Gomoku
The Go-moku (from Japanese "go" = five, and "moku& #34; although it literally means eye, in this case it is taken as a point, also called five in a row or five in a row)[quote required] is an abstract strategy board game. Traditionally it is played with go pieces (black and white stones) on a go board. It can be played using the 15×15 or 19×19 board. Because the pieces are not normally moved or removed from the board, gomoku can also be played as a pencil and paper game. The game is known in various countries under different names.
Origin
Gomoku has existed in Japan since the Meiji Restoration. The name "gomoku" It comes from the Japanese language, where it is known as gomokunarabe (五 目 並 べ). Go means five, moku is a number word for pieces, and narabe means alignment. The game is also popular in Korea, where it is called omok (오목 [五 目]) and has the same structure and origin as the Japanese name.
In the 19th century, the game was introduced to Britain, where it was known as Go Bang, and is said to be a corruption of the Japanese word goban, which in turn was an adaptation of the Chinese k'i pan (qí pán) "go-board".
Official Rules
Players alternate turns placing a stone of their color on an empty intersection. Black plays first. The winner is the first player to form an unbroken chain of five stones horizontally, vertically, or diagonally. Placing so as to create a line of more than five stones of the same color does not result in a win. These are called overlapping lines.
Because in gomoku you have a huge first-mover advantage when unrestricted, the Swap2 rule is currently adapted in tournaments between professional players, including the gomoku world championships.
In the Swap2 rule, the first player starts by placing three stones, 2 black and 1 white, on the board. The second player selects one of three options: play black, play white and place another white stone, or place two more stones, one white and one black, and let the first player choose the color. This is essentially a more elaborate cake rule.
Swap2 solves the first move advantage problem.
Variants
Most variations are based on freestyle gomoku or standard gomoku.
- The free-style gomoku requires a row of five or more stones to win.
- Standard gomoku requires a row of exactly five stones for a victory: rows of six or more, called overlinesThey don't count.
Optional ("internal") rules
It has long been known that Black (the player who makes the first move) had a huge advantage, even before L. Victor Allis showed that Black could force a win (see below). So a number of variations are played with additional rules that aim to reduce Black's advantage.
- The rule of three and three It prohibits a movement that simultaneously forms two open rows of three stones (flames not blocked by an opponent's stone at any end).
- The rule of four and four It prohibits a movement that simultaneously forms two rows of four stones (open or not).
- Alternatively, a handicap can be granted such that after the first move "three and three" has been made, the opponent can place two stones in his next turn. These stones must block the rank of three of an opponent.
- Efforts to improve equity by reducing the advantage of the first movement include the rule of law exchange, generalizable as "swap- (x, and, z)" and characterized as a partially composite and partly iterated version of the cake rule ("rebanadas de una persona; the other chooses "): One player" A "coloca on the board x first color moving stones and a smaller number and stones of the second color in motion (" slice "in the metaphor of the cake); the other player "B" has the right to choose between a) play from the initial position, in which case the player "B" also has the right to choose which color to play, (usually [(x - y) + 1]) more stones on the board in the locations of the player's choice ("rebanded" in the metaphor of the cake, with limitations created by the existing setup of the board similar to the limitations that arise from the existing cuts in cake), in which case the player "A" has the right to play.
Specific variants
- The Renju is played on a 15×15 board, with the rules of three and three, four and four, and overlines applied only to blacks and with opening rules, some of which follow the pattern of exchange.
- In Caro (also called gomoku+, popular among Vietnamese), the winner must have a top line or an uninterrupted row of five stones that should not be blocked in both extremes (the upper lines are immune to this rule). This makes gomoku more balanced and provides more power for whites to defend.
- Omok is played as the standard gomoku; however, it is played on a 19×19 board and includes the rule of three and three. The rules of overlinesThey don't count.
- Ninuki-renju or Wu is a variant that adds capture to the game; it was published in the United States in a modified version with the name Pente.
Theoretical generalizations
- The games m,n,k are a generalization of gomoku to a board with m × n intersections, and k in a row necessary to win.
- Connecting games (m,n,k,p,q) are another generalization of gomoku to a board with m × n intersections, k in a row necessary to win, p stones for each player to place and q stones for the first player place only for the first move. Each player can play only in the lowest unoccupied place in a column. In particular, Connect (m,n,6,2,1) is called Connect6.
Sample game
This game on the 15 × 15 board is adapted from the document "Go-Moku and Threat-Space Search".
The opening moves clearly show Black's advantage. An open row of three (one not blocked by an opponent's stone at either end) must be immediately blocked or countered with a threat elsewhere on the board. If not blocked or countered, the open file of three will spill over into an open file of four, which threatens to win in two ways.
White has to block open files of three on moves 10, 14, 16 and 20, but Black only has to do it on move 9. Move 20 is a mistake for White (should have been played alongside black 19). Black can now force a win against any white defense, starting on move 21.
There are two forced 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 White's moves are forced. Such long force sequences are typical of gomoku, and expert players can read force sequences of 20 to 40 moves quickly and accurately.
The diagram on the right shows the second forcing sequence. This diagram shows why white 20 was an error; if it had been next to black 19 (at move position 32 in this diagram), black 31 would not be a threat and therefore the forcing sequence would fail.
World Championships
The World Championships in gomoku have been held 2 times in 1989, 1991. Since 2009 tournament play has resumed, with the opening rule changed to swap2.
Below is the list of tournaments and winners.
| Year | Headquarters | Gold | Silver | Bronze | Opening rule |
|---|---|---|---|---|---|
| 1989 |  Kyoto, Japan
|  Sergey Chernov
| Yuriy Tarannikov
| Hirouji Sakamoto
| Pro |
| 1991 | Moscow, Soviet Union
| Yuriy Tarannikov
| Ando Meritee
| Sergey Chernov
| Pro |
| 2009 |  Pardubice, Czech Republic
|  Artur Tamioła
|  Attila Demján
| Pavel Laube
| Swap2 |
| 2011 |  Huskvarna, Sweden
| Attila Demján
| Artur Tamioła
| Michał Żukowski
| Swap2 |
| 2013 |  Tallinn, Estonia
| Attila Demján
| Pavel Laube
|  Mikhail Kozhin
| Swap2 |
| 2015 | Suzdal, Russia
| Rudolf Dupszki
| Gergő Tóth
| Mikhail Kozhin
| Swap2 |
| 2017 | Prague, Czech Republic
| Zoltán László
| Rudolf Dupszki
| Denis Osipov
| Swap2 |
| 2019 | Tallinn, Estonia
| Martin Muzika
|  Oleg Bulatowsky
| Michał Żukowski
| Swap2 |
| Year | Headquarters | Gold | Silver | Bronze | Opening rule | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2016 | Tallinn, Estonia
| Michał Żukowski Michał Zajk Łukasz Majksner Piotr Małowiejski | Pavel Laube Igor Eged Štěpán Tesařík Marek Hanzl |  Lu Wei-Yuan Chen Ko-Han Chang Yi-Feng Sung Pei-Jung | Swap2 | |||||
| 2018 | Płock, Poland
| -1 Edvard Rizvanov Denis Osipov Ilya Muratov Maksim Karasev Mikhail Kozhin | Zoltán László Gergő Tóth Márk Horváth Gábor Gyenes Attila Hegedűs | Łukasz Majksner Michał Żukowski Michał Zajk Marek Gorzecki Paweł Tarasiński | Swap2 | |||||
| 2020 |
| |||||||||
Computers and Gomoku
Researchers have been applying artificial intelligence techniques to playing gomoku for several decades. In 1994, L. Victor Allis proposed the algorithm for trial number search (pn-search) and dependency-based search (db-search), and showed that when starting from an empty 15 × 15 board, the first player has a strategic win using these search algorithms. This applies to both freestyle gomoku and standard gomoku without opening rules. It seems very likely that Black will also win on larger boards. At any table size, gomoku freestyle is an m,n,k game, hence it is known that the first player can force a win or draw. In 2001, Allis's winning strategy was also approved for renju, a variation of gomoku, when there was no limitation on the opening stage.
However, neither the theoretical values of all legal positions, nor the opening rules like Swap2 used by professional gomoku players have been worked out yet, so the issue of gomoku artificial intelligence remains a challenge. for computer scientists, such as the problem of how to improve gomoku algorithms to make them more strategic and competitive. Today, most state-of-the-art gomoku algorithms are based on the alpha-beta pruning framework.
Reisch showed that the generalized gomoku is PSPACE-complete. He also observed that the reduction can be adapted to the k-in-a-Row rules for fixed k. Although he did not specify exactly what values of k are allowed, the reduction would seem to generalize to any k ≥ 5.
There have been several well-known tournaments for gomoku programs since 1989. The Computer Olympiad began with the game of gomoku in 1989, but gomoku has not been on the list since 1993. The Renju World Computer Championships began in 1991 and it was held for 4 times until 2004. The Gomocup tournament has been played since 2000 and takes place every year, still active now, with more than 30 participants from about 10 countries. The Hungarian Computer Go-Moku Tournament was also played twice in 2005. Two Computer vs. Human in the Czech Republic, in 2006 and 2011. It was not until 2017 that computer programs were shown to outperform the human world champion in public competitions. At the 2017 Gomoku World Championship, there was a match between the world champion program Yixin and the world champion human player Rudolf Dupszki. Yixin won the match with a score of 2-0.
Strategies
In the game of Five in a Row, there are many strategies, and all of them are linked to the same goal, forming a four, since with it formed, if the enemy has not blocked any end of the line, you have already won. Let's look at these graphs:
Basic Line
| Basic Line |
|---|
 日本語
|
This strategy is the mother of all the following, since it's a 1 × 4 row, column, or diagonal, and with nothing blocking your ends, victory is assured. Let's see all its variants and various ways to play it.
Fish
| Fish |
|---|
 日本語
|
This strategy consists of forming a 2 × 2 square with an enlarged end in the last column and row, its facilities are that when you have it formed you have 2 lines of 3 formed horizontally and vertically, 5 diagonals of 2 formed in all the directions and that each one complements and amplifies.
Multiple threes
In the game, when forming a line of three with the free ends, it is a danger for the opponent, who always, in order not to lose, will have to play in one of the ends around this row: in order to prevent do the basic line on the next turn. This can classically be used to "bind" to play in certain areas, thus forming the desired strategy easily.
Further reading
- Five-in-a-Row (Renju) for beginners and advanced players ISBN 4-87187-301-3