Go (game)

From Wikipedia, the free encyclopedia
  (Redirected from Go game)
Jump to: navigation, search
"Goe" redirects here. For other uses, see GOE (disambiguation).
This article is about weiqi. For other things named "Go", see Go (disambiguation).
Go
photograph of Go equipment with game in progress
Go is played on a grid of black lines (usually 19×19). Game pieces, called stones, are played on the line intersections.
Years active Zhou Dynasty (1046–256 BC) to present
Genre(s) Board game
Abstract strategy game
Players 2
Age range 3+[1][nb 1]
Setup time Minimal
Playing time Casual: 20–90 minutes
Tournament: 1–6 hours[a]
Random chance None
Skill(s) required Strategy, tactics, observation
Synonym(s) Igo
Baduk / Paduk
Weiqi ("way-chee")
a Some professional games exceed 16 hours and are played in sessions spread over two days.

Go (simplified Chinese: 围棋; traditional Chinese: 圍棋; pinyin: wéiqí, Japanese: 囲碁 igo,[nb 2] literal meaning: "encircling game", Korean: 바둑 baduk[nb 3]) is a board game involving two players that originated in ancient China more than 2,500 years ago. It was considered one of the four essential arts of a cultured Chinese scholar in antiquity. Its earliest written reference dates back to the Confucian Analects.

There is significant strategy and philosophy[2][3][4] involved in the game, and the number of possible games is vast (10761 compared, for example, to the 10120 possible in chess),[5] despite its relatively simple rules.

The two players alternately place black and white playing pieces, called "stones", on the vacant intersections ("points") of a board with a 19x19 grid of lines. Beginners often play on smaller 9×9 and 13×13 boards,[6] and archaeological evidence shows that game was played in earlier centuries on a board with a 17×17 grid. By the time the game had spread to Korea and Japan in about the 5th and 7th centuries AD respectively, however, boards with a 19×19 grid had become standard.[7]

The objective of the game—as the translation of its name implies—is to have surrounded a larger total area of the board with one's stones than the opponent by the end of the game,[8] although this result typically involves many more intricacies than simply using surrounding areas directly.

Once placed on the board, stones may not be moved, but stones may be removed from the board if captured—this is done by surrounding an opposing stone or group of stones by occupying all orthogonally-adjacent points.[9] The two players place stones alternately until they reach a point at which neither player wishes to make another move; the game has no set ending conditions beyond this. When a game concludes, the territory is counted along with captured stones and komi to determine the winner.[10] Games may also be won by resignation.

As of mid-2008, there were well over 40 million Go players worldwide, the overwhelming majority of them living in East Asia.[11] As of May 2012, the International Go Federation has a total of 74 member countries and four Association Members covering multiple countries.[12]

Overview[edit]

The first 60 moves of a Go game animated. This particular game quickly developed into a complicated fight in the lower left and bottom.(Click on the board, to restart the play, in a larger window.)

Go is an adversarial game with the objective of having surrounded a larger total area of the board with one's stones than the opponent. As the game progresses, the players place stones which map out formations and potential territories. Areas are contested in battles between opposing stones, which are often complex and may result in the expansion, reduction, or wholesale capture and loss of the contested area.

Games are often full of the possibility for "trades", where a player's gain in one part of the board is a disadvantage in another. Conversely, loss in one part of the board can be compensated for or mitigated by a gain in another part of the board. It is often the case that one player can forcefully gain an advantage locally which results in a larger, more global loss. These many possible "trades" form much of Go's complexity in strategy. Most prospective moves have many subtle advantages and pitfalls.

The four liberties (adjacent empty points) of a single black stone (A), as White reduces those liberties by one (B, C, and D). When Black has only one liberty left (D), that stone is "in atari".[13] White may capture that stone (remove from board) with a play on its last liberty (at D-1).

A basic principle of Go is that stones must have at least one "liberty" (Chinese: 氣) to remain on the board. "A liberty" is an open "point" (intersection) next to a stone.[9] An enclosed liberty (or liberties) is called an "eye" (眼), and a group of stones with at least two separate eyes is said to be unconditionally "alive".[14] Such groups cannot be captured, even if surrounded.[15] "Dead" stones are stones that are surrounded and in groups with poor shape (one or no eyes), and thus cannot resist eventual capture.[16]

The general strategy of Go is to expand one's territory where possible, attack the opponent's weak groups (groups that can possibly be killed), and always stay mindful of the "life status" of one's own groups.[17][18] The liberties of groups are countable. Situations where two opposing groups must capture the other to live are called capturing races ('semeai' [攻め合い] in Japanese).[19] In a capturing race, the group with more liberties (and/or better "shape") will ultimately be able to capture the opponent's stones.[19][20] Capturing races and questions of life and death are examples of what makes Go challenging.

The game ends when both players pass, and players pass when there are no more profitable moves to be made.[21] The game is then scored: The player with the greater number of controlled (surrounded) points, factoring in the number of captured stones and komi, wins the game.[22] Games may also be won by resignation, for example if a player has lost a large group of stones.

Finer points[edit]

In the opening stages of the game, players typically establish positions (or "bases") in the corners and around the sides of the board. These bases help to quickly develop strong shapes which have many options for life (self-viability for a group of stones which prevents capture and removal from the board) and establish formations for potential territory.[23] Players usually start in the corners, because it is more efficient to make life and to establish territory with the aid of two edges of the board.[24] Established corner opening sequences are called "joseki" (Japanese, 定石) or "jungsuk" (in Korean) and are often studied independently.[25]

"駄目" (pronounced [dame], 'neutral points') 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" (Chinese: 共活) are mutually alive pairs of white and black groups where neither has two eyes. A "ko" (Chinese and Japanese: 劫) is a repeated-position shape that may be contested by making forcing moves elsewhere. After the forcing move is played, the ko may be "taken back" and returned to its original position.[26] Some "ko fights" may be important and decide 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.[27] The Japanese call it a hanami (flower-viewing) ko.[28]

Playing with others usually requires a knowledge of each player's strength, as indicated by their rank (30kyu→1kyu|1dan→6dan|1dan pro→9dan pro). Handicaps can be given if there is a difference in rank—Black is allowed to place two or more stones on the board to compensate for White's greater strength.[29][30] There are different rule-sets (Japanese, Chinese, AGA, etc.), which are almost entirely equivalent, except for certain special-case positions.

Game theory[edit]

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.

Other game theoretical taxonomy elements include the facts that Go is finitely bounded (strictly speaking, because our lifetimes are finite); the strategy is associative (every strategy is a function of board position); format is non-cooperative (not a team sport); positions are extensible (can be represented by board position trees); game is zero-sum (player choices do not increase resources available–colloquially, rewards in the game are fixed and if one player wins, the other loses) and the utility function is restricted (in the sense of win/lose; however, ratings, monetary rewards, national and personal pride and other factors can extend utility functions, but generally not to the extent of removing the win/lose restriction). Affine transformations are beyond the scope of this article, but they can theoretically add non zero and complex utility aspects even to two player games (see the Maschler reference on go/chess that follows here, p. 111).[31]

Rules[edit]

Main article: Rules of Go

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:

  • Rule 1 (the rule of liberty) states that every stone remaining on the board must have at least one open "point" (an intersection, called a "liberty") directly next to it (up, down, left, or right), or must be part of a connected group that has at least one such open point ("liberty") next to it. Stones or groups of stones which lose their last liberty are removed from the board.
  • Rule 2 (the "ko rule") states that the stones on the board must never repeat a previous position of stones. Moves which would do so are forbidden, and thus only moves elsewhere on the board are permitted that turn.

Almost all other information about how the game is played is a heuristic, meaning it is learned information about how the game is played, rather than a rule. Other rules are specialized, as they come about through different rule-sets, but the above two rules cover almost all of any played game.

Although there are some minor differences between rule sets used in different countries,[32] most notably in Chinese and Japanese scoring rules,[33] these differences do not greatly affect the tactics and strategy of the game.

Except where noted otherwise, the basic rules presented here are valid independent of the scoring rules used. The scoring rules are explained separately. Go terms for which there are no ready English equivalent are commonly called by their Japanese names.

Basic rules[edit]

One black chain and two white chains, with their liberties marked with dots. Liberties are shared among all stones of a chain and can be counted. Here the black group has 5 liberties, while the two white chains have 4 liberties each.

Two players, Black and White, take turns placing a stone (game piece) of their own color on a vacant point (intersection) of the grid on a Go board. Black moves first. If there is a large difference in skill between the players, Black is typically allowed to place two or more stones on the board to compensate for the difference (see Go handicaps). The official grid comprises 19×19 lines, though the rules can be applied to any grid size. 13×13 and 9×9 boards are popular choices to teach beginners.[34] Once placed, a stone may not be moved to a different point.[35]

Vertically and horizontally adjacent stones of the same color form a chain (also called a string or group) that cannot subsequently be subdivided and, in effect, becomes a single larger stone.[36] 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 can be connected together by placing a stone on an intersection that is adjacent to two or more chains of the same color.

If White plays at A, the black chain loses its last liberty. It is captured and removed from the board.

A vacant point adjacent to a stone is called a liberty for that stone.[37][nb 4] 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.

The ko rule[edit]

Go ul.svg Go u.svg Go u.svg Go u.svg Go ur.svg
Go l.svg Go b.svg Go w.svg Go.svg Go r.svg
Go b.svg Go c.svg Go b1.svg Go w.svg Go r.svg
Go l.svg Go b.svg Go w.svg Go.svg Go r.svg
Go dl.svg Go d.svg Go d.svg Go d.svg Go dr.svg

An example of a situation in which the ko rule applies

Players are not allowed to make a move that returns the game to the previous position. This rule, called the ko rule (Chinese: 劫; Japanese: 劫 "eon", Korean: 패; 'pae'), prevents unending repetition.[38] As shown in the example pictured to the right: Black has just played the stone marked 1, capturing a white stone at the intersection marked with a circle. If White were now allowed to play on the marked intersection, that move would capture the black stone marked 1 and recreate the situation before Black made the move marked 1. Allowing this could result in an unending cycle of captures by both players. The ko rule therefore prohibits White from playing at the marked intersection immediately. Instead White must play elsewhere, or pass; Black can then end the ko by filling at the marked intersection, creating a five-stone black chain. If White wants to continue the ko (that specific repeating position), White tries to find a play elsewhere on the board that Black must answer; if Black answers, then White can retake the ko. A repetition of such exchanges is called a ko fight.[39]

While the various rule-sets 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.

Passing[edit]

Instead of placing a stone, a player may choose to pass. This usually occurs when they believe there are no more useful moves left. When both players pass consecutively, the game ends and is then scored.[40]

Suicide[edit]

Under normal rules, White cannot play at A because that point has no liberties. Under the Ing[41] and New Zealand rules,[42] White may play A (a ko threat), leaving an empty three-space eye. Black naturally answers by playing at A, creating two eyes.

A player may not place 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 latter case, the enemy group is captured, leaving the new stone with at least one liberty.[43] 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 the outside, it can be killed with a stone placed in its single eye.

The Ing and New Zealand rules do not have this rule,[44] and there a player might destroy one of its own groups—"commit suicide". This play would only be useful in a limited set of situations involving a small interior space.[45]

Komi[edit]

Main article: Komidashi

Because Black has the advantage of playing the first move, the idea of awarding White some compensation came into being during the 20th century. On a 19x19 goban this predetermined compensation, called "komidashi", ("komi") means that White may receive, say, 6.5 points compensation for Black's first move advantage.[46] If there is one stone (rank) difference in strength between players, the stronger player takes white, and White may receive only 0.5 points komi, to break a possible tie ("jigo"). In handicap games with two or more handicap stones, White may also take 0.5 points komi to break a tie but it is more common that there is no komi.[47]

Scoring rules[edit]

A simplified game at its end. Black's territory (A) is counted and compared to White's territory (B). In this example, both Black and White attempted to invade and live (C and D groups) to reduce the other's total territory. Only Black's invading group (C) was successful in living, as White's group (D) was killed with a black stone at E. The points in the middle (F) are "dame", meaning they belong to neither player.

Two general types of scoring system are used, and players determine which to use before play. Both systems almost always give the same result. Territory scoring counts the number of empty points a player's stones surround, together with the number of stones he captured. While it originated in China, today it is commonly associated with Japan and Korea where it became the game of nobleman and samurai.[48] Area scoring counts the number of points your stones occupy and surround. It is associated with contemporary Chinese play and was probably established there during the Ming Dynasty in the 15th or 16th century.[49]

After both players have passed consecutively, the stones that are still on the board but unable to avoid capture, called dead stones, are removed.

Area scoring (including Chinese): A player's score is the number of stones he has on the board, plus the number of empty intersections surrounded by that player's stones.

Territory scoring (including Japanese and Korean): In the course of the game, each player retains the stones they capture, termed prisoners. Any dead stones removed at the end of the game become prisoners. The score is the number of empty points enclosed by a player's stones, plus the number of prisoners captured by that player.[nb 5]

If there is disagreement about which stones are dead, then under area scoring rules, the players simply resume play to resolve the matter. The score is computed using the position after the next time the players pass consecutively. Under territory scoring, the rules are considerably more complex; however, in practice, players generally play on, and, once the status of each stone has been determined, return to the position at the time the first two consecutive passes occurred and remove the dead stones. For further information, see Rules of Go.

Given that the number of stones 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.[50]

Life and death[edit]

See also: Life and death

While not actually mentioned in 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.[51]

Go ulc.svg Go b.svg Go b.svg Go w.svg Go u.svg Go w.svg Go b.svg Go uc.svg Go b.svg
Go b.svg Go c.svg Go b.svg Go w.svg Go.svg Go w.svg Go b.svg Go b.svg Go rc.svg
Go b.svg Go b.svg Go w.svg Go w.svg Go.svg Go w.svg Go w.svg Go b.svg Go b.svg
Go w.svg Go w.svg Go w.svg Go.svg Go.svg Go.svg Go w.svg Go b.svg Go rc.svg
Go l.svg Go.svg Go.svg Go.svg Go.svg Go.svg Go w.svg Go b.svg Go b.svg
Go w.svg Go w.svg Go.svg Go.svg Go.svg Go.svg Go w.svg Go w.svg Go w.svg
Go b.svg Go w.svg Go w.svg Go w.svg Go w.svg Go.svg Go w.svg Go b.svg Go b.svg
Go A.svg Go b.svg Go b.svg Go b.svg Go w.svg Go.svg Go w.svg Go b.svg Go rc.svg
Go b.svg Go b.svg Go dc.svg Go b.svg Go w.svg Go d.svg Go w.svg Go b.svg Go b.svg

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.

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 the owner of the group is allowed the first move. Otherwise, the group is said to be unsettled: in such a situation, the player that moves first may be able to either make it alive if he is the owner, or kill it if he is the group owner's opponent.[51]

To be alive, a group must be able to create at least two "eyes" if threatened. An eye is an empty point that is surrounded by friendly stones, where the opponent can never play due to the suicide rule. If two such eyes exist, the opponent can never capture a group of stones, because it always has at least two liberties. One eye is not enough for life, because a point that would normally be suicide may be played upon if doing so fills the last liberty of opposing stones, thereby capturing those stones. 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 a black stone. Such a point is often called a false eye.[51]

Seki (mutual life)[edit]

Example of seki (mutual life). Neither Black nor White can play on the marked points without reducing their own liberties for those groups to one (self-atari).

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 player's 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.[nb 6]

Seki can occur in many ways. The simplest are: (1) each player has a group without eyes and they share two liberties, and (2) each player has a group with one eye and they share one more liberty. 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 is unusual, but can result from an attempt by one player to invade and kill a nearly settled group of the other player.[51]

Tactics[edit]

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.

Capturing tactics[edit]

There are several tactical constructs aimed at capturing stones.[52] These are among the first things a player learns after understanding the rules. Recognizing the possibility that stones can be captured using these techniques is an important step forward.

Go ul.svg Go u.svg Go u.svg Go u.svg Go u.svg Go u.svg Go u.svg Go u.svg Go u.svg
Go l.svg Go.svg Go w.svg Go.svg Go.svg Go.svg Go.svg Go.svg Go.svg
Go l.svg Go w.svg Go b.svg Go w.svg Go.svg Go.svg Go.svg Go.svg Go.svg
Go l.svg Go w.svg Go b1.svg Go b3.svg Go w4.svg Go.svg Go.svg Go.svg Go.svg
Go l.svg Go.svg Go w2.svg Go b5.svg Go b7.svg Go w8.svg Go.svg Go.svg Go.svg
Go l.svg Go.svg Go.svg Go w6.svg Go b9.svg Go.svg Go.svg Go.svg Go.svg
Go l.svg Go.svg Go.svg Go.svg Go 10.svg Go.svg Go.svg Go.svg Go.svg
Go l.svg Go.svg Go.svg Go.svg Go.svg Go.svg Go.svg Go.svg Go.svg
Go l.svg Go.svg Go.svg Go.svg Go.svg Go.svg Go.svg Go.svg Go.svg

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.[53] To capture stones in a ladder, a player uses a constant series of capture threats—called atari—to force the opponent into a zigzag pattern as shown in the diagram to the right. 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.

Go ul.svg Go u.svg Go u.svg Go u.svg Go u.svg Go u.svg Go u.svg Go u.svg Go u.svg
Go l.svg Go.svg Go b.svg Go.svg Go.svg Go.svg Go.svg Go.svg Go.svg
Go b.svg Go.svg Go b.svg Go w.svg Go w.svg Go.svg Go.svg Go.svg Go.svg
Go l.svg Go b.svg Go w.svg Go bT.svg Go w.svg Go.svg Go.svg Go.svg Go.svg
Go l.svg Go.svg Go w.svg Go bT.svg Go.svg Go.svg Go.svg Go.svg Go.svg
Go l.svg Go.svg Go w.svg Go bT.svg Go.svg Go.svg Go.svg Go.svg Go.svg
Go l.svg Go.svg Go w.svg Go.svg Go w1.svg Go.svg Go.svg Go.svg Go.svg
Go l.svg Go.svg Go.svg Go.svg Go.svg Go.svg Go.svg Go.svg Go.svg
Go l.svg Go.svg Go.svg Go.svg Go.svg Go.svg Go.svg Go.svg Go.svg

A net. The chain of three marked black stones cannot escape in any direction.

Another technique to capture stones is the so-called net,[54] 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 diagram to the left. 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.

Go ul.svg Go u.svg Go u.svg Go u.svg Go u.svg Go u.svg Go u.svg Go u.svg Go u.svg
Go l.svg Go.svg Go.svg Go b.svg Go b.svg Go.svg Go.svg Go.svg Go.svg
Go l.svg Go.svg Go b.svg Go.svg Go.svg Go.svg Go.svg Go.svg Go.svg
Go l.svg Go.svg Go b.svg Go w.svg Go w.svg Go.svg Go.svg Go.svg Go.svg
Go l.svg Go.svg Go w.svg Go b.svg Go c.svg Go w.svg Go.svg Go.svg Go.svg
Go l.svg Go.svg Go w.svg Go b.svg Go w1.svg Go b.svg Go b.svg Go.svg Go.svg
Go l.svg Go.svg Go.svg Go w.svg Go b.svg Go.svg Go.svg Go.svg Go.svg
Go l.svg Go.svg Go.svg Go w.svg Go b.svg Go.svg Go.svg Go.svg Go.svg
Go l.svg Go.svg Go.svg Go.svg Go b.svg Go.svg Go.svg Go.svg Go.svg

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.[55] In a snapback, one player allows a single stone to be captured, then immediately plays on the point formerly occupied by that stone; by so doing, the player captures a larger group of their opponent's stones, in effect snapping back at those stones. 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.

Reading ahead[edit]

One of the most important skills required for strong tactical play is the ability to read ahead.[56] Reading ahead includes considering available moves to play, the possible responses to each move, and the subsequent possibilities after each of those responses. Some of the strongest players of the game can read up to 40 moves ahead even in complicated positions.[57]

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.[58] In such problems, players are challenged to find the vital move sequence that kills a group of the opponent or saves a group of their own. Tsumego are considered an excellent way to train a player's ability at reading ahead,[58] and are available for all skill levels, some posing a challenge even to top players.

Ko fighting[edit]

A simplified ko fight on a 9×9 board. The ko is at the point marked with a square—Black has "taken the ko" first. The ko fight determines the life of the A and B groups—only one survives and the other is captured. White may play C as a ko threat, and Black properly answers at D. White can then "take the ko" by playing at the square-marked point (capturing the one black stone). E is a possible ko threat for Black.

In situations when the Ko rule applies, a ko fight may occur.[39] If the player who is prohibited from capture is of the opinion that the capture is important, because it prevents a large group of stones from being captured for instance, the player may play a ko threat.[39] This is a move elsewhere on the board that threatens to make a large profit if the opponent does not respond. 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.[39] They thereby win the ko, but at a cost. 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.[59]

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.[39] In some cases, this leads to another ko fight at a neighboring location.

Strategy[edit]

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.

Go is not easy to play well. With each new level comes a deeper appreciation for the subtlety and nuances involved and for the insight of stronger players. The acquisition of major concepts of the game comes slowly. Novices often start by randomly placing stones on the board, as if it were a game of chance; they inevitably lose to experienced players who know how to create effective formations. 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.[nb 7] It is necessary to play thousands of games before one can get close to one's ultimate potential skill level in Go. A player who both plays aggressively and can handle adversity is said to display kiai, or fighting spirit, in the game.

Familiarity with the board shows first the tactical importance of the edges, and then the efficiency of developing in the corners first, then sides, then center. The more advanced beginner understands that territory and influence are somewhat interchangeable—but there needs to be a balance. This intricate struggle of power and control makes the game highly dynamic.

Basic concepts[edit]

Main article: Go terms

Basic strategic aspects include the following:

  • Connection: Keeping one's own stones connected means that fewer groups need to make living shape, and one has fewer groups to defend.
  • Cut: Keeping opposing stones disconnected means that the opponent needs to defend and make living shape for more groups.
  • Stay alive: The simplest way to stay alive is to establish a foothold in the corner or along one of the sides. At a minimum, a group must have two eyes (separate open points) to be "alive". An opponent cannot fill in either eye, as any such move is suicidal and prohibited in the rules.
  • Mutual life (seki) is better than dying: A situation in which neither player can play on a particular point without then allowing the other player to play at another point to capture. The most common example is that of adjacent groups that share their last few liberties—if either player plays in the shared liberties, they can reduce their own group to a single liberty (putting themselves in atari), allowing their opponent to capture it on the next move.
  • Death: A group that lacks living shape is eventually removed from the board as captured.
  • Invasion: Set up a new living group inside an area where the opponent has greater influence, means one reduces the opponents score in proportion to the area one occupies.
  • Reduction: Placing a stone far enough into the opponent's area of influence to reduce the amount of territory they eventually get, but not so far in that it can be cut off from friendly stones outside.
  • Sente: A play that forces one's opponent to respond (gote). A player who can regularly play sente has the initiative and can control the flow of the game.
  • Sacrifice: Allowing a group to die in order to carry out a play, or plan, in a more important area.

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.

Opening strategy[edit]

In the opening of the game, players usually play in the corners of the board first, as the presence of two edges make it easier for them to surround territory and establish their stones.[60] After the corners, focus moves to the sides, where there is still one edge to support a player's stones. Opening moves are generally on the third and fourth line from the edge, with occasional moves on the second and fifth lines. In general, stones on the third line offer stability and are good defensive moves, whereas stones on the fourth line influence more of the board and are good attacking moves. The opening is the most difficult part of the game for professional players and takes a disproportionate amount of the playing time.[61]

In the opening, players often play established sequences called joseki, which are locally balanced exchanges;[62] 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.

Phases of the game[edit]

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 make it easier for them to surround territory and establish their stones.[63] From a secure position in a corner, it is possible to lay claim to more territory by extending along the side of the board.[64] The opening is the most theoretically difficult part of the game, and takes a large proportion of professional players' thinking time.[63]

The middle phase of the game is the most combative, and usually lasts for more than 100 moves. During the middlegame, the players invade each other's territories, and attack formations that lack the necessary two eyes for viability. Such groups be saved or sacrificed for something more significant on the board.[65] 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 a way as to construct territories rather than kill.[66]

The end of the middlegame and transition to the endgame is marked by a few features. The game breaks up into areas that do not affect each other (with a caveat about 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.

History[edit]

Go
Chinese name
Traditional Chinese 圍棋
Simplified Chinese 围棋
Literal meaning surround game
Tibetan name
Tibetan མིག་མངས
Korean name
Hangul 바둑
Japanese name
Kanji 碁, 囲碁 ("surround game")
Main article: History of Go
Woman Playing Go (Tang Dynasty c. 744), discovered at the Astana Graves

Origin in China[edit]

The earliest written reference to the game is generally recognized as the historical annal Zuo Zhuan[67][68] (c. 4th century BC),[69] referring to a historical event of 548 BC. It is also mentioned in Book XVII of the Analects of Confucius[69] and in two books written by Mencius[70][71] (c. 3rd century BC).[69] In all of these works, the game is referred to as (). Today, in China, it is known as weiqi (simplified Chinese: 围棋; traditional Chinese: 圍棋; pinyin: wéiqí; Wade–Giles: wei ch'i), literally the "encirclement board game".

Go was originally played on a 17×17 line grid, but a 19×19 grid became standard by the time of the Tang Dynasty (618–907).[72] Legends trace the origin of the game to the Chinese emperor Yao (2337–2258 BC), who said to have had his counselor Shun design it for his unruly son, Danzhu, to favorably influence him.[73] Other theories suggest that the game was derived from Chinese tribal warlords and generals, who used pieces of stone to map out attacking positions.[74][75]

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.[76]

Spread to Korea and Japan[edit]

Weiqi was introduced to Korea sometime between the 5th and 7th centuries CE, and was popular among the higher classes. In Korea, the game is called baduk (hangul: 바둑), and a variant of the game called Sunjang baduk was developed by the 16th century. Sunjang baduk became the main variant played in Korea until the end of the 19th century.[77][78]

Korean players, in traditional dress, play in a photograph dated between 1910 and 1920.

The game reached Japan in the 7th century CE—where it is called go (?) or igo (囲碁?)—the game became popular at the Japanese imperial court in the 8th century,[79] and among the general public by the 13th century.[80] In 1603, Tokugawa Ieyasu re-established Japan's unified national government. In the same year, he assigned the then-best player in Japan, a Buddhist monk named Nikkai (né Kanō Yosaburo, 1559), to the post of Godokoro (Minister of Go).[81] Nikkai took the name Honinbo Sansa and founded the Honinbo Go school.[81] Several competing schools were founded soon after.[81] These officially recognized and subsidized Go schools greatly developed the level of play and introduced the dan/kyu style system of ranking players.[82] Players from the four schools (Honinbo, Yasui, Inoue and Hayashi) competed in the annual castle games, played in the presence of the shogun.[83]

Go in the West[edit]

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 game.[84] By the early 20th century, Go had spread throughout the German and Austro-Hungarian empires. In 1905, Edward Lasker learned the game while in Berlin. When he moved to New York, Lasker founded the New York Go Club together with (amongst others) Arthur Smith, who had learned of the game while touring the East and had published the book The Game of Go in 1908.[85] Lasker's book Go and Go-moku (1934) helped spread the game throughout the U.S.,[85] and in 1935, the American Go Association was formed. Two years later, in 1937, the German Go Association was founded.

World War II put a stop to most Go activity, but after the war, Go continued to spread.[86] For most of the 20th century, the Japan Go Association (Nihon Ki-in) played a leading role in spreading Go outside East Asia by publishing the English-language magazine Go Review in the 1960s; establishing Go centers in the U.S., Europe and South America; and often sending professional teachers on tour to Western nations.[87] Internationally, the game is now commonly known by its shortened Japanese name, and terms for common Go concepts are derived from their Japanese pronunciation.

In 1996, NASA astronaut Daniel Barry and Japanese astronaut Koichi Wakata became the first people to play Go in space. They used a special Go set, which was named Go Space, designed by Wai-Cheung Willson Chow.[88] Both astronauts were awarded honorary dan ranks by the Nihon Ki-in.[88]

As of May 2012, the International Go Federation has 57 member countries outside Asia.[12]

Competitive play[edit]

Ranks and ratings[edit]

Main article: Go ranks and ratings
Three Japanese professional Go players observe some younger amateurs as they dissect a life and death problem in the corner of the board, at the US Go Congress in Houston, Texas, 2003.

In Go, rank indicates a player's skill in the game. Traditionally, ranks are measured using kyu and dan grades,[89] a system also adopted by many martial arts. More recently, mathematical rating systems similar to the Elo rating system have been introduced.[90] Such rating systems often provide a mechanism for converting a rating to a kyu or dan grade.[90] Kyu grades (abbreviated k) are considered student grades and decrease as playing level increases, meaning 1st kyu is the strongest available kyu grade. 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.[91] Professional players have professional dan ranks (abbreviated p). These ranks are separate from amateur ranks.

The rank system comprises, from the lowest to highest ranks:

Rank Type Range Stage
Double-digit kyu 30–21k Beginner
Double-digit kyu 20–10k Casual player
Single-digit kyu 9–1k Intermediate/club player
Amateur dan 1–7d (where 8d is special title) Advanced player
Professional dan 1–9p (where 10p is special title) Professionals

Tournament and match rules[edit]

See also: Go competitions

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,[92] 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.[93]

Tournament rules may also set the following:

  • compensation points, called komi, which compensate the second player for the first move advantage of his opponent; tournaments commonly use a compensation in the range of 5–8 points,[94] generally including a half-point to prevent draws;
  • handicap stones placed on the board before alternate play, allowing players of different strengths to play competitively (see Go handicap for more information); and
  • superko: Although the basic ko rule described above covers more than 95% of all cycles occurring in games,[95] there are some complex situations—triple ko, eternal life,[nb 8] etc.—that are not covered by it but would allow the game to cycle indefinitely. To prevent this, the ko rule is sometimes extended to disallow the repetition of any previous position. This extension is called superko.[95]

Top players and professional go[edit]

A Go professional is a professional player of the game of Go. There are five countries with professional go associations, these are: China (China Qiyuan), Japan (Nihon Ki-in, Kansai Ki-in), Korea (Korea Baduk Association), Taiwan (Taiwan Chi Yuan Culture Foundation) and the United States (AGA Professional System).

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). The only three players to receive this honor were Dosaku, Jowa and Shusaku, all of the house Honinbo.[96]

Honinbo Shusai (left), last head of house Honinbo, plays against then-up-and-coming Go Seigen in the game of the century.

After the end of the Tokugawa shogunate and the Meiji Restoration period, the Go houses slowly disappeared, and in 1924, the Nihon Ki-in (Japanese Go Association) was formed. Top players from this period often played newspaper-sponsored matches of 2–10 games.[97] Of special note are the (Chinese-born) player Go Seigen (Chinese: Wu Qingyuan), who scored 80% in these matches,[98] and Minoru Kitani, who dominated matches in the early 1930s.[99] These two players are also recognized for their groundbreaking work on new opening theory (Shinfuseki).[100]

For much of the 20th century, Go continued to be dominated by players trained in Japan. Notable names included Eio Sakata, Rin Kaiho (born in China), Masao Kato, Koichi Kobayashi and Cho Chikun (born Cho Ch'i-hun, South Korea).[101] Top Chinese and Korean talents often moved to Japan, because the level of play there was high and funding was more lavish. One of the first Korean players to do so was Cho Namchul, who studied in the Kitani Dojo 1937–1944. 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.[102] In China, the game declined during the Cultural Revolution (1966–1976) but quickly recovered in the last quarter of the 20th century, bringing Chinese players, such as Nie Weiping and Ma Xiaochun, on par with their Japanese and Korean counterparts.[103] The Chinese Weiqi Association (today part of the China Qiyuan) was established in 1962, professional dan grades started being issued in 1982.[104]

Korean player Lee Chang-ho, regarded by many as one of the best modern Go players, plays against Russian player Alexandre Dinerchtein, seven-time European Champion and one of the few Western players to reach professional status.

With the advent of major international titles from 1989 onward, it became possible to compare the level of players from different countries more accurately. Korean players such as Lee Chang-ho, Cho Hunhyun, Lee Sedol and Yoo Changhyuk dominated international Go and won many titles.[105] Several Chinese players also rose to the top in international Go, most notably Ma Xiaochun, Chang Hao and Gu Li. As of 2013, Japan lags behind in the international Go scene.

Historically, as with most sports and games, 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.[106]

The level in other countries has traditionally been much lower, except for some players who had preparatory professional training in Asia.[nb 9] Knowledge of the game has been scant elsewhere up until the 20th century. A famous player of the 1920s was Edward Lasker.[nb 10] It was not until the 1950s that more than a few Western players took up the game as other than a passing interest. In 1978, Manfred Wimmer became the first Westerner to receive a professional player's certificate from an Asian professional Go association.[107] In 2000, a Westerner, Michael Redmond, finally achieved the top rank awarded by an Asian Go association, 9 dan. In total, as of 2008, only nine non-Asian Go players have ever achieved professional status in Asian associations.

Equipment[edit]

Main article: Go equipment
A traditional Japanese set, with a solid wooden floor board (碁盤 goban), 2 bowls (碁笥 goke) and 361 stones (碁石 goishi)

It is possible to play Go with a simple paper board and coins or plastic tokens for the stones. 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.

Traditional equipment[edit]

Boards[edit]

The Go board (generally referred to by its Chinese name goban (碁盤)) typically measures between 45 and 48 cm (18 and 19 in) in length (from one player's side to the other) and 42 to 44 cm (17 to 17 in) in width. Chinese boards are slightly larger, as a traditional Chinese Go stone is slightly larger to match. The board is not square; there is a 15:14 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.[108] There are two main types of boards: a table board similar in most respects to other gameboards like that used for chess, and a floor board, which is its own free-standing table and at which the players sit.

The traditional Japanese goban is between 10 and 18 cm (3.9 and 7.1 in) thick and has legs; it sits on the floor (see picture).[108] It is preferably made from the rare golden-tinged Kaya tree (Torreya nucifera), with the very best made from Kaya trees up to 700 years old. 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. nucifera and T. californica take many hundreds of years to grow to the necessary size, and they are now extremely rare, raising the price of such equipment tremendously.[109] As Kaya trees are a protected species in Japan, they cannot be harvested until they have died. Thus, an old-growth, floor-standing Kaya goban can easily cost in excess of $10,000 with the highest-quality examples costing more than $60,000.[110]

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).[109] So-called Shin Kaya is a potentially confusing merchant's term: shin means "new", and thus shin kaya is best translated "faux kaya", because the woods so described are biologically unrelated to Kaya.[109]

Stones[edit]

A full set of Go stones (goishi) usually contains 181 black stones and 180 white ones; a 19×19 grid has 361 points, so there are enough stones to cover the board, and Black gets the extra odd stone because that player goes first.

Traditional Japanese stones are double-convex, and made of clamshell (white) and slate (black).[111] The classic slate is nachiguro stone mined in Wakayama Prefecture and the clamshell from the Hamaguri clam; however, due to a scarcity in the Japanese supply of this clam, the stones are most often made of shells harvested from Mexico.[111] Historically, the most prized stones were made of jade, often given to the reigning emperor as a gift.[111]

In China, the game is traditionally played with single-convex stones[111] 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 1920s during the Chinese Civil War, was rediscovered in the 1960s by the now state-run Yunzi company. The material is praised for its colors, its pleasing sound as compared to glass or to synthetics such as melamine, and its lower cost as opposed to other materials such as slate/shell. 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.[111][nb 11]

An example of single-convex stones and Go Seigen bowls. These particular stones are made of Yunzi material, and the bowls of jujube wood.

Bowls[edit]

The bowls for the stones are shaped like a flattened sphere with a level underside.[112] The lid is loose fitting and upturned before play to receive stones captured during the game. 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".[96]

Playing technique and etiquette[edit]

Go players in Shanghai demonstrate the traditional technique of holding a stone.

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.[113] One can also place a stone on the board and then slide it into position under appropriate circumstances (where it does not move any other stones). It is considered respectful towards White for Black to place the first stone of the game in the upper right-hand corner.[114] (Because of symmetry, this has no effect on the game's outcome.)

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.

Time control[edit]

See also: Time control and Byoyomi

A game of Go may be timed using a game clock. Formal time controls were introduced into the professional game during the 1920s and were controversial.[115] Adjournments and sealed moves began to be regulated in the 1930s. 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.[nb 12] The most widely used time control system is the so-called byoyomi[nb 13] system. 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:[116]

  • Standard byoyomi: After the main time is depleted, a player has a certain number of time periods (typically around thirty seconds). After each move, the number of full-time periods that the player took (often zero) is subtracted. For example, if a player has three thirty-second time periods and takes thirty or more (but less than sixty) seconds to make a move, they lose one time period. With 60–89 seconds, they lose two time periods, and so on. If, however, they take less than thirty seconds, the timer simply resets without subtracting any periods. Using up the last period means that the player has lost on time.
  • Canadian byoyomi: After using all of their main time, a player must make a certain number of moves within a certain period of time, such as twenty moves within five minutes.[116][nb 14] If the time period expires without the required number of stones having been played, then the player has lost on time.[nb 15]

Notation and recording games[edit]

See also: Kifu

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 (4-4 point), hybrid (K3), and purely alphabetical.[117] The Smart Game Format uses alphabetical coordinates internally, but most editors represent the board with hybrid coordinates as this reduces confusion. The Japanese word kifu is sometimes used to refer to a game record.

In Unicode, Go stones are encoded in the block Miscellaneous Symbols:

  • U+2686 white circle with dot right (HTML: ⚆)[118]
  • U+2687 white circle with two dots (HTML: ⚇)
  • U+2688 black circle with dot right (HTML: ⚈)
  • U+2689 black circle with two dots (HTML: ⚉)

Computers and Go[edit]

Nature of the game[edit]

In combinatorial game theory terms, Go is a zero-sum, perfect-information, partisan, deterministic strategy game, putting it in the same class as chess, checkers (draughts) and Reversi (Othello); however it differs from these in its game play. Although the rules are simple, the practical strategy is extremely 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.[119] Its large board and lack of restrictions allow great scope in strategy and expression of players' individuality. 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.[nb 16]

Software players[edit]

Main article: Computer Go

Go poses a daunting challenge to computer programmers. The best Go programs only manage to reach amateur dan level.[120] On the small 9×9 board, the computer fares better, and some programs now win a fraction of their 9×9 games against professional players. Many in the field of artificial intelligence consider Go to require more elements that mimic human thought than chess.[121]

A finished beginner's game on a 13×13 board. Go software can reach stronger levels on a smaller board size.

The reasons why computer programs do not play Go at the professional dan level include:[122]

  • The number of spaces on the board is much larger (over five times the number of spaces on a chess board—361 vs. 64). On most turns there are many more possible moves in Go than in chess. Throughout most of the game, the number of legal moves stays at around 150–250 per turn, and rarely falls below 50 (in chess, the average number of moves is 37).[123] Because an exhaustive computer program for Go must calculate and compare every possible legal move in each ply (player turn), its ability to calculate the best plays is sharply reduced when there are a large number of possible moves. Most computer game algorithms, such as those for chess, compute several moves in advance. Given an average of 200 available moves through most of the game, for a computer to calculate its next move by exhaustively anticipating the next four moves of each possible play (two of its own and two of its opponent's), it would have to consider more than 320 billion (3.2×1011) possible combinations. To exhaustively calculate the next eight moves, would require computing 512 quintillion (5.12×1020) possible combinations. As of March 2014, the most powerful supercomputer in the world, NUDT's "Tianhe-2", can sustain 33.86 petaflops.[124] At this rate, even given an exceedingly low estimate of 10 operations required to assess the value of one play of a stone, Tianhe-2 would require 4 hours, to assess all possible combinations of the next eight moves in order to make a single play.
  • The placement of a single stone in the initial phase can affect the play of the game a hundred or more moves later. A computer would have to predict this influence, and it would be unworkable to attempt to exhaustively analyze the next hundred moves.
  • In capture-based games (such as chess), a position can often be evaluated relatively easily, such as by calculating who has a material advantage or more active pieces.[nb 17] In Go, there is often no easy way to evaluate a position.[125] However a 6-kyu human can evaluate a position at a glance, to see which player has more territory, and even beginners can estimate the score within 10 points, given time to count it. The number of stones on the board (material advantage) is only a weak indicator of the strength of a position, and a territorial advantage (more empty points surrounded) for one player might be compensated by the opponent's strong positions and influence all over the board. Normally a 3-dan can easily judge most of these positions.

As an illustration, the greatest handicap normally given to a weaker opponent is 9 stones. It was not until August 2008 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.[126][127]

Software assistance[edit]

Main article: Go software
A 9×9 game with graphical aids. Colors and markings show evaluations by the computer assistant.

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[128] 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.[nb 18]

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. Such software generally lists common follow-up moves that have been played by professionals and gives statistics on win/loss ratio in opening situations.

Internet-based Go servers allow access to competition with players all over the world, for real-time and turn-based games.[nb 19] Such servers also allow easy access to professional teaching, with both teaching games and interactive game review being possible.[nb 20]

In popular culture and science[edit]

Apart from technical literature and study material, Go and its strategies have been the subject of several works of fiction, such as The Master of Go by Nobel prize-winning author Yasunari Kawabata[nb 21] and The Girl Who Played Go by Shan Sa. Other books have used Go as a theme or minor plot device. For example, the novel Shibumi by Trevanian centers around the game and uses Go metaphors,[129] and The Way of Go: 8 Ancient Strategy Secrets for Success in Business and Life by Troy Anderson applies Go strategy to business.[130] GO: An Asian Paradigm for Business Strategy[131] by Miura Yasuyuki, a manager with Japan Airlines,[132] uses Go to describe the thinking and behavior of business men.[133]

Of particular note is the manga (Japanese comic book) and anime series Hikaru no Go, released in Japan in 1998, which had a large impact in popularizing Go among young players, both in Japan and—as translations were released—abroad.[134][135] Go Player is a similar animated series about young Go players that aired in China.

Similarly, Go has been used as a subject or plot device in film, such as π, A Beautiful Mind, Tron: Legacy, and The Go Master, a biopic of Go professional Go Seigen.[136][nb 22] 2013's Tôkyô ni kita bakari or Tokyo Newcomer portrays a Chinese foreigner Go player moving to Tokyo.[137] In King Hu's wuxia film The Valiant Ones, the characters are color-coded as Go stones (black or other dark shades for the Chinese, white for the Japanese invaders), Go boards and stones are used by the characters to keep track of soldiers prior to battle, and the battles themselves are structured like a game of Go.[138]

The corporation and brand Atari was named after the Go term.[139]

Psychology[edit]

A 2004 review of literature by Fernand Gobet, de Voogt & Retschitzki[140] shows that relatively little scientific research has been carried out on the psychology of Go, compared with other traditional board games such as chess and Mancala. Computer Go research has shown that given the large search tree, knowledge and pattern recognition are more important in Go than in other strategy games, such as chess.[140] A study of the effects of age on Go-playing[141] has shown that mental decline is milder with strong players than with weaker players. 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.[142] showed greater activation in the right hemisphere among Go players than among chess players. There is some evidence to suggest a correlation between playing board games and reduced risk of Alzheimer's disease and dementia.[143]

Comparisons[edit]

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 kill one individual piece (the king). This comparison has also been applied to military and political history, with Scott Boorman's 1969 book The Protracted Game exploring the strategy of the Communist Party of China in the Chinese Civil War through the lens of Go.[144]

A similar comparison has been drawn among Go, chess and backgammon, perhaps the three oldest games that enjoy worldwide popularity.[145] Backgammon is a "man vs. fate" contest, with chance playing a strong role in determining the outcome. Chess, with rows of soldiers marching forward to capture each other, embodies the conflict of "man vs. man". 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. self".[145]

See also[edit]

Notes[edit]

  1. ^ Children below a certain age may swallow or choke on stones.
  2. ^ The full Japanese name igo is derived from its Chinese name weiqi, which roughly translates as "board game of surrounding"; see Etymology Of Go at Sensei's Library for more information. To differentiate the game Go from the common English verb to go, it is generally capitalized (Gao 2007) or, in events sponsored by the Ing Foundation, spelled goe.
  3. ^ The Korean word 'baduk' derives from the Middle Korean word 'Badok', the meaning of which is controversial; the more plausible etymologies include the suffix '-ok' added to 'Bad' creating the meaning 'flat and wide board', or the joining of 'Bad', 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 排子, meaning 'to arrange pieces'.See 조, 항범 (October 8, 2005). 그런 우리말은 없다. 태학사. ISBN 9788959660148. Retrieved June 3, 2014. 
  4. ^ Compare "liberty", a small local government unit in medieval England – the "local area under control".
  5. ^ Exceptionally, in Japanese and Korean rules, empty points, even those surrounded by stones of a single color, may count as neutral territory if some of them are alive by seki. See the section on "Life and Death" for seki.
  6. ^ In game theoretical terms, seki positions are an example of a Nash equilibrium.
  7. ^ Whether or not a group is weak or strong refers to the ease with which it can be killed or made to live. See this article by Benjamin Teuber, amateur 6 dan, for some views on how important this is felt to be.
  8. ^ A full explanation of the eternal life position can be found on Sensei's Library, it also appears in the official text for Japanese Rules, see translation.
  9. ^ Kaku Takagawa toured Europe around 1970, and reported (Go Review) a general standard of amateur 4 dan. This is a good amateur level but no more than might be found in ordinary Asian clubs. Published current European ratings would suggest around 100 players stronger than that, with very few European 7 dans.
  10. ^ European Go has been documented by Franco Pratesi, Eurogo (Florence 2003) in three volumes, up to 1920, 1920–1950, and 1950 and later.
  11. ^ See Overshoot in Western typography for similar subtle adjustment to create a uniform appearance.
  12. ^ Roughly, one has the time to play the game and then a little time to finish it off. Time-wasting tactics are possible in Go, so that sudden death systems, in which time runs out at a predetermined point however many plays are in the game, are relatively unpopular (in the West).
  13. ^ Literally in Japanese byōyomi means 'reading of seconds'.
  14. ^ Typically, players stop the clock, and the player in overtime sets his/her clock for the desired interval, counts out the required number of stones and sets the remaining stones out of reach, so as not to become confused. If twenty moves are made in time, the timer is reset to five minutes again.
  15. ^ In other words, Canadian byoyomi is essentially a standard chess-style time control, based on N moves in a time period T, imposed after a main period is used up. It is possible to decrease T, or increase N, as each overtime period expires; but systems with constant T and N, for example 20 plays in 5 minutes, are widely used.
  16. ^ The number of board positions is at most 3361 (about 10172) since each position can be white, black, or vacant. Ignoring (illegal) suicide moves, there are at least 361! games (about 10768) since every permutation of the board positions corresponds to a game. See Go and mathematics for more details, which includes much larger estimates.
  17. ^ While chess position evaluation is simpler than Go position evaluation, it is still more complicated than simply calculating material advantage or piece activity; pawn structure and king safety matter, as do the possibilities in further play. The complexity of the algorithm differs per engine.
  18. ^ Lists of such programs may be found at Sensei's Library or GoBase.
  19. ^ Lists of Go servers are kept at Sensei's Library and the AGA website
  20. ^ The British Go Association provides a list of teaching services
  21. ^ A list of books can be found at Sensei's Library
  22. ^ A list of films can de found at the EGF Internet Go Filmography

References[edit]

Citations[edit]

  1. ^ "Info for School Teachers and other Youth Go Organisers". British Go Association. Who can play go?. Retrieved 2011-08-10. 
  2. ^ "Great Quotes: Sensei's Library". "The board is a mirror of the mind of the players as the moments pass. When a master studies the record of a game he can tell at what point greed overtook the pupil, when he became tired, when he fell into stupidity, and when the maid came by with tea. ". Retrieved 31 August 2014. 
  3. ^ "Go and Martial Arts". Sensei's Library. Retrieved 31 August 2014. 
  4. ^ "Harmony". Sensei's Library. 
  5. ^ "OMNI Magazine" (June 1991). 
  6. ^ Matthews, Charles. Teach Yourself Go, p.1
  7. ^ Cho Chikun, p.18
  8. ^ Matthews, Charles. Teach Yourself Go, p.2
  9. ^ a b Iwamoto, p.22
  10. ^ Iwamoto, p.18
  11. ^ About the IGF, retrieved June 5, 2012 
  12. ^ a b International Go Federation, IGF members, retrieved June 5, 2012 
  13. ^ Cobb p.12
  14. ^ Cho Chikun, p.21
  15. ^ Iwamoto, p.77
  16. ^ Cho Chikun, p.27
  17. ^ Cho Chikun, p.28
  18. ^ Cobb p.21
  19. ^ a b Cho Chikun, p.69
  20. ^ Cobb p.20
  21. ^ Cho Chikun, p.35
  22. ^ "KGS Go Tutorial: Game End". KGS. Retrieved 5 June 2014. 
  23. ^ Cho Chikun, p.107
  24. ^ Iwamoto, p.93
  25. ^ Cho Chikun, p.119
  26. ^ Cho Chikun, p.33
  27. ^ Cho Chikun, p.37
  28. ^ "Hanami Ko at Sensei's Library". Senseis.xmp.net. 2013-01-09. Retrieved 2014-03-25. 
  29. ^ Iwamoto, p.109
  30. ^ Cho Chikun, p.91
  31. ^ Maschler, Michael (2013). Game Theory. Cambridge University Press. ISBN 978-1-107-00548-8. [page needed]
  32. ^ British Go Association, Comparison of some go rules, retrieved 2007-12-20 
  33. ^ NRICH Team, Going First, University of Cambridge, retrieved 2007-06-16 
  34. ^ Kim 1994 pp. 3–4
  35. ^ How to place Go stones, Nihon Kiin, retrieved 2007-03-04 
  36. ^ Matthews, Charles, Behind the Rules of Go, University of Cambridge, retrieved 2008-06-09 
  37. ^ Kim 1994 p. 12
  38. ^ Kim 1994 pp 48–49
  39. ^ a b c d e Kim 1994 pp. 144–147
  40. ^ "KGS Go Tutorial: Game End". KGS. Retrieved 24 May 2014. 
  41. ^ Ing rules of Go, translation archived by American Go Association website [1], retrieved 5 August 2012
  42. ^ American Go Association Rules of Go. [2] retrieved 5 August 2012
  43. ^ Kim 1994 p. 30
  44. ^ "Comparison of Some Go Rules". British Go association. Retrieved 15 May 2014. 
  45. ^ Kim 1994 p. 28
  46. ^ "A change in Komi". Retrieved 31 May 2014. 
  47. ^ "Life in 9x9: What is a reasonable komi value? • Life In 19x19". Retrieved 31 May 2014. 
  48. ^ The Game of Go, 361 pointes, retrieved 2014-05-06 
  49. ^ Fairbairn, John, "The Rules Debate", New in Go, Games of Go on Disc, retrieved 2007-11-27 
  50. ^ Hansen, Fred, Demonstration of the Relationship of Area and Territory Scoring, American Go Association, retrieved 2008-06-16 
  51. ^ a b c d Matthews 2002[page needed]
  52. ^ Kim 1994 pp. 80–98
  53. ^ Kim 1994 pp. 88–90
  54. ^ Kim 1994 pp. 91–92
  55. ^ Kim 1994 pp. 93–94
  56. ^ Davies, James (1995). Tesuji. Elementary Go Series 3. Kiseido Publishing Company. p. 5. ISBN 4-906574-12-2. 
  57. ^ Nakayama, Noriyuki (1984), "Memories of Kitani", The Treasure Chest Enigma, Slate & Shell, pp. 16–19, ISBN 1-932001-27-1 
  58. ^ a b van Zeijst, Rob, Whenever a player asks a top professional ..., Yomiuri Shimbun, retrieved 2008-06-09 
  59. ^ Tavernier, Karel (Spring 1998). "Analyzing Ko Struggles Theoretically". British Go Journal Nr. 110, Spring 1998, page 11. Retrieved 8 October 2013. 
  60. ^ Otake, Hideo (2002), Opening Theory Made Easy, Kiseido Publishing Company, ISBN 4-906574-36-X 
  61. ^ Ishigure, Ikuro (2006). In the Beginning: the Opening in the Game of Go. Elementary Go Series 1 (8 ed.). Japan: Kiseido Publishing Company. p. 6. ISBN 4-906574-10-6. 
  62. ^ Ishida, Yoshio (1977), Dictionary of Basic Joseki, Kiseido Publishing Company 
  63. ^ a b In the Beginning (Beginner and Elementary Go Books). ISBN 978-4906574100. 
  64. ^ Risuke, Otake. Le Sabre et le Divin: Héritage spirituel de la Tenshin Shoden Katori Shint Ryu (in French). p. 2. ISBN 978-2846170031. 
  65. ^ David, Ormerod. "Thinking big in Go". GoGameGuru. Retrieved 5 June 2014. 
  66. ^ David, Ormerod. "Go technique: Induction in the game of Go". GoGameGuru. Retrieved 5 June 2014. 
  67. ^ Burton, Watson (April 15, 1992). The Tso Chuan (reprint ed.). ISBN 978-0231067157. 
  68. ^ Fairbairn 1995[page needed]
  69. ^ a b c Brooks 2007[page needed]
  70. ^ Potter 1984[page needed]
  71. ^ Fairbairn 1995[page needed]
  72. ^ Fairbairn 1995[page needed]
  73. ^ Yang, Lihui; Deming An, Jessica Anderson Turner (2005), Handbook of Chinese mythology, ABC-CLIO Ltd, p. 228, ISBN 978-1-57607-806-8 
  74. ^ Masayoshi 2005[page needed]
  75. ^ Lasker 1934[page needed]
  76. ^ Pickard 1989[page needed]
  77. ^ History of Korean baduk, Korean Baduk Association, retrieved 2008-11-13 
  78. ^ Fairbairn 2000[page needed]
  79. ^ History of Go in Japan: part 2, Nihon Kiin, retrieved 2007-11-02 
  80. ^ History of Go in Japan: part 3, Nihon Kiin, retrieved 2007-11-02 
  81. ^ a b c GoGoD (Fairbairn & Hall) (2007), "Timeline 1600–1867", History and Timelines 
  82. ^ GoGoD (Fairbairn & Hall) (2007), "Honinbo Dosaku", Articles on Famous Players [page needed]
  83. ^ GoGoD (Fairbairn & Hall) (2007), "Castle Games 1626–1863", History and Timelines [page needed]
  84. ^ Pinckard, William (1992), History and Philosophy of Go  in Bozulich, 2001 pp. 23–25
  85. ^ a b AGA 1995 Historical Book, American Go Association, retrieved 2008-06-11 
  86. ^ Bozulich, Richard, The Magic of Go – 40. Go in Europe, Yomiuri Shimbun, archived from the original on 2004-10-11, retrieved 2008-06-16 
  87. ^ British Go Association, Pro Go Player visits to UK & Ireland (since 1964), retrieved 2007-11-17 
  88. ^ a b Peng & Hall 1996[page needed]
  89. ^ Go. The World's Most Fascinating Game, Tokyo, Japan: Nihon Kiin, 1973, p. 188 
  90. ^ a b Cieply, Ales, EGF Official Ratings, European Go Federation (EGF), retrieved 2009-11-06 
  91. ^ EGF Tournament Database, Association for Go in Italy (AGI), retrieved 2008-06-19 
  92. ^ The McMahon system in a nutshell, British Go Association, archived from the original on 2008-05-18, retrieved 2008-06-11 
  93. ^ GoGoD (Fairbairn & Hall) (2007), A quick guide to pro tournaments [page needed]
  94. ^ GoGoD (Fairbairn & Hall) (2007), "History of Komi", History and Timelines [page needed]
  95. ^ a b Jasiek, Robert (2001), Ko Rules, retrieved 2007-11-30 
  96. ^ a b Fairbairn, John. "MindZine - Go - Feature: Honinbo Jowa". Mind Sports WorldWide. Archived from the original on 9 July 2011. Retrieved 15 May 2014. 
  97. ^ Fairbairn, John, History of Newspaper Go, retrieved 2007-06-14 
  98. ^ Go Seigen: Match Player, GoBase.org, retrieved 2007-06-14 
  99. ^ Fairbairn, John, Kitani's Streak, retrieved 2007-06-14 
  100. ^ Fairbairn, John, Kubomatsu's central thesis, retrieved 2008-01-17 
  101. ^ List of Japanese titles, prizemoney and winners, GoBase.org, retrieved 2008-06-11 
  102. ^ Kim, Janice, KBA Founder Cho Nam Chul passes, American Go Association, retrieved 2008-06-11 
  103. ^ Matthews, Charles, Weiqi in Chinese Culture, retrieved 2007-06-04 
  104. ^ Go The Board Game, retrieved 2008-06-11 
  105. ^ List of International titles, prizemoney and winners, GoBase.org, retrieved 2008-06-11 
  106. ^ Shotwell, Peter (2003), Go! More Than a Game, Tuttle Publishing, ISBN 0-8048-3475-X 
  107. ^ Wimmer, Kerwin, Make Professional Shodan, British Go Association, retrieved 2008-06-11 
  108. ^ a b Fairbairn 1992 pp. 142–143
  109. ^ a b c Fairbairn 1992 pp. 143–149
  110. ^ Kiseido clearance sale  lists the regular price for a Shihomasa Kaya Go Board with legs (20.4 cm or 8.0 in thick) as $60,000+
  111. ^ a b c d e Fairbairn 1992 pp. 150–153
  112. ^ Fairbairn 1992 pp. 153–155
  113. ^ A stylish way to play your stones, Nihon Ki-in, retrieved 2007-02-24 
  114. ^ "Sensei's Library: Playing the first move in the upper right corner". Senseis.xmp.net. 2011-09-19. Retrieved 2014-03-25. 
  115. ^ Bozulich 2001 pp. 92–93
  116. ^ a b EGF General Tournament Rules, European Go Federation, retrieved 2008-06-11 
  117. ^ Stas Bekman: stas (at) stason.org. "Go FAQ". Stason.org. Retrieved 2014-03-25. 
  118. ^ "Go markers". The Unicode Standard. 
  119. ^ Top Ten Reasons to Play Go, American Go Association, retrieved 2008-06-11 
  120. ^ Wedd, Nick. "Human-Computer Go Challenges". computer-go.info. Retrieved 2011-10-28. 
  121. ^ Johnson, George (1997-07-29), "To Test a Powerful Computer, Play an Ancient Game", The New York Times, retrieved 2008-06-16 
  122. ^ Overview of Computer Go, Intelligent Go Foundation, archived from the original on 2008-05-31, retrieved 2008-06-16 
  123. ^ Keene, Raymond; Levy, David (1991), How to beat your chess computer, Batsford Books, p. 85 
  124. ^ Davey Alba (2014-06-17). "China's Tianhe-2 Caps Top 10 Supercomputers". IEEE Spectrum. Retrieved 2014-24-14. 
  125. ^ Stern, David. "Modelling Uncertainty in the Game of Go" (PDF). Cornell University. Archived from the original on 15 May 2014. Retrieved 15 May 2014. 
  126. ^ "Supercomputer with innovative software beats Go Professional". Retrieved 2008-12-19. 
  127. ^ "AGA News: Kim Prevails Again In Man Vs Machine Rematch". Retrieved 2009-08-08. 
  128. ^ Peepo.com
  129. ^ McDonald, Brian (2002) [1995], "Shibumi" (PDF), in Shotwell, Peter, Go in Western Literature, American Go Association, pp. 5–6, archived from the original on 2006-09-21, retrieved 2008-06-16 
  130. ^ Anderson, Troy (August 3, 2004), The Way of Go: 8 Ancient Strategy Secrets for Success in Business and Life 
  131. ^ Yasuyuki, Miura (1998), Go, an Asian Paradigm for Business Strategy, Kiseido Publishing Company, ISBN 4-906574-99-8 
  132. ^ Bozulich, Richard, The Magic of Go – 33. Go and business (1), Yomiuri Shimbun, archived from the original on 2004-12-09, retrieved 2013-11-27 
  133. ^ Shotwell, p.176
  134. ^ Shimatsuka, Yoko, Do Not Pass Go, Asiaweek, archived from the original on 2007-06-10, retrieved 2007-03-26 
  135. ^ Scanlon, Charles (2002-08-01). "Young Japanese go for Go". World News (BBC). Retrieved 2009-05-21. 
  136. ^ Scott, A.O. (2007-03-14), "A Prodigy's Life Is Played Out In a Japanese Game of Skill", The New York Times, retrieved 2008-06-16 
  137. ^ (film; 2013) Tokyo Newcomer
  138. ^ Ng Ho (1998), "King Hu and the Aesthetics of Space", in Teo, Stephen, Transcending the Times:King Hu & Eileen Chan, Hong Kong International Film Festival, Hong Kong: Provisional Urban Council of Hong Kong, p. 45 
  139. ^ "The Rise and Fall of Atari". Retrieved May 5, 2014. 
  140. ^ a b Gobet, F; de Voogt, A. J; Retschitzki, J (2004), Moves in Mind: The Psychology of Board Games, Hove, UK: Psychology Press, ISBN 1-84169-336-7 
  141. ^ Masunaga, H; Horn, J. (2001), "Expertise and age-related changes in components of intelligence", Psychology and Aging 16 (16): 293–311, doi:10.1037/0882-7974.16.2.293 
  142. ^ Chen et al. (2003), "A functional MRI study of high-level cognition II. The game of GO", Science Direct – Cognitive Brain Research 16: 32, doi:10.1016/S0926-6410(02)00206-9, retrieved 2008-06-16 
  143. ^ Verghese et al. (2003), "Leisure Activities and the Risk of Dementia in the Elderly", New England Journal of Medicine 348 (25): 2508–16, doi:10.1056/NEJMoa022252, PMID 12815136 
  144. ^ Boorman, Scott A. (1969), The Protracted Game: A Wei Ch'i Interpretation of Maoist Revolutionary Strategy, New York, NY: Oxford University Press, ISBN 0-19-500490-6 
  145. ^ a b Pinckard, William, Go and the Three Games, Kiseido Publications, retrieved 2008-06-11  in Bozulich 2001

Bibliography[edit]

Further reading[edit]

Introductory books

Historical interest

External links[edit]