Caro / Gomoku

The origin of Caro / Gomoku seems to be from China. The name "Caro" is from Vietnam. The name "Gomoku" is from the Japanese language and is better known to the world: Go means "five", Moku means "stone".

Gomoku in different countries

This game is well-known in many countries and every country calls it differently. See country-specific names by language.

Variations and opening rules

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Black was long known to have a big advantage, even before L. Victor Allis proved that black could force a win (see below). So a number of variations are played with extra rules that aimed to reduce black's advantage.

• Free-style gomoku is the basic game as described above.
• 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).
• Gomoku+(also called 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.
• The rule of four and four bans a move that simultaneously forms two rows of four stones (open or not).
• The Little Golem game server has a "forbidden zone" where black cannot play his second move.

These restrictions are often applied only to black.

• Renju 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 Pente.
• m,n,k-games are a generalization 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 generalization 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. Among these games, Connect(m,n,6,2,1) is the most interesting one, and is called Connect6.

The only fair opening rule currently is swap2 based on swap from Renju and first seen on kurnik.org. The first player places 3 stones (2 black 1 white, if black goes first) on the board, the second player has the choice to take black/white or place 2 more stones to change the shape and let the first player choose color. This is essentially a slightly more elaborate pie rule.

Analysis

Computer search by L. Victor Allis has shown that on a 15×15 board, black wins with perfect play.[2] 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.[citation needed] 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.

References

1. L. Victor Allis, H. J. van den Herik, M. P. H. Huntjens. "Go-Moku and Threat-Space Search".
2. L. Victor Allis (1994). Searching for Solutions in Games and Artificial Intelligence. Ph.D. thesis, University of Limburg, The Netherlands. ISBN 9090074880.
3. Stefan Reisch (1980). "Gobang ist PSPACE-vollständig (Gomoku is PSPACE-complete)". Acta Informatica 13: 59–66.

(From Wikipedia, the free encyclopedia)