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[[Image:Modern game board of Go the game.jpg|right|thumb|225px|{{#ifexist:Template:Modern game board of Go the game.jpg/credit|{{Modern game board of Go the game.jpg/credit}}<br/>|}}Modern game board of Go the game.]]
{{Image|Modern game board of Go the game.jpg|right|225px|A modern Go board}}
''Go'' is a board game played by two players. It is also referred to as Weiqi in Chinese (圍棋; 围棋), Baduk in Korea (<span style="font-family: Batang, Serif">바둑</span>) and Igo or Go in Japanese (囲碁; 碁). Go is the worlds oldest game that is played in its original form, with a documented history of over 2.500 years.
'''Go''' is a board game played by two players. It is called Weiqi (圍棋; 围棋) in Chinese, Baduk (<span style="font-family: Batang, Serif">바둑</span>) in Korean, and Igo or Go (囲碁; 碁) in Japanese.
{{editintro}}
== Character ==
Go is played on a flat board with a grid of 19x19 intersections. Two sets of white and black stones are used. The game is played in turns and unlike Chess, black makes the first move in go. Each stone is placed on an intersection and the goal is to capture more territory than the opponent.
In go, it often matters whether a given move is beautiful or produces good shape.


It is possible to play essentially the same game on a board of size different from the standard 19 by 19. Beginners, children and those in a hurry, often play on 13 by 13 board, or even on 9 by 9.
Go is the world's oldest game that is still played in its original form, with a documented history of over 2,500 years. It originated in China, is a traditional game throughout East Asia, is considered the national game of Japan [http://www.amazon.com/Game-Go-National-Japan/dp/0804802025], and is now played around the world. It is the second most played board game in the world, after [[Chinese chess]].


== Geometric concepts of the game ==
Go reached the West via Japan, so in English the name of the game and many of the words used to describe positions or strategic concepts are borrowed from Japanese. We indicate such words by putting them in ''italics'' the first time they are used below.


=== The geometric-analytic representation of the go board ===
There is a large Wiki devoted to discussing the game, [http://senseis.xmp.net/ Sensei's Library].
{{editintro}}


The go cross-section points can be represented, as in [[analytic geometry]], by ordered pairs of integers, <math>\ (x,y)</math>,&nbsp; where the two coordinates vary between <math>\ 0</math>&nbsp; and <math>\ 18.</math> For instance, the row of points near the player of the white stones consists of:
== Character ==
Go is played on a flat board (a ''goban'') with a grid of 19x19 intersections. Two sets of stones, white and black, are used. The game is played in turns and unlike Chess, black makes the first move in go. Each stone is placed on an intersection and the goal is to capture more territory than the opponent.
In go, it often matters whether a given move is beautiful or produces good shape.


:(0,18) &nbsp; (1,18) &nbsp; . . . &nbsp; (18,18)
It is possible to play essentially the same game on a board of size different from the standard 19-line board. 13-line and 9-line boards also moderately common, mainly used to get a quicker game or to keep things relatively simple for teaching. Each of these sizes roughly doubles the number of intersections: 9<sup>2</sup>=81, 13<sup>2</sup>=169, 19<sup>2</sup>=361. Historically, 15-line boards were once normal in China and 17-line in China, Tibet and Japan. There has been some experimentation with 21 and 23-line boards.


while the row of points near the player of the black stones consists of:
==Rules==
There are a few different Rule Sets for playing Go. They are very similar to each other and for most games the different rules give similar results.


:(0,0) &nbsp; (1,0) &nbsp; . . . &nbsp; (18,0)
The core rules are:


Two points, <math>\ (x,y)</math>&nbsp; and <math>\ (x',y'),</math>&nbsp; are called '''adjacent''', or the '''nearest neighbors''' (as in the theory of [[lattice system]]s of [[statistical mechanics]]) if they are next to each other in a row or in a column;&nbsp; formally, if:
#Each turn a player places a stone on one empty intersection. Afterwards it's the other player's turn.
#A stone is a member of a "chain" of stones if one stone is connected to another stone of the group with the same color via a single line (i.e. they are on orthogonally adjacent points; there are no direct diagonal connections).
#To remain on the board, at least one stone in a chain must have a connection via a line to an empty intersection (called a ''liberty''). Otherwise, that chain is dead and has to be removed from the board, and the stones become prisoners.
#You aren't allowed to make a move that directly reverses the move of your opponent &mdash; the opponent has just captured just one of your stones and you want to immediately replay that stone and capture only the stone he just played. This is called ''ko''. In some variants you aren't allowed to return to ''any'' previous position, which could be done by means of three kos in turn. More usually, if both players insist on doing this, the game is annulled.
#You also aren't allowed to fill in the last liberty of a chain of your own, unless doing so also fills in the last liberty of an opposing chain, in which case you get priority and capture. (The complexity of the game can result in situations where you might want to "commit suicide", but this isn't allowed.) This rule is omitted in some variants.
#Either player may pass, skip their move. If both players pass in the same position, the game is over. All stones that could be captured through adding additional stones are dead and get removed from the board and become prisoners. 


:::<math>|x-x'|+|y-y'|\ =\ 1</math>
While the above rules are sufficient for most games, specific rules that exactly define the terms that are used in the rules can be a bit longer.<ref>[http://home.snafu.de/jasiek/rules.html Rules sets compiled and analyzed by Robert Jasiek]</ref>
 
For instance, points (2,5) and (2,6) are adjacent; also (2,5) and (1,5); while points (2,2) and (3,3) are not.
 
A sequence of go points is called a '''path''' when its each pair of consecutive points is adjacent.
 
A point is '''adjacent to a set''' of points if it is adjacent to at least one point of that set. We also say that a set is adjacent to another set if the two are not apart, i.e. if there exists an adjacent pair of points which has one point in each of the two sets.
 
=== Connected sets ===
 
A set <math>\ A</math>&nbsp; of go points is called '''disconnected''' if it splits into a union of two disjoint non-empty sets, <math>\ A = B\cup C</math>,&nbsp; such that no point of <math>\ B</math>&nbsp; is adjacent to any point of <math>\ C</math>. And a set is called connected when it is not disconnected. It turns out that a set is connected if and only if for every two of its different points there exists a path which starts at one of these points and ends in the other one.
 
Every set of go points is uniquely a union of its maximal connected subsets, called its connected '''components'''. Each two components are disjoint and even apart one from another, meaning that points from two different components are never adjacent.
 
'''Remark:'''&nbsp; The empty set, and each 1-point set, is connected.
 
'''2-point sets:'''&nbsp; A 2-point set is connected if and only if its points are adjacent.
 
=== Board configuration and groups of stones ===
 
 
Each time you have black and white stones on some of the go points (cross-sections) you get a (board) configuration. Formally, a board '''configuration''' is an arbitrary function
 
:::<math>\ f\ :\ \{0,\dots,18\}\times\{0,\dots,18\}\ \rightarrow\ \{-1,0,1\}</math>
* Equality <math>\ f(x,y)=1</math>&nbsp; is interpreted as: ''black stone occupies point &nbsp;<math>\ (x,y);</math>
* equality <math>\ f(x,y)=-1</math>&nbsp; is interpreted as: ''white stone occupies point &nbsp;<math>\ (x,y);</math>
* equality <math>\ f(x,y)=0</math>&nbsp; is interpreted as: ''point''&nbsp; <math>\ (x,y)</math>&nbsp; ''is vacant''.
 
In the everyday (non-mathematical) language we say that a configuration is any distribution of black and white stones on (the cross-points of) the board. Then we call a collection of the black (respectively white) stones a '''group''' if the points which these stones occupy form a
connected component of the set of all points occupied by the black (resp. white) stones.
 
=== Removal of stones ===


Given a configuration <math>\ f,</math>&nbsp; and a set <math>\ A</math>&nbsp; of stones (each of of either color), the removal of stones of <math>\ A</math>&nbsp; means formally the replacement of the given configuration <math>\ f</math>&nbsp; by configuration <math>\ g,</math>&nbsp; such that <math>\ g(x,y) := 0</math>&nbsp; for every point <math>\ (x,y)</math>&nbsp; of <math>\ A</math>, and <math>\ g(x,y) := f(x,y)</math>&nbsp; for every other point <math>\ (x,y)</math>&nbsp; of the board.
Also see [[Go Rules|Go rules]].


=== Liberties and eyes ===
== Scoring and handicaps ==
There are two systems of scoring, Japanese and Chinese. The Japanese method is generally used in Western countries (except New Zealand). Both systems count territory &mdash; the number of empty intersections that a player's stones surround &mdash; plus something else, but the "something else" is different. Japanese scoring counts territory plus the number of enemy stones captured. Chinese scoring counts territory plus the number of your stones on the board. Since capturing some number of stones reduces the stones the opponent has on the board by exactly that number, the two systems almost always give the same result. In either system, the winner is the player with the higher score.


A vacant point adjacent to a (point occupied by one of the stones of a given) group is called a '''liberty''' of that group. Strong go players are always aware of the number of liberties of each group of stones on the board.
However, a ''seki'', an area where neither player can move because the opponent could then capture, is scored differently in the two systems. In Japanese scoring, a seki does not count for either side since it is not territory and no stones have been captured. In Chinese scoring, both sides count the stones they have on the board in the seki. If one player has more stones involved in the seki than his opponent, the scores will be different in the two systems. It is possible, though extremely rare, to have a game where either player can be scored as the winner depending which system is used.


A group of stones which has no liberties is called '''dead'''.
Go has a widely used and fairly convenient handicap system. Players of more-or-less equal strength start with an empty board, black plays first, and white gets a small bonus in the scoring, called ''komi'', to compensate for that first move advantage. Komi is normally 5.5 points if Japanese scoring is used. For unequal players, some black stones are placed on the board before play begins, giving black a substantial advantage. White then plays first and komi is half a point to make a drawn score impossible. On a 19-line board, handicaps from two to nine stones are normal and up to 17 is possible. On a 13-line board, five is the usual maximum; this gives roughly the same advantage as nine on a 19-line board. The board has markings for the ''hoshi'' points where the handicap stones are placed.


If a vacant point is adjacent to black (resp. white) stones only then it is called a black (resp. white) '''eye''' or 1-point eye.
== Ranking ==
Go has a system of ranks similar to those used for martial arts. A number of different regional groups &mdash; at least Chinese, Japanese, Korean, American, and European &mdash; have ranking systems and the major sites for online play, [http://www.pandanet.co.jp/English/ Internet Go Server] and [http://www.gokgs.com/ Kiseido], each have their own. All these systems are roughly comparable, but no two are exactly the same. It is moderately common to see a player whose ranks in two systems are a few levels different.


More generally, given a configuration <math>\ f,</math>&nbsp; a component <math>\ A</math>&nbsp; of the set of all vacant points is called a black (resp. white) '''eye''' if there does not exist a configuration <math>\ g\le f</math>&nbsp; (resp. <math>\ g\ge f</math>)&nbsp; such that a point of <math>\ A</math>&nbsp; is a white (resp. black) 1-point eye with respect to configuration <math>\ g.</math>
A beginner is ranked as some large number of ''kyu'', 25 or 35 in different systems, and the number decreases as strength increases. In martial arts, the kyu ranks wear colored belts. Above 1 kyu comes 1 ''dan'', ''shodan'', corresponding to a black belt in martial arts. There are amateur ranks up to 6 or 7 dan.


In the ordinary language of go, a black eye is not a result of a fist landing on someone's face, but it is a connected set of vacant points, surrounded by black stones, and such that it is not possible to create a white 1-point eye by filling all but one of these vacant points with white stones so that the remaining single vacant becomes a 1-point white eye (whether or not we also set white stones on the remaining vacant points, outside of the given connected group of vacant points is irrelevant because it will not affect the status of the points of the given vacant component).
The appropriate handicap can be calculated from the ranks. For amateur players, ranks are about one stone apart in strength so a 2 dan would take 5 stones from a 7 dan and would give a 1 kyu 2 stones; both games would then be approximately even. Except for teaching, a 2 dan would not usually play against a 20 kyu since no possible handicap would make an even game of that.


=== Safe groups and families of groups of stones ===
Professional players in Japan, China and Korea each have their own separate ranking system from 1 dan to 9 dan.
However these ranks don't accurately their playing strength as it takes many years for a young professional player to reach the 9 dan even when he has the same playing strength as other 9 dans. The difference in playing strength between the average professional 1 dan and the average 9 dan is also a lot less than one handicap stone.


Let's look at the simple case before stating the general full definition of a '''safe family of groups'''.
The overall range is enormous. A top pro wins easily against a 1 dan amateur at 9 stones; the 1 dan wins easily against a 10 kyu at 9 stones, and the 10 kyu wins easily against a beginner at 13.
 
* A group of black (resp. white) stones is '''safe''' if it surrounds two eyes by itself, meaning that even if we remove from the board all other stones of the same color (outside of the given group), there would be at least two different eyes  (with respect to the modified configuration) of the given color.
 
* In general, a family of groups of stones of the same color is safe if after removing all stones of the same color, which do not belong to any of the groups of the family, each group of the family will be adjacent to at least two different eyes (w.r. to the modified configuration) of the given color.
 
If a family consists of just one group then we get back the simple case (the two definitions above are equivalent for a group and a single-group family).
 
=== Configuration score ===
 
The conceptual notion of the configuration score is virtually necessary in order to define the (practical) notion of the score of a game&mdash;to be defined in the section on ''rules''. But these two related notions should not be confused.
 
Let <math>\ f</math>&nbsp; be an arbitrary fixed configuration (''fixed'' means that we consider just the same one configuration throughout this whole section).
 
'''Definition 1'''&nbsp; Let <math>\ (x,y)</math>&nbsp; and <math>\ (x',y')</math>&nbsp; be arbitrary go points. We say that it is possible '''to reach''' the latter point from the earlier one if there exists a path from <math>\ (x,y)</math>&nbsp; to <math>\ (x',y')</math>&nbsp; such that all intermediate points of that path are vacant.
 
'''Definition 2'''&nbsp; We say that point <math>\ (x,y)</math>&nbsp; is black (resp. white) if it is occupied by a black (resp. white) stone or if it is possible to reach a black (resp. white) stone, but not white (resp. black), from <math>\ (x,y).</math>&nbsp; Otherwise, when a point is neither black nor white, we say that such a point is neutral.
 
'''Definition 3'''&nbsp; The configuration score is the number of black points minus the number of the white points.
 
'''Remark'''&nbsp; The configuration score may sound to a go player at the same time familiar and strange (even silly). This is because a go player almost always thinks about the future configuration and never literally in the terms of the present configuration. Even when the two players agree to end the game, they, as a rule, do not consider the final configuration on the board but one of the equivalent future configurations which would occur if the players cared to make certain obvious moves. Thus they consider the score of one of those potential future final configurations, and not of the final configuration which actually  occurred in the game. But we need the simple notion of the configuration score, as defined above, in order to precisely define the actual game score.
 
==== Examples ====
 
* When there are no stones on the board (i.e. the configuration function is identically equal to zero) then all points are neutral, hence the configuration score is zero.
 
* When there is only one black stone on the 19x19 board then the configuration score is equal to 19x19 = 361.
 
* When there is only one black and one white stone on the board then all points are neutral, and the score is zero.
 
* When <math>\ f(1,0)=f(0,1)=1</math>&nbsp; (two black stones) and  <math>\ f(9,9)=-1</math>&nbsp; (a single white stone in the center) and all other points are vacant, then 3 points are black, 1 point is white, and the score is 2.
 
==Rules==
There are a few different Rule Sets for playing Go. They are very similar to each other and for most games the different rules give similar results.
The core rules are:
 
1. Each turn a player places a stone on one empty intersection. Afterwards it's the other player's turn.
 
2. A stone is a member of a group of stones if one stone is connected to another stone of the group with the same color via a line (there are no direct diagonal connections). If there is no stone that is connected via a line to an empty intersection in a group that group is dead and has to be removed from the board and the stones become prisoners.
 
3. You aren't allowed to make a move that directly reverses the move of your opponent (your move would remove the stone of your opponent and that stone closed the last intersection of one of your stones and you want to replay that stone).
 
4. If nobody wants to make a move and passes the game is over. All stones that could be killed through adding additional stones are dead and get removed from the board and become prisoners.
 
After Japanese rules the winner is the person whose sum of enemy prisoners together with the amount of empty intersections that surround his stones is greater than the other person's.
 
In Chinese rules you add the number of your stones to the number of your surrounded empty interactions and the player that has the most points wins.
 
Because making one prisoner reduces the amount of enemy stones exactly by one both methods usually get the same result, besides the fact that in half of the games there is a one point difference because white passed first and black played one stone more than white.
 
While the above rules are sufficient for most games, specific rules that exactly define the terms that are used in the rules can be a bit longer.<ref>[http://home.snafu.de/jasiek/rules.html Rules sets compiled and analyzed by Robert Jasiek]</ref>


==History==
==History==
Line 128: Line 55:


==Comparison to chess==
==Comparison to chess==
Compared to [[chess]] go requires more activation in the right parietal brain areas.<ref>[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6SYV-46YJ540-4&_coverDate=03%2F31%2F2003&_alid=82770164&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=4844&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=8b624f42de7fab3d239e9b6704715b26  A functional MRI study of high-level cognition II. The game of GO by Xiangchuan Chen et al]</ref>
Go is conceptually simpler than chess (especially when go rules are properly formulated):
Go is conceptually simpler than chess (especially when go rules are properly formulated):


Line 136: Line 61:
* A go player makes only one kind of moves, namely setting a stone on an intersection point (the effect may be different each time, causing sometimes a group of opponent stones to be removed). A chess pawn has four kind of moves: 1.going one step forward, 2.going two steps forward from its initial position, 3.capturing an opponent's piece one step askew from it and landing where the opponent's piece was, 4. capturing opponent's pawn en passant. On the top of it, the pawn, which reaches the last row gets promoted.
* A go player makes only one kind of moves, namely setting a stone on an intersection point (the effect may be different each time, causing sometimes a group of opponent stones to be removed). A chess pawn has four kind of moves: 1.going one step forward, 2.going two steps forward from its initial position, 3.capturing an opponent's piece one step askew from it and landing where the opponent's piece was, 4. capturing opponent's pawn en passant. On the top of it, the pawn, which reaches the last row gets promoted.


* Go has essentially only one (very natural) restriction on moves: a move which would lead to a repetition of position is illegal (not allowed). It has also another rule, which disallows a suicide, but it's only a cultural rule, not essential to the game. In chess too we have a cultural rule which disallows to put your own king in check. In addition, we have also several essential rules which contribute to the total chess rules complexity: castling, en passant, promotion and the rules about draw by repetition or by making 50 moves by both sides without any capturing and without any pawn move.
* Go has essentially only one (very natural) restriction on moves: a move which would lead to a repetition of position is illegal (not allowed). It has also another rule, which disallows a suicide, but it's only a cultural rule, not essential to the game. In chess too we have a cultural rule which disallows to put your own king in check. In addition, we have also several essential rules which contribute to the total chess rules complexity: castling, en passant, promotion and the rules about draw by repetition or by making 50 moves by both sides without any capturing and without any pawn move, or by stalemating your opponent.


Chess as a whole does not admit any natural, regular generalizations onto larger boards (but many chess endings do). In the case of go, one may play the game on the square boards of arbitrary n by n size, and also on rectangular m by n boards. More than that, one may play go on arbitrary finite simple graphs. Thus go is so mathematical that it provides a graph invariant: with arbitrary graph we may associate the result of the game played optimally by both players (mathematical theory of games states that such optimal strategies exist; it's a corollary to the respective Zermelo's theorem, 1913).
Chess as a whole does not admit any natural, regular generalizations onto larger boards (but many chess endings do). In the case of go, one may play the game on the square boards of arbitrary n by n size. More than that, one may play go on rectangular boards or even on arbitrary finite simple graphs. Thus go is so mathematical that it provides a graph invariant: with arbitrary graph we may associate the result of the game played optimally by both players (mathematical theory of games states that such optimal strategies exist; it's a corollary to the respective Zermelo's theorem, 1913). There has been some work on computer programs that exhaustively analyse go on small boards; the 5 by 5 board has been solved [http://erikvanderwerf.tengen.nl/5x5/5x5solved.html].


Go is one of the most complex games in the world, far outweighing games such as [[chess]] in the number of possible game positions.
The handicap system is another important difference. It is much easier for two players of significantly different strength to have an interesting game &mdash; one in which both have to work at it and the outcome is often in doubt &mdash; in go than in chess. Of course, there are limits to this; nothing will make a game between a master and a beginner interesting for the master, but even a master may have trouble against a strong amateur with a large handicap.  


==Major Titles==
There is a saying that "Chess is a battle; Go is a war." The goal is not just to take out the enemy king, but to control more of the board than the opponent. Expert Go players take the overall board position into account in choosing almost every move.


There are 7 major go titles in Japan. The record for winning the most titles over the years is held by Japanese professional [[Cho Chikun]], who has won 71 titles.
Go is one of the most complex games in the world, far outweighing games such as [[chess]] in the number of possible game positions. Indeed, computer chess programs, by year 2000, became as strong or even stronger that the strongest (human) chess players. It took longer to achieve this for go.


{| class="wikitable"
A trivial difference is that in Western games such as chess and checkers, the pieces go on the squares of the board, while in many Far Eastern games such as Go, Gomoku and Chinese chess, they go on the intersections of the lines.
!|Tournament
!|Prize money
!|Current title holder
|-
|Judan
|
|[[Cho Chikun]]
|-
|Tengen
|
|Kono Rin
|-
|Oza
|
|Yamashita Keigo
|-
|Meijin
|
|Takao Shinji
|-
|Gosei
|
|Cho U
|-
|Honinbo
|
|Takao Shinji
|-
|Kisei
|
|Yamashita Keigo
|}


==Cultural Dimensions==
==Cultural Dimensions==
Go strategy is also studied as an metaphor for Asian strategy compared to western strategy.<ref>[http://www.strategicstudiesinstitute.army.mil/pdffiles/PUB378.pdf  Learning from the Stones: A Go Approach to Mastering China's Strategic Concept, Shi, by Dr. David Lai]</ref>
Go strategy is also studied as an metaphor for Asian strategy compared to western strategy.
<ref>{{cite book
|title=The Protracted Game: A Wei-Ch'i Interpretation of Maoist Revolutionary Strategy
|author=Scott Boorman
|publisher=Oxford University Press
|date=1969
|isbn10=0195014936
|isbn13=978-0195014938
}}
</ref><ref>[http://www.strategicstudiesinstitute.army.mil/pdffiles/PUB378.pdf  Learning from the Stones: A Go Approach to Mastering China's Strategic Concept, Shi, by Dr. David Lai]</ref>
 
It is interesting to note that the US engaged the Soviets on multiple "fronts" during the Cold War with buffer states (eg. South Korea as buffer state and Japan as main ally), whereas today "China is in a crescent-shaped ring of encirclement" by US allies.<ref name="hara">Hara, 2001, pp. 371</ref><ref name="encirclement">"NTI: Global Security Newswire - U.S. Wants to Surround China With Missile Defenses, Chinese Experts Claim." ''NTI - Global Security Newswire''. 23 Feb. 2010. Web. 26 Mar. 2011. <http://www.globalsecuritynewswire.org/gsn/nw_20100223_8151.php>.</ref>
 
==Neuroscience Research==
[[Neuroimaging]] research suggests players use the right hemisphere of their brain while playing Go, responsible for position and orientation, slightly more than the left side. The game requires a more global strategy than chess, and thus differs from the more left hemisphere activated activity of playing chess. A study of six subjects suggests successful Go playing requires practice and experience rather than sheer intellectual ability.<ref name="pmid12589886">{{cite journal |author=Chen X, Zhang D, Zhang X, ''et al'' |title=A functional MRI study of high-level cognition. II. The game of GO |journal=Brain Res Cogn Brain Res |volume=16 |issue=1 |pages=32–7 |year=2003 |pmid=12589886 |doi=}}</ref> Another study suggests the ability of professional Go players to assess visual information and nonmotor learning memory processes is mediated in part by the cerebellum and precuneus.<ref name="pmid15820625">{{cite journal |author=Ouchi Y, Kanno T, Yoshikawa E, ''et al'' |title=Neural substrates in judgment process while playing go: a comparison of amateurs with professionals |journal=Brain Res Cogn Brain Res |volume=23 |issue=2-3 |pages=164–70 |year=2005 |pmid=15820625 |doi=10.1016/j.cogbrainres.2004.10.004}}</ref>


== Notes ==
== Notes ==
<references/>
{{reflist|2}}

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A modern Go board

Go is a board game played by two players. It is called Weiqi (圍棋; 围棋) in Chinese, Baduk (바둑) in Korean, and Igo or Go (囲碁; 碁) in Japanese.

Go is the world's oldest game that is still played in its original form, with a documented history of over 2,500 years. It originated in China, is a traditional game throughout East Asia, is considered the national game of Japan [1], and is now played around the world. It is the second most played board game in the world, after Chinese chess.

Go reached the West via Japan, so in English the name of the game and many of the words used to describe positions or strategic concepts are borrowed from Japanese. We indicate such words by putting them in italics the first time they are used below.

There is a large Wiki devoted to discussing the game, Sensei's Library.

[edit intro]

Character

Go is played on a flat board (a goban) with a grid of 19x19 intersections. Two sets of stones, white and black, are used. The game is played in turns and unlike Chess, black makes the first move in go. Each stone is placed on an intersection and the goal is to capture more territory than the opponent. In go, it often matters whether a given move is beautiful or produces good shape.

It is possible to play essentially the same game on a board of size different from the standard 19-line board. 13-line and 9-line boards also moderately common, mainly used to get a quicker game or to keep things relatively simple for teaching. Each of these sizes roughly doubles the number of intersections: 92=81, 132=169, 192=361. Historically, 15-line boards were once normal in China and 17-line in China, Tibet and Japan. There has been some experimentation with 21 and 23-line boards.

Rules

There are a few different Rule Sets for playing Go. They are very similar to each other and for most games the different rules give similar results.

The core rules are:

  1. Each turn a player places a stone on one empty intersection. Afterwards it's the other player's turn.
  2. A stone is a member of a "chain" of stones if one stone is connected to another stone of the group with the same color via a single line (i.e. they are on orthogonally adjacent points; there are no direct diagonal connections).
  3. To remain on the board, at least one stone in a chain must have a connection via a line to an empty intersection (called a liberty). Otherwise, that chain is dead and has to be removed from the board, and the stones become prisoners.
  4. You aren't allowed to make a move that directly reverses the move of your opponent — the opponent has just captured just one of your stones and you want to immediately replay that stone and capture only the stone he just played. This is called ko. In some variants you aren't allowed to return to any previous position, which could be done by means of three kos in turn. More usually, if both players insist on doing this, the game is annulled.
  5. You also aren't allowed to fill in the last liberty of a chain of your own, unless doing so also fills in the last liberty of an opposing chain, in which case you get priority and capture. (The complexity of the game can result in situations where you might want to "commit suicide", but this isn't allowed.) This rule is omitted in some variants.
  6. Either player may pass, skip their move. If both players pass in the same position, the game is over. All stones that could be captured through adding additional stones are dead and get removed from the board and become prisoners.

While the above rules are sufficient for most games, specific rules that exactly define the terms that are used in the rules can be a bit longer.[1]

Also see Go rules.

Scoring and handicaps

There are two systems of scoring, Japanese and Chinese. The Japanese method is generally used in Western countries (except New Zealand). Both systems count territory — the number of empty intersections that a player's stones surround — plus something else, but the "something else" is different. Japanese scoring counts territory plus the number of enemy stones captured. Chinese scoring counts territory plus the number of your stones on the board. Since capturing some number of stones reduces the stones the opponent has on the board by exactly that number, the two systems almost always give the same result. In either system, the winner is the player with the higher score.

However, a seki, an area where neither player can move because the opponent could then capture, is scored differently in the two systems. In Japanese scoring, a seki does not count for either side since it is not territory and no stones have been captured. In Chinese scoring, both sides count the stones they have on the board in the seki. If one player has more stones involved in the seki than his opponent, the scores will be different in the two systems. It is possible, though extremely rare, to have a game where either player can be scored as the winner depending which system is used.

Go has a widely used and fairly convenient handicap system. Players of more-or-less equal strength start with an empty board, black plays first, and white gets a small bonus in the scoring, called komi, to compensate for that first move advantage. Komi is normally 5.5 points if Japanese scoring is used. For unequal players, some black stones are placed on the board before play begins, giving black a substantial advantage. White then plays first and komi is half a point to make a drawn score impossible. On a 19-line board, handicaps from two to nine stones are normal and up to 17 is possible. On a 13-line board, five is the usual maximum; this gives roughly the same advantage as nine on a 19-line board. The board has markings for the hoshi points where the handicap stones are placed.

Ranking

Go has a system of ranks similar to those used for martial arts. A number of different regional groups — at least Chinese, Japanese, Korean, American, and European — have ranking systems and the major sites for online play, Internet Go Server and Kiseido, each have their own. All these systems are roughly comparable, but no two are exactly the same. It is moderately common to see a player whose ranks in two systems are a few levels different.

A beginner is ranked as some large number of kyu, 25 or 35 in different systems, and the number decreases as strength increases. In martial arts, the kyu ranks wear colored belts. Above 1 kyu comes 1 dan, shodan, corresponding to a black belt in martial arts. There are amateur ranks up to 6 or 7 dan.

The appropriate handicap can be calculated from the ranks. For amateur players, ranks are about one stone apart in strength so a 2 dan would take 5 stones from a 7 dan and would give a 1 kyu 2 stones; both games would then be approximately even. Except for teaching, a 2 dan would not usually play against a 20 kyu since no possible handicap would make an even game of that.

Professional players in Japan, China and Korea each have their own separate ranking system from 1 dan to 9 dan. However these ranks don't accurately their playing strength as it takes many years for a young professional player to reach the 9 dan even when he has the same playing strength as other 9 dans. The difference in playing strength between the average professional 1 dan and the average 9 dan is also a lot less than one handicap stone.

The overall range is enormous. A top pro wins easily against a 1 dan amateur at 9 stones; the 1 dan wins easily against a 10 kyu at 9 stones, and the 10 kyu wins easily against a beginner at 13.

History

There is no exact date for the invention of Go. One legend dates the invention to the Emperor Yuo who taught the game to his eldest son Dan Zhu. Most modern writers think, that this legend (and a few similar legends), were written down in the Han period, to make the game appear older than it really is. They date the invention to the period of 1000-400 BC.[2]

Comparison to chess

Go is conceptually simpler than chess (especially when go rules are properly formulated):

  • A go player has only one kind of pieces, called stones. A chess player has six kinds of pieces (king, queen, rook, bishop, knight, pawn, and one of her/his bishops runs on white squares, while the other one on the black--thus they are actually different too).
  • A go player makes only one kind of moves, namely setting a stone on an intersection point (the effect may be different each time, causing sometimes a group of opponent stones to be removed). A chess pawn has four kind of moves: 1.going one step forward, 2.going two steps forward from its initial position, 3.capturing an opponent's piece one step askew from it and landing where the opponent's piece was, 4. capturing opponent's pawn en passant. On the top of it, the pawn, which reaches the last row gets promoted.
  • Go has essentially only one (very natural) restriction on moves: a move which would lead to a repetition of position is illegal (not allowed). It has also another rule, which disallows a suicide, but it's only a cultural rule, not essential to the game. In chess too we have a cultural rule which disallows to put your own king in check. In addition, we have also several essential rules which contribute to the total chess rules complexity: castling, en passant, promotion and the rules about draw by repetition or by making 50 moves by both sides without any capturing and without any pawn move, or by stalemating your opponent.

Chess as a whole does not admit any natural, regular generalizations onto larger boards (but many chess endings do). In the case of go, one may play the game on the square boards of arbitrary n by n size. More than that, one may play go on rectangular boards or even on arbitrary finite simple graphs. Thus go is so mathematical that it provides a graph invariant: with arbitrary graph we may associate the result of the game played optimally by both players (mathematical theory of games states that such optimal strategies exist; it's a corollary to the respective Zermelo's theorem, 1913). There has been some work on computer programs that exhaustively analyse go on small boards; the 5 by 5 board has been solved [2].

The handicap system is another important difference. It is much easier for two players of significantly different strength to have an interesting game — one in which both have to work at it and the outcome is often in doubt — in go than in chess. Of course, there are limits to this; nothing will make a game between a master and a beginner interesting for the master, but even a master may have trouble against a strong amateur with a large handicap.

There is a saying that "Chess is a battle; Go is a war." The goal is not just to take out the enemy king, but to control more of the board than the opponent. Expert Go players take the overall board position into account in choosing almost every move.

Go is one of the most complex games in the world, far outweighing games such as chess in the number of possible game positions. Indeed, computer chess programs, by year 2000, became as strong or even stronger that the strongest (human) chess players. It took longer to achieve this for go.

A trivial difference is that in Western games such as chess and checkers, the pieces go on the squares of the board, while in many Far Eastern games such as Go, Gomoku and Chinese chess, they go on the intersections of the lines.

Cultural Dimensions

Go strategy is also studied as an metaphor for Asian strategy compared to western strategy. [3][4]

It is interesting to note that the US engaged the Soviets on multiple "fronts" during the Cold War with buffer states (eg. South Korea as buffer state and Japan as main ally), whereas today "China is in a crescent-shaped ring of encirclement" by US allies.[5][6]

Neuroscience Research

Neuroimaging research suggests players use the right hemisphere of their brain while playing Go, responsible for position and orientation, slightly more than the left side. The game requires a more global strategy than chess, and thus differs from the more left hemisphere activated activity of playing chess. A study of six subjects suggests successful Go playing requires practice and experience rather than sheer intellectual ability.[7] Another study suggests the ability of professional Go players to assess visual information and nonmotor learning memory processes is mediated in part by the cerebellum and precuneus.[8]

Notes

  1. Rules sets compiled and analyzed by Robert Jasiek
  2. The Game of Go Speculations on its Origins and Symbolism in Ancient China By Peter Shotwell
  3. Scott Boorman (1969). The Protracted Game: A Wei-Ch'i Interpretation of Maoist Revolutionary Strategy. Oxford University Press. 
  4. Learning from the Stones: A Go Approach to Mastering China's Strategic Concept, Shi, by Dr. David Lai
  5. Hara, 2001, pp. 371
  6. "NTI: Global Security Newswire - U.S. Wants to Surround China With Missile Defenses, Chinese Experts Claim." NTI - Global Security Newswire. 23 Feb. 2010. Web. 26 Mar. 2011. <http://www.globalsecuritynewswire.org/gsn/nw_20100223_8151.php>.
  7. Chen X, Zhang D, Zhang X, et al (2003). "A functional MRI study of high-level cognition. II. The game of GO". Brain Res Cogn Brain Res 16 (1): 32–7. PMID 12589886[e]
  8. Ouchi Y, Kanno T, Yoshikawa E, et al (2005). "Neural substrates in judgment process while playing go: a comparison of amateurs with professionals". Brain Res Cogn Brain Res 23 (2-3): 164–70. DOI:10.1016/j.cogbrainres.2004.10.004. PMID 15820625. Research Blogging.