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The The Encircling Game

Go is an abstract strategy board game for two players in which the aim is to surround more territory than the opponent. The game was invented in China more than 2,500 years ago and is believed to be the oldest board game continuously played to the present day.[1][2][3] A 2016 survey by the International Go Federation's 75 member nations found that there are over 46 million people worldwide who know how to play Go and over 20 million current players, the majority of whom live in East Asia.[4]

The The Encircling Game

The playing pieces are called stones. One player uses the white stones and the other, black. The players take turns placing the stones on the vacant intersections (points) of a board. Once placed on the board, stones may not be moved, but stones are removed from the board if the stone (or group of stones) is surrounded by opposing stones on all orthogonally adjacent points, in which case the stone or group is captured.[5] The game proceeds until neither player wishes to make another move. When a game concludes, the winner is determined by counting each player's surrounded territory along with captured stones and komi (points added to the score of the player with the white stones as compensation for playing second).[6] Games may also be terminated by resignation.

The standard Go board has a 1919 grid of lines, containing 361 points. Beginners often play on smaller 99 and 1313 boards,[7] and archaeological evidence shows that the game was played in earlier centuries on a board with a 1717 grid. However, boards with a 1919 grid had become standard by the time the game reached Korea in the 5th century CE and Japan in the 7th century CE.[8]

Despite its relatively simple rules, Go is extremely complex. Compared to chess, Go has both a larger board with more scope for play and longer games and, on average, many more alternatives to consider per move. The number of legal board positions in Go has been calculated to be approximately 2.110170,[12][a] which is greater than the number of atoms in the observable universe, estimated to be of the order of 1080.[14]

The Korean word baduk derives from the Middle Korean word Badok, the origin of which is controversial; the more plausible etymologies include the suffix dok added to Ba to mean 'flat and wide board', or the joining of Bat, meaning 'field', and Dok, meaning 'stone'. Less plausible etymologies include a derivation of Badukdok, referring to the playing pieces of the game, or a derivation from Chinese páizi (排子), meaning 'to arrange pieces'.[17]

Go is an adversarial game with the objective of surrounding a larger total area of the board with one's stones than the opponent.[18] As the game progresses, the players position stones on the board to map out formations and potential territories. Contests between opposing formations are often extremely complex and may result in the expansion, reduction, or wholesale capture and loss of formation stones.

Players may pass rather than place a stone if they think there are no further opportunities for profitable play.[26] The game ends when both players pass[27] or when one player resigns. In general, to score the game, each player counts the number of unoccupied points surrounded by their stones and then subtracts the number of stones that were captured by the opponent. The player with the greater score (after adjusting for komi) wins the game.

In the opening stages of the game, players typically establish positions (or bases) in the corners and around the sides of the board, usually starting on the third or fourth line from the border rather than at the very edge of the board. These bases help to quickly develop strong shapes which have many options for life (self-viability for a group of stones that prevents capture) and establish formations for potential territory.[28] Players usually start in the corners because establishing territory is easier with the aid of two edges of the board.[29] Established corner opening sequences are called joseki and are often studied independently.[30]

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,[36] most notably in Chinese and Japanese scoring rules,[37] these differences do not greatly affect the tactics and strategy of the game.

The two players, Black and White, take turns placing stones of their colour on the intersections of the board, one stone at a time. The usual board size is a 1919 grid, but for beginners or for playing quick games,[38] the smaller board sizes of 1313[39] and 99 are also popular.[40]The board is empty to begin with.[41] Black plays first unless given a handicap of two or more stones, in which case White plays first. The players may choose any unoccupied intersection to play on except for those forbidden by the ko and suicide rules (see below). Once played, a stone can never be moved and can be taken off the board only if it is captured.[42] A player may pass their turn, declining to place a stone, though this is usually only done at the end of the game when both players believe nothing more can be accomplished with further play. When both players pass consecutively, the game ends[43] and is then scored.

Players are not allowed to make a move that returns the game to the previous position. This rule, called the ko rule, prevents unending repetition.[50] As shown in the example pictured: Black has just played the stone marked 1, capturing a white stone at the intersection marked with the red circle. If White were 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.[51]

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.[c]

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.[59]

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.[60]

One of the most important skills required for strong tactical play is the ability to read ahead.[65] 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.[66]

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.[67] 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,[67] and are available for all skill levels, some posing a challenge even to top players.

Strategy deals with global influence, interaction between distant stones, keeping the whole board in mind during local fights, and other issues that involve the overall game. It is therefore possible to allow a tactical loss when it confers a strategic advantage.

Novices often start by randomly placing stones on the board, as if it were a game of chance. An understanding of how stones connect for greater power develops, and then a few basic common opening sequences may be understood. Learning the ways of life and death helps in a fundamental way to develop one's strategic understanding of weak groups.[e] A player who both plays aggressively and can handle adversity is said to display kiai, or fighting spirit, in the game.

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.

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 may be saved or sacrificed for something more significant on the board.[76] 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.[77] 350c69d7ab

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