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Chinese boards are slightly larger, as a traditional Chinese Go stone is slightly larger to match. The board is not square; there is a ratio in length to width, because with a perfectly square board, from the player's viewing angle the perspective creates a foreshortening of the board.
The added length compensates for this. More recently, the related California Torreya Torreya californica has been prized for its light color and pale rings as well as its reduced expense and more readily available stock.
The natural resources of Japan have been unable to keep up with the enormous demand for the slow-growing Kaya trees; both T.
Other, less expensive woods often used to make quality table boards in both Chinese and Japanese dimensions include Hiba Thujopsis dolabrata , Katsura Cercidiphyllum japonicum , Kauri Agathis , and Shin Kaya various varieties of spruce , commonly from Alaska, Siberia and China's Yunnan Province.
However it may happen, especially in beginners' games, that many back-and-forth captures empty the bowls before the end of the game: in that case an exchange of prisoners allows the game to continue.
Traditional Japanese stones are double-convex, and made of clamshell white and slate black. In China, the game is traditionally played with single-convex stones  made of a composite called Yunzi.
The material comes from Yunnan Province and is made by sintering a proprietary and trade-secret mixture of mineral compounds derived from the local stone.
This process dates to the Tang Dynasty and, after the knowledge was lost in the s during the Chinese Civil War , was rediscovered in the s by the now state-run Yunzi company.
The term yunzi can also refer to a single-convex stone made of any material; however, most English-language Go suppliers specify Yunzi as a material and single-convex as a shape to avoid confusion, as stones made of Yunzi are also available in double-convex while synthetic stones can be either shape.
Traditional stones are made so that black stones are slightly larger in diameter than white; this is to compensate for the optical illusion created by contrasting colors that would make equal-sized white stones appear larger on the board than black stones.
The bowls for the stones are shaped like a flattened sphere with a level underside. Chinese bowls are slightly larger, and a little more rounded, a style known generally as Go Seigen ; Japanese Kitani bowls tend to have a shape closer to that of the bowl of a snifter glass, such as for brandy.
The bowls are usually made of turned wood. Mulberry is the traditional material for Japanese bowls, but is very expensive; wood from the Chinese jujube date tree, which has a lighter color it is often stained and slightly more visible grain pattern, is a common substitute for rosewood, and traditional for Go Seigen-style bowls.
Other traditional materials used for making Chinese bowls include lacquered wood, ceramics , stone and woven straw or rattan.
The names of the bowl shapes, Go Seigen and Kitani , were introduced in the last quarter of the 20th century by the professional player Janice Kim as homage to two 20th-century professional Go players by the same names, of Chinese and Japanese nationality, respectively, who are referred to as the "Fathers of modern Go".
The traditional way to place a Go stone is to first take one from the bowl, gripping it between the index and middle fingers, with the middle finger on top, and then placing it directly on the desired intersection.
It is considered respectful towards White for Black to place the first stone of the game in the upper right-hand corner.
It is considered poor manners to run one's fingers through one's bowl of unplayed stones, as the sound, however soothing to the player doing this, can be disturbing to one's opponent.
Similarly, clacking a stone against another stone, the board, or the table or floor is also discouraged. However, it is permissible to emphasize select moves by striking the board more firmly than normal, thus producing a sharp clack.
Additionally, hovering one's arm over the board usually when deciding where to play is also considered rude as it obstructs the opponent's view of the board.
Apart from the points above it also points to the need to remain calm and honorable, in maintaining posture, and knowing the key specialised terms, such as titles of common formations.
Generally speaking, much attention is paid to the etiquette of playing, as much as to winning or actual game technique. In combinatorial game theory terms, Go is a zero-sum , perfect-information , partisan , deterministic strategy game , putting it in the same class as chess, draughts checkers , and Reversi Othello ; however it differs from these in its game play.
Although the rules are simple, the practical strategy is complex. The game emphasizes the importance of balance on multiple levels and has internal tensions.
To secure an area of the board, it is good to play moves close together; however, to cover the largest area, one needs to spread out, perhaps leaving weaknesses that can be exploited.
Playing too low close to the edge secures insufficient territory and influence, yet playing too high far from the edge allows the opponent to invade.
It has been claimed that Go is the most complex game in the world due to its vast number of variations in individual games. Decisions in one part of the board may be influenced by an apparently unrelated situation in a distant part of the board.
Plays made early in the game can shape the nature of conflict a hundred moves later. The game complexity of Go is such that describing even elementary strategy fills many introductory books.
In fact, numerical estimates show that the number of possible games of Go far exceeds the number of atoms in the observable universe. Research of go endgame by John H.
Conway led to the invention of the surreal numbers. Go long posed a daunting challenge to computer programmers , putting forward "difficult decision-making tasks, an intractable search space, and an optimal solution so complex it appears infeasible to directly approximate using a policy or value function".
Many in the field of artificial intelligence consider Go to require more elements that mimic human thought than chess. The reasons why computer programs had not played Go at the professional dan level prior to include: .
As an illustration, the greatest handicap normally given to a weaker opponent is 9 stones. It was not until August that a computer won a game against a professional level player at this handicap.
It was the Mogo program, which scored this first victory in an exhibition game played during the US Go Congress.
In March , Google next challenged Lee Sedol , a 9 dan considered the top player in the world in the early 21st century,  to a five-game match.
Leading up to the game, Lee Sedol and other top professionals were confident that he would win;  however, AlphaGo defeated Lee in four of the five games.
In October , DeepMind announced a significantly stronger version called AlphaGo Zero which beat the previous version by games to 0. An abundance of software is available to support players of the game.
This includes programs that can be used to view or edit game records and diagrams, programs that allow the user to search for patterns in the games of strong players, and programs that allow users to play against each other over the Internet.
Some web servers [ citation needed ] provide graphical aids like maps, to aid learning during play. These graphical aids may suggest possible next moves, indicate areas of influence, highlight vital stones under attack and mark stones in atari or about to be captured.
There are several file formats used to store game records, the most popular of which is SGF, short for Smart Game Format. Programs used for editing game records allow the user to record not only the moves, but also variations, commentary and further information on the game.
Electronic databases can be used to study life and death situations, joseki , fuseki and games by a particular player. Programs are available that give players pattern searching options, which allow players to research positions by searching for high-level games in which similar situations occur.
Internet-based Go servers allow access to competition with players all over the world, for real-time and turn-based games. China's salami slicing strategy is considered a manifestation of Go game.
Other books have used Go as a theme or minor plot device. The manga Japanese comic book and anime series Hikaru no Go , released in Japan in , had a large impact in popularizing Go among young players, both in Japan and—as translations were released—abroad.
Despite this Go still features heavily in her character's personality. Go has also been featured in a number of television series. Starz 's science fiction thriller Counterpart , for instance, is rich in references the opening itself featuring developments on a Go board , including applications of the game's metaphors, a book about life and death being displayed, and Go matches, accurately played, relevant to the plot.
The corporation and brand Atari was named after the Go term. In the endgame, it can often happen that the state of the board consists of several subpositions that do not interact with the others.
The whole board position can then be considered as a mathematical sum, or composition, of the individual subpositions.
A review of literature by Fernand Gobet , de Voogt and Jean Retschitzki shows that relatively little scientific research has been carried out on the psychology of Go, compared with other traditional board games such as chess.
According to the review of Gobet and colleagues, the pattern of brain activity observed with techniques such as PET and fMRI does not show large differences between Go and chess.
On the other hand, a study by Xiangchuan Chen et al. There is some evidence to suggest a correlation between playing board games and reduced risk of Alzheimer's disease and dementia.
In formal game theory terms, Go is a non-chance, combinatorial game with perfect information. Informally that means there are no dice used and decisions or moves create discrete outcome vectors rather than probability distributions , the underlying math is combinatorial, and all moves via single vertex analysis are visible to both players unlike some card games where some information is hidden.
Perfect information also implies sequence—players can theoretically know about all past moves.
Affine transformations can theoretically add non-zero and complex utility aspects even to two player games. Go begins with an empty board.
It is focused on building from the ground up nothing to something with multiple, simultaneous battles leading to a point-based win.
Black 1 captures twelve stones in the upper left, four stones in the lower left, three stones in the upper right and three stones in the lower right.
When you capture stones in a game, you put them in your prisoner pile. Then, at the end of the game, these captured stones are placed inside your opponent's territory.
Let's look at a game to see how this actually works. After Black plays 3 in Figure 7, White makes an invasion inside Black's sphere of influence with 4.
White 10 ataris the black stone at 7. Therefore, black connects at 11 in Figure 8, but White ataris again at The marked stone cannot be rescued, so Black has to sacrifice it.
He plays his own atari with 13 in Figure 9. White then captures with 14 and Black ataris two white stones with With 16 in Figure 10, White maps out the territory on the left side, and Black expands his territory on the right side with 17 to The moves from White 22 to Black 24 are the same kind of endgame sequence we saw in Figure 4 of the first game.
White 26 forces Black to capture two white stones with Next, the moves at White 28 and 30 each reduce Black's territory by one point. Black 31 ataris the two white stones at 26 and 30, so White must connect at 32 to save them.
Finally, Black 33 reduces White's territory on the left by one point. The game ends when White blocks at Figure 12 show what the board looks like at the end of this game.
White has one black stone in his prisoner pile, while Black has two white stones in his. Go combines beauty and intellectual challenge. In Asia, it is often played on a traditional, carved wooden board, with black and white stones made from slate and clamshell, but good affordable equipment is also available.
In either case, the patterns formed by the black and white stones are visually striking and can exercise an almost hypnotic attraction as one "sees" more and more in the constantly evolving positions.
The game appeals to many kinds of minds -- to musicians and artists, to mathematicians and computer programmers, to entrepreneurs and options traders.