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100-453: There are many variations of the simple rules of Go . Some are ancient digressions, while other are modern deviations. They are often side events at tournaments, for example, the U.S. Go Congress holds a "Crazy Go" event every year. The difficulty in defining the rules of Go has led to the creation of many subtly different rulesets. They vary in areas like scoring method, ko, suicide, handicap placement, and how neutral points are dealt with at

200-410: A ko threat . Because Black has the advantage of playing the first move, the idea of awarding White some compensation came into being during the 20th century. This is called komi , which gives white a 5.5-point compensation under Japanese rules, 6.5-point under Korean rules, and 15/4 stones, or 7.5-point under Chinese rules (number of points varies by rule set). Under handicap play, White receives only

300-414: A 0.5-point komi, to break a possible tie ( jigo ). Two general types of scoring procedures are used, and players determine which to use before play. Both procedures almost always give the same winner. Both procedures are counted after both players have passed consecutively, the stones that are still on the board but unable to avoid capture, called dead stones, are removed. Given that the number of stones

400-430: A 15×15 square-celled board using square-tiled pieces. Quantum Go is a Go variant which provides a straightforward illustration of interesting quantum phenomena. Players alternatively play pairs of go stones which are entangled, in the sense that each entangled pair of stones will reduce to a single go stone at some point in the game. A process of quantum-like collapse occurs when a stone is played in contact with one of

500-623: A Golden Jubilee Award for Technological Innovation from the IEEE Information Theory Society . Along with Tom M. Rodgers he was one of the founders of Gathering 4 Gardner and was on its board for many years. In the mid-1980s, he was president of Cyclotomics, Inc. , a corporation that developed error-correcting code technology. He studied various games, including dots and boxes , fox and geese , and, especially, Go . Berlekamp and co-author David Wolfe describe methods for analyzing certain classes of Go endgames in

600-447: 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

700-464: A capture if your opponent made a capture on the previous move. All other rules are the same as in Go. Suicide of one or more stones is not allowed, and area scoring is used. All known forced Go cycles are impossible with this rule. The nature of the rule itself suggests that forced cycles are either impossible or astronomically rarer than they are in Go when the superko rule is not used. Ko fights proceed in

800-404: A circled point, because doing so would allow the opponent to capture their group on the next move. The outer groups in this example, both black and white, are alive. Seki can result from an attempt by one player to invade and kill a nearly settled group of the other player. Tactics deal with immediate fighting between stones, capturing and saving stones, life, death and other issues localized to

900-422: A finite number of moves, and no ko rule is needed. Nothing is ever rubbed out. It differs from standard Go in the following ways: (Conventional Go can also be played on paper by drawing circles of different colors. Captured stones are marked with a line. Then if the square is replayed, a smaller circle is placed inside the larger circle.) Also named Tetromino Go . Devised by R. Wayne Schmittberger, each player

1000-435: A game concludes, the winner is determined by counting each player's surrounded territory along with captured stones and komi (points added to the score of the player with the white stones as compensation for playing second). Games may also end by resignation. The standard Go board has a 19×19 grid of lines, containing 361 points. Beginners often play on smaller 9×9 or 13×13 boards, and archaeological evidence shows that

1100-399: A group of stones that prevents capture) and establish formations for potential territory. Players usually start near the corners because establishing territory is easier with the aid of two edges of the board. Established corner opening sequences are called joseki and are often studied independently. However, in the mid-game, stone groups must also reach in towards the large central area of

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1200-405: A handicap) or both of the players cannot see the board in this variant. Therefore, they have to remember the whole position. This is considered much more difficult than playing blindfold chess . A few club standard players can play blindfold chess, but only professional players are able to complete a game of blind 19×19 Go. The two players use stones of the same color. This variation is regarded as

1300-490: A handicap—Black is allowed to place two or more stones on the board to compensate for White's greater strength. There are different rulesets (Korean, Japanese, Chinese, AGA, etc.), which are almost entirely equivalent, except for certain special-case positions and the method of scoring at the end. Basic strategic aspects include the following: The strategy involved can become very abstract and complex. High-level players spend years improving their understanding of strategy, and

1400-405: A liberty at the coin. There are different ways to determine intersections occupied by coins: Coins may not be captured through liberty shortage. For scoring, coins do not contribute to territory. Normal scoring rules apply. Since playing as Black might have the potential of being a significant advantage in this variant, players may use the "Pie rule" to determine who plays which color: Pair Go

1500-490: A move is not suicide because the Black stones are removed first. In the "Examples of eyes" diagram, all the circled points are eyes. 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

1600-416: A novice may play many hundreds of games against opponents before being able to win regularly. Strategy deals with global influence, the 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

1700-432: A player has on the board is directly related to the number of prisoners their opponent has taken, the resulting net score, that is, the difference between Black's and White's scores is identical under both rulesets (unless the players have passed different numbers of times during the course of the game). Thus, the net result given by the two scoring systems rarely differs by more than a point. While not actually mentioned in

1800-472: A player who occupies or surrounds all four corner points (the 1-1 points) receives a bonus of 40 points, plus another 10 if the player also controls the center point. Sunjang baduk is a different form of Go (baduk) that evolved in Korea, which dates to the 16th century. Its most distinctive feature is the prescribed opening. The starting position dictates the placement of 16 stones (8 black, 8 white) as shown, and

1900-507: A similar manner to those of Go, with the difference that captures and moves answered by captures aren't valid ko threats. Although snapbacks are not possible in the basic variant (as it is necessary to make a ko threat before any consecutive capture occurs), they can be explicitly allowed with an extra rule while retaining the property that all known forced cycles are impossible. Environmental Go , also called Coupon Go , invented by Elwyn Berlekamp , adds an element of mathematical precision to

2000-454: A situation in which the ko rule applies Players are not allowed to make a move that returns the game to the immediately prior position. This rule, called the ko rule , prevents unending repetition (a stalemate). As shown in the example pictured: White had a stone where the red circle was, and Black has just captured it by playing a stone at 1 (so the White stone has been removed). However, it

2100-600: A son with his wife Jennifer. He lived in Piedmont, California and died in April 2019 at the age of 78 from complications of pulmonary fibrosis . Berlekamp was a professor of electrical engineering at the University of California, Berkeley from 1964 until 1966, when he became a mathematics researcher at Bell Labs . In 1971, Berlekamp returned to Berkeley as professor of mathematics and computer science, where he served as

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2200-491: A specific part of the board. Larger issues which encompass the territory of the entire board and planning stone-group connections are referred to as Strategy and are covered in the Strategy section above. There are several tactical constructs aimed at capturing stones. These are among the first things a player learns after understanding the rules. Recognizing the possibility that stones can be captured using these techniques

2300-400: A stone can never be moved and can be taken off the board only if it is captured . A player may pass their turn, declining to place a stone, though this is usually only done at the end of the game when both players believe nothing more can be accomplished with further play. When both players pass consecutively, the game ends and is then scored . Vertically and horizontally adjacent stones of

2400-403: A stone such that it or its group immediately has no liberties unless doing so immediately deprives an enemy group of its final liberty. In the second case, the enemy group is captured, leaving the new stone with at least one liberty, so the new stone can be placed. This rule is responsible for the all-important difference between one and two eyes: if a group with only one eye is fully surrounded on

2500-433: A time. The usual board size is a 19×19 grid, but for beginners or for playing quick games, the smaller board sizes of 13×13 and 9×9 are also popular. The board is empty to begin with. Black plays first unless given a handicap of two or more stones, in which case White plays first. The players may choose any unoccupied intersection to play on except for those forbidden by the ko and suicide rules (see below). Once played,

2600-399: A two-dimensional doughnut shaped surface. It can be played on a computer app or simulated on a standard board, but requires imagination on the part of the players to perform an abstract join at the edges. Tactics become more elegant without the need for special border and corner cases ( joseki ) since a toroidal board has only "middle" space. There have been several tournaments for Torus Go at

2700-471: A useful tool for developing one's memory and reading skills by forcing both players to remember who placed each stone. An external program or a third person may be used to keep track of who captures what in case one or both players forget the true color of a stone. These variants are not purely strategic games, as the element of luck is quite important. This game requires two players, a referee and three playing sets. Each player sees only their own board, while

2800-666: 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

2900-462: Is a competitive game played by two pairs, with each team consisting of a male and a female, sharing a single Go board. The pairs play alternately: first, the female player of the two holding black; next, the female player of the pair holding white; next, the male player of the pair holding black; and next, the male player of the pair holding white. Pair Go is based on the rules of Go, but the inventor of Pair Go, Hisao Taki devised his own rules to maximise

3000-423: Is adjacent to two or more chains of the same color. A vacant point adjacent to a stone, along one of the grid lines of the board, is called a liberty for that stone. Stones in a chain share their liberties. A chain of stones must have at least one liberty to remain on the board. When a chain is surrounded by opposing stones so that it has no liberties, it is captured and removed from the board. An example of

3100-492: Is allowed to play up to four stones in a turn, provided they are solidly connected on adjacent points. (There are five four-stone patterns possible, two three-stone patterns, and one two-stone pattern, ignoring rotations and reflections.) There is no komi; Black is restricted on their first turn to playing no more than two stones. The winner is determined by Chinese scoring: occupied and surrounded points each count 1 point; captured stones do not have point value. The inventor suggests

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3200-483: Is an important step forward. Elwyn Berlekamp Elwyn Ralph Berlekamp (September 6, 1940 – April 9, 2019) was a professor of mathematics and computer science at the University of California, Berkeley . Berlekamp was widely known for his work in computer science, coding theory and combinatorial game theory . Berlekamp invented an algorithm to factor polynomials and the Berlekamp switching game , and

3300-449: Is called "the refill"). The size of the stone reserve will change depending on the total number of players and the number of players on each team. Micaël Go has several interesting properties that make team play especially exciting : Micaël Go does not alter the basic rules of the game. It is therefore a great opportunity for players of different levels to enjoy a game together, ask questions and share tips on how to improve. One (as

3400-407: Is deemed to have been played, which necessitates resignation. In Multi-player Go , stones of different colors are used so that three or more players can play together. The rules must be somewhat altered to create balance in power, as those who play first (especially the first four, on a four-cornered board) have significant advantage. There are various optional rules that enable cooperation between

3500-421: Is readily apparent that now Black's stone at 1 is immediately threatened by the three surrounding White stones. If White were allowed to play again on the red circle, it would return the situation to the original one, but the ko rule forbids that kind of endless repetition. Thus, White is forced to move elsewhere, or pass. If White wants to recapture Black's stone at 1 , White must attack Black somewhere else on

3600-425: Is surrounded by the opponent on the outside, because each eye constitutes a liberty that must be filled by the opponent as the final step in capture. A formation having two or more eyes is said to be unconditionally alive , so it can evade capture indefinitely, and a group that cannot form two eyes is said to be dead and can be captured. The general strategy is to place stones to fence-off territory, attack

3700-422: Is worth at each stage in the game. The professional players Jiang Zhujiu and Rui Naiwei played the first Environmental Go game in April 1998. Since then the variant has seen little activity on the international scene. In Cards Go players draw from a pack of cards contain instructions to play one of a fixed set of commonly occurring shapes. If the said shape cannot be placed on the board, then an illegal move

3800-510: The European Go Congress , the last one in 2023. TriGo uses a triangular-grid goban , where each stone has up to six liberties. To compensate for this, there are several rule changes: ko and superko are limited in scope, komi is not used, and after the first stone is placed, every turn consists of placing two stones. After both players have passed a turn, the score is counted (the sum of captured stones and territory), and in

3900-456: The number of atoms in the observable universe , which is estimated to be on the order of 10 . The name Go is a short form of the Japanese word igo ( 囲碁 ; いご ), which derives from earlier wigo ( ゐご ), in turn from Middle Chinese ɦʉi gi ( 圍棋 , Mandarin : wéiqí , lit.   ' encirclement board game ' or ' board game of surrounding ' ). In English,

4000-633: The 16th century. It became antiquated in the early 20th century when it was largely replaced by modern go due to Japanese influence. There are around 45 surviving game records of Sunjang baduk, mostly from the 1880s. The last official game record was published in the Chosun Ilbo newspaper in March 1937. The game is between No Sa-ch'o and Ch'ae Keuk-mun. In the early 20th century, the top ten strongest players ranged from about 4 dan amateur to 2 dan professional in terms of strength. From 1910 to 1945, Korea

4100-423: The Black stones. (Such a move is forbidden according to the suicide rule in most rule sets, but even if not forbidden, such a move would be a useless suicide of a White stone.) If a Black group has two eyes, White can never capture it because White cannot remove both liberties simultaneously. If Black has only one eye, White can capture the Black group by playing in the single eye, removing Black's last liberty. Such

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4200-766: The advisor for over twenty doctoral students. He was a member of the National Academy of Engineering (1977) and the National Academy of Sciences (1999). He was elected a Fellow of the American Academy of Arts and Sciences in 1996, and became a fellow of the American Mathematical Society in 2012. In 1991, he received the IEEE Richard W. Hamming Medal , and in 1993, the Claude E. Shannon Award . In 1998, he received

4300-437: The black group with false eye a can be killed by white in two turns. When a group of stones is mostly surrounded and has no options to connect with friendly stones elsewhere, the status of the group is either alive, dead or unsettled . A group of stones is said to be alive if it cannot be captured, even if the opponent is allowed to move first. Conversely, a group of stones is said to be dead if it cannot avoid capture, even if

4400-413: The board (in seki). Neither player receives any points for those groups, but at least those groups themselves remain living, as opposed to being captured. Seki can occur in many ways. The simplest are: In the "Example of seki (mutual life)" diagram, the two circled points are liberties shared by both a black and a white group. Both of these interior groups are at risk, and neither player wants to play on

4500-495: The board are worth different points values. The other principal difference is that both players place three stones before the game begins, and may also place a special "hidden stone", which affects the board as a regular stone but is invisible to the opponent. Batoo became a short-lived fad among young people in Korea around 2011. The first player to capture a stone wins. It was invented by Japanese professional Yasutoshi Yasuda, who describes it in his book Go As Communication . Yasuda

4600-401: The board do not apply. Sygo is a two player abstract strategy game created in 2010 by Christian Freeling . It differs from Go by using a move protocol from Symple , another of Christian Freeling's games, and " othelloanian capture" where stones change colors when captured instead of being removed from the board. The goal of Sygo is to control the most territory on the board as determined by

4700-428: The board so forcefully that Black moves elsewhere to counter that, giving White that chance. If White's forcing move is successful, it is termed "gaining the sente "; if Black responds elsewhere on the board, then White can retake Black's stone at 1 , and the ko continues, but this time Black must move elsewhere. A repetition of such exchanges is called a ko fight . To stop the potential for ko fights , two stones of

4800-457: The board to capture more territory. Dame are points that lie in between the boundary walls of black and white, and as such are considered to be of no value to either side. Seki are mutually alive pairs of white and black groups where neither has two eyes. Ko (Chinese and Japanese: 劫 ) is a potentially indefinitely repeated stone-capture position. The rules do not allow a board position to be repeated. Therefore, any move which would restore

4900-456: The board with one's stones than the opponent. As the game progresses, the players place stones on the board creating stone "formations" and enclosing spaces. Stones are never moved on the board, but when "captured" are removed from the board. Stones are linked together into a formation by being adjacent along the black lines, not on diagonals (of which there are none). Contests between opposing formations are often extremely complex and may result in

5000-411: 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 . A player who both plays aggressively and can handle adversity is said to display kiai , or fighting spirit, in

5100-506: The book Winning Ways for your Mathematical Plays , leading to his recognition as one of the founders of combinatorial game theory . The dedication of their book says, "To Martin Gardner, who has brought more mathematics to more millions than anyone else." Berlekamp and Gardner both had great love for and were strong advocates of recreational mathematics. Conferences called Gathering 4 Gardner (G4G) are held every two years to celebrate

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5200-419: The book Mathematical Go. Berlekamp was a close friend of Scientific American columnist Martin Gardner and was an important member of the gifted and diverse group of people that Gardner nurtured and acted as a conduit for; people who inspired Gardner and who were in turn inspired by him. Berlekamp teamed up with John Horton Conway and Richard K. Guy , two other close associates of Gardner, to co-author

5300-430: The case of a draw the player passing first wins. TriPlan , for three players, uses a triangular grid, where each stone has up to six liberties. Stones can be captured in two ways. If one player's stones are surrounded by those of one opponent, the surrounding player captures them and counts them as points at the end of the game. If one player's stones are surrounded by those of both opponents, they must be played as

5400-439: The complete game and informs a player if their move was illegal, in which case they can try again. The referee removes captured stones from all affected boards. Although Go is most commonly played on a board with 19×19 lines, 9×9 and 13×13 boards are also available. They are used by beginners and by players who want a game that finishes more quickly. Due to flexibility of configuration, the two smaller sizes are more often played on

5500-432: The elements of life or death are the primary challenges of Go. In the end game players may pass rather than place a stone if they think there are no further opportunities for profitable play. The game ends when both players pass or when one player resigns. In general, to score the game, each player counts the number of unoccupied points surrounded by their stones and then subtracts the number of stones that were captured by

5600-494: The end. These differences are usually small enough to maintain the character and strategy of the game, and are typically not considered variants. Different rulesets are explained in Rules of Go . In some of the examples below, the effects of rule differences on actual play are minor, but the tactical consequences are substantial. Tibetan Go is played on a 17×17 board, and starts with six stones (called Bo) from each color placed on

5700-407: The enjoyment of playing in pairs. The word "Pair Go" is the registered trademark of the public interest incorporated foundation Japan Pair Go Association in many countries. In many countries, Pair Go is treated as a mind game separate from the traditional Go. Rengo (Japanese: 連碁 ), which is the origin of Pair Go , is a more general form of Pair Go where players can be of any gender. Each player in

5800-414: The expansion, reduction, or wholesale capture and loss of formations and their enclosed empty spaces (called "eyes"). Another essential component of the game is control of the sente (that is, controlling the offense, so that one's opponent is forced into defensive moves); this usually changes several times during play. Initially the board is bare, and players alternate turns to place one stone per turn. As

5900-441: The first move is prescribed for Black at the center of the board. At the end of the game, stones inside friendly territory, which are irrelevant to boundary definition, are removed before counting territory. Classical Chinese go was played with the diagonal placement of two black stones and two white stones on the four star points in the corners. It is likely that Koreans played go in this form until it developed into Sunjang baduk in

6000-417: The game and takes a large proportion of professional players' thinking time. The first stone played at a corner of the board is generally placed on the third or fourth line from the edge. Players tend to play on or near the 4–4 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

6100-411: The game by compelling players to make quantitative decisions. In lieu of playing a stone, a player may take the highest remaining card from a pack of cards valued in steps of 1 ⁄ 2 from 1 ⁄ 2 to 20: the player's score will be the territory captured, plus the total value of cards taken. In effect, the players participate in a downward auction for the number of points they think sente

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6200-522: The game is played is heuristic, meaning it is learned information about how the patterns of the stones on the board function, rather than a rule. Other rules are specialized, as they come about through different rulesets, but the above two rules cover almost all of any played game. Although there are some minor differences between rulesets used in different countries, most notably in Chinese and Japanese scoring rules, these differences do not greatly affect

6300-549: The game proceeds, players try to link their stones together into "living" formations (meaning that they are permanently safe from capture), as well as threaten to capture their opponent's stones and formations. Stones have both offensive and defensive characteristics, depending on the situation. An essential concept is that a formation of stones must have, or be capable of making, at least two enclosed open points known as eyes to preserve itself from being captured. A formation having at least two eyes cannot be captured, even after it

6400-480: 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. Aside from the order of play (alternating moves, Black moves first or takes a handicap) and scoring rules, there are essentially only two rules in Go: Almost all other information about how

6500-407: The game was played in earlier centuries on a board with a 17×17 grid. Boards with a 19×19 grid had become standard, however, by the time the game reached Korea in the 5th century CE and Japan in the 7th century CE. Go was considered one of the four essential arts of the cultured aristocratic Chinese scholars in antiquity. The earliest written reference to the game is generally recognized as

6600-406: The game. 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 the eyes they need. From a secure position in a corner, it is possible to lay claim to more territory by extending along the side of the board. The opening is the most theoretically difficult part of

6700-524: The game. If there were no resignations, the player with the most points wins. Hexagonal Go , like hexagonal chess , played on boards composed of hexagon cells, where each stone has up to six liberties. Other 2D variants can also be performed with edges joined in three other ways , resulting in a topological sphere , Klein bottle or real projective plane . Multiple boards can be used to form other Riemann surfaces . Go (board game) The playing pieces are called stones . One player uses

6800-412: The historical annal Zuo Zhuan ( c.  4th century BCE). Despite its relatively simple rules , Go is extremely complex. Compared to chess , Go has both a larger board with more scope for play and longer games and, on average, many more alternatives to consider per move. The number of legal board positions in Go has been calculated to be approximately 2.1 × 10 , which is far greater than

6900-417: The joining of Bat , meaning 'field', and Dok , meaning 'stone'. Less plausible etymologies include a derivation of Badukdok , referring to the playing pieces of the game, or a derivation from Chinese páizi ( 排子 ), meaning 'to arrange pieces'. Go is an adversarial game between two players with the objective of capturing territory. That is, occupying and surrounding a larger total empty area of

7000-475: The life of a large group, while others may be worth just one or two points. Some ko fights are referred to as picnic kos when only one side has a lot to lose. In Japanese, it is called a hanami ko. Playing with others usually requires a knowledge of each player's strength, indicated by the player's rank (increasing from 30 kyu to 1 kyu, then 1 dan to 7 dan, then 1 dan pro to 9 dan pro). A difference in rank may be compensated by

7100-509: 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. It is possible that one player may succeed in capturing a large weak group of the opponent's, which often proves decisive and ends the game by a resignation. However, matters may be more complex yet, with major trade-offs, apparently dead groups reviving, and skillful play to attack in such

7200-552: The name Go when used for the game is often capitalized to differentiate it from the common word go . In events sponsored by the Ing Chang-ki Foundation, it is spelled goe . The Korean name baduk (바둑) derives from the Middle Korean word Badok , the origin of which is controversial; the more plausible etymologies include the suffix dok added to Ba to mean 'flat and wide board', or

7300-400: The number of a player's stones on the board as well as the empty points completely surrounded by the players stones. The game ends when one player either resigns or both players pass on successive turns. In Coin Go , a stone cannot be played on certain intersections of the board by either player. A coin may be placed on these intersections as a visual aid. Stones adjacent to a coin do not have

7400-404: The online Go servers such as KGS Go Server , and board sizes from 2×2 to 38×38 are also allowed. The annual Milton Keynes Go Tournament has a popular side-event that is played on a stylised map of Milton Keynes. Its non-conventional lattice presents some interesting possibilities. Harald Schwarz invented a Go variant that is played on a circular lattice. Toroidal (or Torus Go) is played on

7500-448: 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 100 moves. During

7600-427: The opponent's weak groups (trying to kill them so they will be removed), and always stay mindful of the life status of one's own groups. The liberties of groups are countable. Situations where mutually opposing groups must capture each other or die are called capturing races, or semeai . In a capturing race, the group with more liberties will ultimately be able to capture the opponent's stones. Capturing races and

7700-481: The opponent. The player with the greater score (after adjusting for handicapping called komi ) wins the game. In the opening stages of the game, players typically establish groups of stones (or bases ) near the corners and around the sides of the board, usually starting on the third or fourth line in from the board edge rather than at the very edge of the board. The edges and corners make it easier to develop groups which have better options for life (self-viability for

7800-433: The outside, it can be killed with a stone placed in its single eye. (An eye is an empty point or group of points surrounded by a group of stones). The Ing and New Zealand rules do not have this rule, and there a player might destroy one of its own groups (commit suicide). This play would only be useful in limited sets of situations involving a small interior space or planning. In the example at right, it may be useful as

7900-413: The owner of the group is allowed the first move. Otherwise, the group is said to be unsettled: the defending player can make it alive or the opponent can kill it, depending on who gets to play first. An eye is an empty point or group of points surrounded by a group of stones. If the eye is surrounded by Black stones, White cannot play there unless such a play would take Black's last liberty and capture

8000-497: The player capturing the most stones wins. This variation is often called Atari Go in the West, where it is becoming increasingly popular as a preliminary means of introducing Go itself to beginners, since, afterward, it is natural to introduce the idea of capturing territory, not just the opponent's stones. In Stoical Go , invented by abstract game designer Luis Bolaños Mures, standard ko rules don't apply. Instead, it's illegal to make

8100-448: The player is told whether the intersection is occupied or there is illegal ko capture). The player is allowed to make another move. This is a crossover between rengo and shadow Go. There are two teams with two players each, a referee and five Go sets. The players move alternatingly as in rengo. Each player keeps track of their own moves on their own board; they are not informed about teammates' or opponents' moves. The referee keeps track of

8200-536: The players of the largest team playing fewer moves. Each team begins the game with an equal number of stones and shares these stones equally among its members. For instance, in a game of 3 players against 4, each team could get 12 (or 24) stones. Players from the 3-player team would get 4 (or 8) stones each while players from the 4-player team would get 3 (or 6) stones. Players then play their stones in no set order until both teams exhaust their stones and have to take 12 (or 24) new stones to distribute amongst themselves (this

8300-462: The players wager on the outcome of the game. A fixed stake (" bang ") is paid for every ten points on the board by which the loser is beaten. Batoo is a modern Korean variant. The name stems from a combination of the Korean words baduk and juntoo ("battle"). It is played entirely in cyberspace , and differs from standard Go in a number of ways, most noticeably in the way in which certain areas of

8400-422: The players, e.g. division of captured stones among neighbors, or forming alliances for adding up territory points. A variant called parallel multiplayer go also exists, where the moves are announced simultaneously. If two moves overlap, they count as passes. Paper and pencil go is a Go variant that can be played with just paper and pencil. Unlike standard Go, games played under these rules are guaranteed to end in

8500-431: The previous board position would not be allowed, and the next player would be forced to play somewhere else. If the play requires a strategic response by the first player, further changing the board, then the second player could "retake the ko," and the first player would be in the same situation of needing to change the board before trying to take the ko back. And so on. Some of these ko fights may be important and decide

8600-592: The purpose of late night after-club team play at the local Etoh bar. The variant later spread to the United States, Europe and Korea as it was demonstrated by Montreal players traveling to various tournaments (notably the European Go Congress of 2024 in Toulouse, France) and discovered by players visiting Montreal from abroad. The variant allows for teams of unequal size to enjoy a match without

8700-403: The referee can see them both and also has his/her own set. This variant is usually played on a 9×9 board. Players place stones on their boards, with no knowledge of what other players are doing. A referee keeps track of the game on the central board. If any player makes an illegal move, the referee informs them about it (some play that the referee says only that the move is illegal, while some, that

8800-412: The rules of Go (at least in simpler rule sets, such as those of New Zealand and the U.S.), the concept of a living group of stones is necessary for a practical understanding of the game. Examples of eyes (marked). The black groups at the top of the board are alive, as they have at least two eyes. The black groups at the bottom are dead as they only have one eye. The point marked a is a false eye, thus

8900-410: The same color form a chain (also called a string or group ), forming a discrete unit that cannot then be divided. Only stones connected to one another by the lines on the board create a chain; stones that are diagonally adjacent are not connected. Chains may be expanded by placing additional stones on adjacent intersections, and they can be connected together by placing a stone on an intersection that

9000-451: The same color would need to be added to the group, making either a group of 5 Black or 5 White stones. While the various rulesets agree on the ko rule prohibiting returning the board to an immediately previous position, they deal in different ways with the relatively uncommon situation in which a player might recreate a past position that is further removed. See Rules of Go § Repetition for further information. A player may not place

9100-405: The stones in an entangled pair. Block Go was a variant of Go played at the 20th Annual Computer Olympiad in which tetris pieces are utilized instead of go stones. In this variant, intersections at the opposite sides of the board are considered adjacent, like on a torus . Therefore, the playing board has no corners or sides and standard opening strategies that focus on capturing those parts of

9200-413: The surrounded player's next turn. If a player resigns, the two other players will determine who continues the game against the other two. That player will play alone, aiming to achieve a higher minimum score at the end of the game. At the end all captured stones and all stones on the board are counted. If the player reach his achieved goal, he wins. If the lone player doesn't reach the goal, the other two win

9300-411: The tactics and strategy of the game. Except where noted, the basic rules presented here are valid independent of the scoring rules used. The scoring rules are explained separately. Go terms for which there is no ready English equivalent are commonly called by their Japanese names. The two players, Black and White, take turns placing stones of their color on the intersections of the board, one stone at

9400-534: The team must play in turn, playing out of sequence will normally result in a small penalty (usually three prisoners). Partners may not consult on how to play, or engage in any form of signaling. Communication between partners may only take the following forms listed below. Micaël Go is a multiplayer variant originally designed in 2023 by a member of the André-Grasset College go club in Montreal, for

9500-401: The third line. White makes the first move. There is a unique ko rule: a stone may not be played at an intersection where the opponent has just removed a stone. This ko rule is so different from other major rulesets that it alone significantly changes the character of the game. For instance, snapbacks must be delayed by at least one move, allowing an opponent the chance to create life. Finally,

9600-452: The white stones and the other black. The players take turns placing their stones on the vacant intersections ( points ) on the board . Once placed, stones may not be moved, but captured stones are immediately removed from the board. A single stone (or connected group of stones) is captured when surrounded by the opponent's stones on all orthogonally adjacent points. The game proceeds until neither player wishes to make another move. When

9700-436: Was a Japanese colony. The similarity between Sunjang Baduk and modern go as well as Japanese influence encouraged players to switch to the modern game. The strength and fame of visiting Japanese professional go players encouraged Koreans to abandon Sunjang baduk. This was supported by the father of modern Korean go, Cho Nam-ch'eol , who established close links to Japan by studying go there. In another Korean variant, bangneki,

9800-763: Was born in Dover, Ohio . His family moved to Northern Kentucky, where Berlekamp graduated from Ft. Thomas Highlands high school in Ft. Thomas, Campbell county, Kentucky. While an undergraduate at the Massachusetts Institute of Technology (MIT), he was a Putnam Fellow in 1961. He completed his bachelor's and master's degrees in electrical engineering in 1962. Continuing his studies at MIT, he finished his Ph.D. in electrical engineering in 1964; his advisors were Robert G. Gallager , Peter Elias , Claude Shannon , and John Wozencraft . Berlekamp had two daughters and

9900-472: Was inspired by the need for a medium to address the problem of bullying in Japan, but soon found that "first capture" also works as an activity for senior citizens and even developmentally delayed individuals. He sees it as a game in its own right, not just as a prelude to Go, but also as a way to introduce simple concepts that lead to Go. For the latter purpose, he recommends progressing to "most capture", in which

10000-743: Was one of the inventors of the Berlekamp–Welch algorithm and the Berlekamp–Massey algorithms , which are used to implement Reed–Solomon error correction . He also co-invented the Berlekamp–Rabin algorithm , Berlekamp–Zassenhaus algorithm , and the Berlekamp–Van Lint–Seidel graph . Berlekamp had also been active in investing , and ran Axcom, which became the Renaissance Technologies ' Medallion Fund. Berlekamp

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