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The two black groups in the upper corners are alive, as both have at least two eyes. The groups in the lower corners are dead, as both have only one eye.
The group in the lower left may seem to have two eyes, but the surrounded empty point marked a is not actually an eye.
White can play there and take a black stone. Such a point is often called a false eye. There is an exception to the requirement that a group must have two eyes to be alive, a situation called seki or mutual life.
Where different colored groups are adjacent and share liberties, the situation may reach a position when neither player wants to move first, because doing so would allow the opponent to capture; in such situations therefore both players' stones remain on the board in mutual life or "seki".
Neither player receives any points for those groups, but at least those groups themselves remain living, as opposed to being captured.
In the "Example of seki mutual life " diagram, the circled points are liberties shared by both a black and a white group.
Neither player wants to play on a circled point, because doing so would allow the opponent to capture. All the other groups in this example, both black and white, are alive with at least two eyes.
Seki can result from an attempt by one player to invade and kill a nearly settled group of the other player. In Go, tactics deal with immediate fighting between stones, capturing and saving stones, life, death and other issues localized to a specific part of the board.
Larger issues, not limited to only part of the board, are referred to as strategy , and are covered in their own section.
There are several tactical constructs aimed at capturing stones. Recognizing the possibility that stones can be captured using these techniques is an important step forward.
A ladder. Black cannot escape unless the ladder connects to black stones further down the board that will intercept with the ladder. The most basic technique is the ladder.
Unless the pattern runs into friendly stones along the way, the stones in the ladder cannot avoid capture. Experienced players recognize the futility of continuing the pattern and play elsewhere.
The presence of a ladder on the board does give a player the option to play a stone in the path of the ladder, thereby threatening to rescue their stones, forcing a response.
Such a move is called a ladder breaker and may be a powerful strategic move. In the diagram, Black has the option of playing a ladder breaker.
Another technique to capture stones is the so-called net ,  also known by its Japanese name, geta.
This refers to a move that loosely surrounds some stones, preventing their escape in all directions. An example is given in the adjacent diagram.
It is generally better to capture stones in a net than in a ladder, because a net does not depend on the condition that there are no opposing stones in the way, nor does it allow the opponent to play a strategic ladder breaker.
A snapback. Although Black can capture the white stone by playing at the circled point, the resulting shape for Black has only one liberty at 1 , thus White can then capture the three black stones by playing at 1 again snap back.
A third technique to capture stones is the snapback. An example can be seen on the right. As with the ladder, an experienced player does not play out such a sequence, recognizing the futility of capturing only to be captured back immediately.
One of the most important skills required for strong tactical play is the ability to read ahead. Some of the strongest players of the game can read up to 40 moves ahead even in complicated positions.
As explained in the scoring rules, some stone formations can never be captured and are said to be alive, while other stones may be in the position where they cannot avoid being captured and are said to be dead.
Much of the practice material available to players of the game comes in the form of life and death problems, also known as tsumego.
Tsumego are considered an excellent way to train a player's ability at reading ahead,  and are available for all skill levels, some posing a challenge even to top players.
In situations when the Ko rule applies, a ko fight may occur. If the opponent does respond to the ko threat, the situation on the board has changed, and the prohibition on capturing the ko no longer applies.
Thus the player who made the ko threat may now recapture the ko. Their opponent is then in the same situation and can either play a ko threat as well, or concede the ko by simply playing elsewhere.
If a player concedes the ko, either because they do not think it important or because there are no moves left that could function as a ko threat, they have lost the ko, and their opponent may connect the ko.
Instead of responding to a ko threat, a player may also choose to ignore the threat and connect the ko. The choice of when to respond to a threat and when to ignore it is a subtle one, which requires a player to consider many factors, including how much is gained by connecting, how much is lost by not responding, how many possible ko threats both players have remaining, what the optimal order of playing them is, and what the size —points lost or gained—of each of the remaining threats is.
Frequently, the winner of the ko fight does not connect the ko but instead captures one of the chains that constituted their opponent's side of the ko.
Strategy deals with global influence, interaction between distant stones, keeping the whole board in mind during local fights, and other issues that involve the overall game.
It is therefore possible to allow a tactical loss when it confers a strategic advantage. Novices often start by randomly placing stones on the board, as if it were a game of chance.
An understanding of how stones connect for greater power develops, and then a few basic common opening sequences may be understood.
Learning the ways of life and death helps in a fundamental way to develop one's strategic understanding of weak groups. The strategy involved can become very abstract and complex.
High-level players spend years improving their understanding of strategy, and a novice may play many hundreds of games against opponents before being able to win regularly.
In the opening of the game, players usually play and gain territory in the corners of the board first, as the presence of two edges makes it easier for them to surround territory and establish their stones.
Players tend to play on or near the star point during the opening. Playing nearer to the edge does not produce enough territory to be efficient, and playing further from the edge does not safely secure the territory.
In the opening, players often play established sequences called joseki , which are locally balanced exchanges;  however, the joseki chosen should also produce a satisfactory result on a global scale.
It is generally advisable to keep a balance between territory and influence. Which of these gets precedence is often a matter of individual taste.
The middle phase of the game is the most combative, and usually lasts for more than moves. During the middlegame, the players invade each other's territories, and attack formations that lack the necessary two eyes for viability.
Such groups may be saved or sacrificed for something more significant on the board. However, matters may be more complex yet, with major trade-offs, apparently dead groups reviving, and skillful play to attack in such a way as to construct territories rather than kill.
The end of the middlegame and transition to the endgame is marked by a few features. Near the end of a game, play becomes divided into localized fights that do not affect each other,  with the exception of ko fights, where before the central area of the board related to all parts of it.
No large weak groups are still in serious danger. Moves can reasonably be attributed some definite value, such as 20 points or fewer, rather than simply being necessary to compete.
Both players set limited objectives in their plans, in making or destroying territory, capturing or saving stones.
These changing aspects of the game usually occur at much the same time, for strong players. In brief, the middlegame switches into the endgame when the concepts of strategy and influence need reassessment in terms of concrete final results on the board.
In China, Go was considered one of the four cultivated arts of the Chinese scholar gentleman , along with calligraphy , painting and playing the musical instrument guqin  In ancient times the rules of go were passed on verbally, rather than being written down.
Go was introduced to Korea sometime between the 5th and 7th centuries CE, and was popular among the higher classes. Sunjang baduk became the main variant played in Korea until the end of the 19th century, when the current version was reintroduced from Japan.
It became popular at the Japanese imperial court in the 8th century,  and among the general public by the 13th century. In , Tokugawa Ieyasu re-established Japan's unified national government.
Despite its widespread popularity in East Asia, Go has been slow to spread to the rest of the world. Although there are some mentions of the game in western literature from the 16th century forward, Go did not start to become popular in the West until the end of the 19th century, when German scientist Oskar Korschelt wrote a treatise on the ancient Han Chinese game.
In , Edward Lasker learned the game while in Berlin. Two years later, in , the German Go Association was founded. World War II put a stop to most Go activity, since it was a game coming from Japan, but after the war, Go continued to spread.
Both astronauts were awarded honorary dan ranks by the Nihon Ki-in. In Go, rank indicates a player's skill in the game.
Traditionally, ranks are measured using kyu and dan grades,  a system also adopted by many martial arts.
More recently, mathematical rating systems similar to the Elo rating system have been introduced. Dan grades abbreviated d are considered master grades, and increase from 1st dan to 7th dan.
First dan equals a black belt in eastern martial arts using this system. The difference among each amateur rank is one handicap stone.
For example, if a 5k plays a game with a 1k, the 5k would need a handicap of four stones to even the odds. Top-level amateur players sometimes defeat professionals in tournament play.
These ranks are separate from amateur ranks. Tournament and match rules deal with factors that may influence the game but are not part of the actual rules of play.
Such rules may differ between events. Rules that influence the game include: the setting of compensation points komi , handicap, and time control parameters.
Rules that do not generally influence the game are: the tournament system, pairing strategies, and placement criteria.
Common tournament systems used in Go include the McMahon system ,  Swiss system , league systems and the knockout system.
Tournaments may combine multiple systems; many professional Go tournaments use a combination of the league and knockout systems.
A game of Go may be timed using a game clock. Formal time controls were introduced into the professional game during the s and were controversial.
Go tournaments use a number of different time control systems. All common systems envisage a single main period of time for each player for the game, but they vary on the protocols for continuation in overtime after a player has finished that time allowance.
The top professional Go matches have timekeepers so that the players do not have to press their own clocks. Two widely used variants of the byoyomi system are: .
Go games are recorded with a simple coordinate system. This is comparable to algebraic chess notation , except that Go stones do not move and thus require only one coordinate per turn.
Coordinate systems include purely numerical point , hybrid K3 , and purely alphabetical. The Japanese word kifu is sometimes used to refer to a game record.
In Unicode, Go stones can be represented with black and white circles from the block Geometric Shapes :. The block Miscellaneous Symbols includes "Go markers"  that were likely meant for mathematical research of Go:  .
A Go professional is a professional player of the game of Go. Although the game was developed in China, the establishment of the Four Go houses by Tokugawa Ieyasu at the start of the 17th century shifted the focus of the Go world to Japan.
State sponsorship, allowing players to dedicate themselves full-time to study of the game, and fierce competition between individual houses resulted in a significant increase in the level of play.
During this period, the best player of his generation was given the prestigious title Meijin master and the post of Godokoro minister of Go.
Of special note are the players who were dubbed Kisei Go Sage. After the end of the Tokugawa shogunate and the Meiji Restoration period, the Go houses slowly disappeared, and in , the Nihon Ki-in Japanese Go Association was formed.
Top players from this period often played newspaper-sponsored matches of 2—10 games. For much of the 20th century, Go continued to be dominated by players trained in Japan.
After his return to Korea, the Hanguk Kiwon Korea Baduk Association was formed and caused the level of play in South Korea to rise significantly in the second half of the 20th century.
With the advent of major international titles from onward, it became possible to compare the level of players from different countries more accurately.
His disciple Lee Chang-ho was the dominant player in international Go competitions for more than a decade spanning much of s and early s; he is also credited with groundbreaking works on the endgame.
As of [update] , Japan lags behind in the international Go scene. Historically, more men than women have played Go. Special tournaments for women exist, but until recently, men and women did not compete together at the highest levels; however, the creation of new, open tournaments and the rise of strong female players, most notably Rui Naiwei , have in recent years highlighted the strength and competitiveness of emerging female players.
The level in other countries has traditionally been much lower, except for some players who had preparatory professional training in East Asia.
A famous player of the s was Edward Lasker. In , Manfred Wimmer became the first Westerner to receive a professional player's certificate from an East Asian professional Go association.
It is possible to play Go with a simple paper board and coins, plastic tokens, or white beans and coffee beans for the stones; or even by drawing the stones on the board and erasing them when captured.
More popular midrange equipment includes cardstock, a laminated particle board , or wood boards with stones of plastic or glass.
More expensive traditional materials are still used by many players. The most expensive Go sets have black stones carved from slate and white stones carved from translucent white shells, played on boards carved in a single piece from the trunk of a tree.
Chinese boards are slightly larger, as a traditional Chinese Go stone is slightly larger to match. The board is not square; there is a ratio in length to width, because with a perfectly square board, from the player's viewing angle the perspective creates a foreshortening of the board.
The added length compensates for this. More recently, the related California Torreya Torreya californica has been prized for its light color and pale rings as well as its reduced expense and more readily available stock.
The natural resources of Japan have been unable to keep up with the enormous demand for the slow-growing Kaya trees; both T.
Other, less expensive woods often used to make quality table boards in both Chinese and Japanese dimensions include Hiba Thujopsis dolabrata , Katsura Cercidiphyllum japonicum , Kauri Agathis , and Shin Kaya various varieties of spruce , commonly from Alaska, Siberia and China's Yunnan Province.
However it may happen, especially in beginners' games, that many back-and-forth captures empty the bowls before the end of the game: in that case an "exchange of prisoners" allows the game to continue.
Traditional Japanese stones are double-convex, and made of clamshell white and slate black. In China, the game is traditionally played with single-convex stones  made of a composite called Yunzi.
The material comes from Yunnan Province and is made by sintering a proprietary and trade-secret mixture of mineral compounds derived from the local stone.
This process dates to the Tang Dynasty and, after the knowledge was lost in the s during the Chinese Civil War , was rediscovered in the s by the now state-run Yunzi company.
The term "yunzi" can also refer to a single-convex stone made of any material; however, most English-language Go suppliers specify Yunzi as a material and single-convex as a shape to avoid confusion, as stones made of Yunzi are also available in double-convex while synthetic stones can be either shape.
Traditional stones are made so that black stones are slightly larger in diameter than white; this is to compensate for the optical illusion created by contrasting colors that would make equal-sized white stones appear larger on the board than black stones.
The bowls for the stones are shaped like a flattened sphere with a level underside. Chinese bowls are slightly larger, and a little more rounded, a style known generally as Go Seigen ; Japanese Kitani bowls tend to have a shape closer to that of the bowl of a snifter glass, such as for brandy.
The bowls are usually made of turned wood. Mulberry is the traditional material for Japanese bowls, but is very expensive; wood from the Chinese jujube date tree, which has a lighter color it is often stained and slightly more visible grain pattern, is a common substitute for rosewood, and traditional for Go Seigen-style bowls.
Other traditional materials used for making Chinese bowls include lacquered wood, ceramics , stone and woven straw or rattan.
The names of the bowl shapes, "Go Seigen" and "Kitani", were introduced in the last quarter of the 20th century by the professional player Janice Kim as homage to two 20th-century professional Go players by the same names, of Chinese and Japanese nationality, respectively, who are referred to as the "Fathers of modern Go".
The traditional way to place a Go stone is to first take one from the bowl, gripping it between the index and middle fingers, with the middle finger on top, and then placing it directly on the desired intersection.
It is considered respectful towards White for Black to place the first stone of the game in the upper right-hand corner. It is considered poor manners to run one's fingers through one's bowl of unplayed stones, as the sound, however soothing to the player doing this, can be disturbing to one's opponent.
Similarly, "clacking" a stone against another stone, the board, or the table or floor is also discouraged.
However, it is permissible to emphasize select moves by striking the board more firmly than normal, thus producing a sharp clack. Additionally, hovering one's arm over the board usually when deciding where to play is also considered rude as it obstructs the opponent's view of the board.
Apart from the points above it also points to the need to remain calm and honorable, in maintaining posture, and knowing the key specialised terms, such as titles of common formations.
Generally speaking, much attention is paid to the etiquette of playing, as much as to winning or actual game technique.
In combinatorial game theory terms, Go is a zero-sum , perfect-information , partisan , deterministic strategy game , putting it in the same class as chess, draughts checkers , and Reversi Othello ; however it differs from these in its game play.
Although the rules are simple, the practical strategy is complex. The game emphasizes the importance of balance on multiple levels and has internal tensions.
To secure an area of the board, it is good to play moves close together; however, to cover the largest area, one needs to spread out, perhaps leaving weaknesses that can be exploited.
Playing too low close to the edge secures insufficient territory and influence, yet playing too high far from the edge allows the opponent to invade.
It has been claimed that Go is the most complex game in the world due to its vast number of variations in individual games. Decisions in one part of the board may be influenced by an apparently unrelated situation in a distant part of the board.
Plays made early in the game can shape the nature of conflict a hundred moves later. The game complexity of Go is such that describing even elementary strategy fills many introductory books.
In fact, numerical estimates show that the number of possible games of Go far exceeds the number of atoms in the observable universe.
Research of go endgame by John H. Conway led to the invention of the surreal numbers. Go long posed a daunting challenge to computer programmers , putting forward "difficult decision-making tasks, an intractable search space, and an optimal solution so complex it appears infeasible to directly approximate using a policy or value function".
Many in the field of artificial intelligence consider Go to require more elements that mimic human thought than chess. The reasons why computer programs had not played Go at the professional dan level prior to include: .
As an illustration, the greatest handicap normally given to a weaker opponent is 9 stones. It was not until August that a computer won a game against a professional level player at this handicap.
It was the Mogo program, which scored this first victory in an exhibition game played during the US Go Congress. In March , Google next challenged Lee Sedol , a 9 dan considered the top player in the world in the early 21st century,  to a five-game match.
Leading up to the game, Lee Sedol and other top professionals were confident that he would win;  however, AlphaGo defeated Lee in four of the five games.
In October , DeepMind announced a significantly stronger version called AlphaGo Zero which beat the previous version by games to 0.
An abundance of software is available to support players of the game. This includes programs that can be used to view or edit game records and diagrams, programs that allow the user to search for patterns in the games of strong players, and programs that allow users to play against each other over the Internet.
Some web servers [ citation needed ] provide graphical aids like maps, to aid learning during play. These graphical aids may suggest possible next moves, indicate areas of influence, highlight vital stones under attack and mark stones in atari or about to be captured.
There are several file formats used to store game records, the most popular of which is SGF, short for Smart Game Format.
Programs used for editing game records allow the user to record not only the moves, but also variations, commentary and further information on the game.
Electronic databases can be used to study life and death situations, joseki , fuseki and games by a particular player.
Programs are available that give players pattern searching options, which allow players to research positions by searching for high-level games in which similar situations occur.
Internet-based Go servers allow access to competition with players all over the world, for real-time and turn-based games.
Other books have used Go as a theme or minor plot device. The manga Japanese comic book and anime series Hikaru no Go , released in Japan in , had a large impact in popularizing Go among young players, both in Japan and—as translations were released—abroad.
Despite this Go still features heavily in her character's personality. Go has also been featured in a number of television series.
Starz 's science fiction thriller Counterpart , for instance, is rich in references the opening itself featuring developments on a Go board , including applications of the game's metaphors, a book about life and death being displayed, and Go matches, accurately played, relevant to the plot.
The corporation and brand Atari was named after the Go term. In the endgame, it can often happen that the state of the board consists of several subpositions that do not interact with the others.
The whole board position can then be considered as a mathematical sum, or composition, of the individual subpositions. A review of literature by Fernand Gobet , de Voogt and Jean Retschitzki shows that relatively little scientific research has been carried out on the psychology of Go, compared with other traditional board games such as chess.
According to the review of Gobet and colleagues, the pattern of brain activity observed with techniques such as PET and fMRI does not show large differences between Go and chess.
On the other hand, a study by Xiangchuan Chen et al. There is some evidence to suggest a correlation between playing board games and reduced risk of Alzheimer's disease and dementia.
In formal game theory terms, Go is a non-chance, combinatorial game with perfect information. Informally that means there are no dice used and decisions or moves create discrete outcome vectors rather than probability distributions , the underlying math is combinatorial, and all moves via single vertex analysis are visible to both players unlike some card games where some information is hidden.
Perfect information also implies sequence—players can theoretically know about all past moves. Affine transformations can theoretically add non-zero and complex utility aspects even to two player games.
Go begins with an empty board. It is focused on building from the ground up nothing to something with multiple, simultaneous battles leading to a point-based win.
Chess is tactical rather than strategic, as the predetermined strategy is to trap one individual piece the king. A similar comparison has been drawn among Go, chess and backgammon , perhaps the three oldest games that enjoy worldwide popularity.
Chess, with rows of soldiers marching forward to capture each other, embodies the conflict of "man vs. Because the handicap system tells Go players where they stand relative to other players, an honestly ranked player can expect to lose about half of their games; therefore, Go can be seen as embodying the quest for self-improvement, "man vs.
From Wikipedia, the free encyclopedia. Abstract strategy board game for two players. This article is about the board game. For other things named "Go", see Go disambiguation.
Game pieces, called stones , are played on the lines' intersections. Main article: Rules of Go. Main article: Ko fight. An example of a situation in which the ko rule applies.
Main article: Komidashi. See also: Life and death. Main article: Go strategy and tactics. A net. The chain of three marked black stones cannot escape in any direction.
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