing a stone of their color on an empty intersection. The winner is the first player to get an unbroken row of five stones horizontally, vertically, or diagonally.
Origin
The name "Gomoku" is from the Japanese languageJapanese language
is a language spoken by over 130 million people in Japan and in Japanese emigrant communities. It is a member of the Japonic language family, which has a number of proposed relationships with other languages, none of which has gained wide acceptance among historical linguists .Japanese is an...
, in which it is referred to as . Go means five, moku is a counter word for piece
Piece
Piece or pieces may refer to:* A single unit of something* An informative or creative work, such as a work of art, journalism, academic research, etc.** Musical piece, a work of music, sometimes called an opus* Chess piece* Jigsaw puzzle piece...
s and narabe means line-up. The game is also popular in Korea, where it is called omok (오목(五目)) which has the same structure and origin as the Japanese name.
In the nineteenth century, the game was introduced to Britain where it was known as Go Bang, said to be a corruption of Japanese goban, said to be adapted from Chinese chee bahn (qí bàn) 'chess-board'.
Example game
This game on the 15×15 board is adapted from the paper "Go-Moku and Threat-Space Search".The opening moves show clearly black's advantage. An open row of three (one that is not blocked by an opponent's stone at either end) has to be blocked immediately, or countered with a threat elsewhere on the board. If not blocked or countered, the open row of three will be extended to an open row of four, which threatens to win in two ways. White has to block open rows of three at moves 10, 14, 16 and 20, but black only has to do so at move 9.
Move 20 is a blunder for white (it should have been played next to black 19). Black can now force a win against any defence by white, starting with move 21.
There are two forcing sequences for black, depending on whether white 22 is played next to black 15 or black 21. The diagram on the right shows the first sequence. All the moves for white are forced. Such long forcing sequences are typical in gomoku, and expert players can read out forcing sequences of 20 to 40 moves rapidly and accurately.
The diagram on the right shows the second forcing sequence. This diagram shows why white 20 was a blunder; if it had been next to black 19 (at the position of move 32 in this diagram) then black 31 would not be a threat and so the forcing sequence would fail.
Standard Gomoku
- Standard gomoku requires a row of exactly five stones for a win: rows of six or more, called overlines, do not count.
- The rule of three and three bans a move that simultaneously forms two open rows of three stones (rows not blocked by an opponent's stone at either end).
- The rule of four and four bans a move that simultaneously forms two rows of four stones (open or not).
Caro
- In Caro, popular among Vietnamese, the winner must have an unbroken row of five stones and this row must not be blocked at either end. This rule makes Gomoku more flexible and provides more power for White to defend.
Omok
- Omok is played the same as Standard Gomoku; however, it is played on a 15×15 board and does not include the rule of four and four. The overlines and three and three rules still apply.
Other Similar Games
- RenjuRenjuRenju is the professional variant of Gomoku, a board game originated from Japan in Heian Period. It was named Renju by Japanese journalist Ruikou Kuroiwa on December 6, 1899 in a Japanese newspaper Yorozu chouhou . It is played with black and white stones on a 15x15 intersection Go board...
is played on a 15×15 board, with the rules of three and three, four and four, and overlines applied to black only. There are special rules for the opening. - Ninuki-renju or Wu is a variant which adds capturing to the game; it was published in the USA in a slightly simplified form under the name PentePentePente is a strategy board game created in 1977 by Gary Gabrel, based on the Japanese game ninuki-renju, a variant of renju or gomoku which is played on a Go board of 19 x 19 intersections with white and black stones. In contrast to renju, ninuki-renju and Pente allow captures, but Pente added a...
. - m,n,k-games are a generalizationGeneralized gameIn computational complexity theory, a generalized game is a game that has been generalized so that it can be played on a board of any size. For example, generalized chess is the game of chess played on an n-by-n board, with 2n pieces on each side.Complexity theory studies the asymptotic difficulty...
of gomoku to a board with m×n intersections, and k in a row needed to win. - Connect(m,n,k,p,q) games are another generalizationGeneralized gameIn computational complexity theory, a generalized game is a game that has been generalized so that it can be played on a board of any size. For example, generalized chess is the game of chess played on an n-by-n board, with 2n pieces on each side.Complexity theory studies the asymptotic difficulty...
of gomoku to a board with m×n intersections, k in a row needed to win, p stones for each player to place, and q stones for the first player to place for the first move only.
Analysis
Computer search by L. Victor Allis has shown that on a 15×15 board, black wins with perfect play. This applies regardless of whether overlines are considered as wins, but it assumes that the rule of three and three is not used. It seems very likely that black wins on larger boards too. In any size of a board, freestyle gomoku is an m,n,k-game, and it is known that the second player does not win. With perfect play, either the first player wins or the result is a draw.Generalized
Generalized game
In computational complexity theory, a generalized game is a game that has been generalized so that it can be played on a board of any size. For example, generalized chess is the game of chess played on an n-by-n board, with 2n pieces on each side.Complexity theory studies the asymptotic difficulty...
gomoku is PSPACE-complete
PSPACE-complete
In complexity theory, a decision problem is PSPACE-complete if it is in the complexity class PSPACE, and every problem in PSPACE can be reduced to it in polynomial time...
.
See also
- Game theoryGame theoryGame theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
- Board gameBoard gameA board game is a game which involves counters or pieces being moved on a pre-marked surface or "board", according to a set of rules. Games may be based on pure strategy, chance or a mixture of the two, and usually have a goal which a player aims to achieve...
- IrenseiIrenseiIrensei is an abstract strategy board game. It is traditionally played with Go pieces on a Go board , but any equipment with which Go can be played is also suitable for Irensei....
- Solved board gamesSolved gameA solved game is a game whose outcome can be correctly predicted from any position when each side plays optimally. Games which have not been solved are said to be "unsolved"...
- Connect6Connect6Connect6 introduced in 2003 by Professor I-Chen Wu at Department of Computer Science and Information Engineering, National Chiao Tung University, is a two-player game similar to Gomoku....
, a revised version of Gomoku - PentePentePente is a strategy board game created in 1977 by Gary Gabrel, based on the Japanese game ninuki-renju, a variant of renju or gomoku which is played on a Go board of 19 x 19 intersections with white and black stones. In contrast to renju, ninuki-renju and Pente allow captures, but Pente added a...
- Connect FourConnect FourConnect Four is a two-player game in which the players first choose a color and then take turns dropping their colored discs from the top into a seven-column, six-row vertically-suspended grid...
- ReversiReversiReversi is a board game involving abstract strategy and played by two players on a board with 8 rows and 8 columns and a set of distinct pieces for each side. Pieces typically are disks with a light and a dark face, each face belonging to one player...