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.
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The name "Gomoku" is from the Japanese language, in which it is referred to as gomokunarabe (五目並べ). Go means five, moku is a counter word for pieces 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. It is said to have originated in China.[1]
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 k'i pan (qí bàn) 'chess-board'.[1]
This game on the 15×15 board is adapted from the paper "Go-Moku and Threat-Space Search".[2]
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.
Free-style gomoku is the basic game as described above.
Computer search by L. Victor Allis has shown that on a 15×15 board, black wins with perfect play.[3] 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 gomoku is PSPACE-complete.[4]