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...
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. 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.
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 is captured. 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). Games may also be terminated by resignation.
The standard Go board has a 19×19 grid of lines, containing 361 points. Beginners often play on smaller 9×9 and 13×13 boards, and archaeological evidence shows that the game was played in earlier centuries on a board with a 17×17 grid. However, boards with a 19×19 grid had become standard by the time the game reached Korea in the 5th century CE and Japan in the 7th century CE.
Go was considered one of the four essential arts of the cultured aristocratic Chinese scholars in antiquity. The earliest written reference to the game is generally recognized as the historical annal Zuo Zhuan (c. 4th century BCE).
Despite its relatively simple rules, Go is extremely complex. Compared to chess, Go has both a larger board with more scope for play and longer games and, on average, many more alternatives to consider per move. The number of legal board positions in Go has been calculated to be approximately 2.1 × 10170, which is vastly greater than the number of atoms in the known, observable universe, estimated to be about 1 × 1080.
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KALAH
Kalah, also called Kalaha or Mancala, is a game in the mancala family invented in the United States by William Julius Champion, Jr. in 1940. This game...
Kalah, also called Kalaha or Mancala, is a game in the mancala family invented in the United States by William Julius Champion, Jr. in 1940. This game is sometimes also called "Kalahari", possibly by false etymology from the Kalahari desert in Namibia.
As the most popular and commercially available variant of mancala in the West, Kalah is also sometimes referred to as Warri or Awari, although those names more properly refer to the game Oware.
For most of its variations, Kalah is a solved game with a first-player win if both players play perfect games. The Pie rule can be used to balance the first-player's advantage.
Mark Rawlings has written a computer program to extensively analyze both the "standard" version of Kalah and the "empty capture" version, which is the primary variant. The analysis was made possible by the creation of the largest endgame databases ever made for Kalah. They include the perfect play result of all 38,902,940,896 positions with 34 or fewer seeds. In 2015, for the first time ever, each of the initial moves for the standard version of Kalah(6,4) and Kalah(6,5) have been quantified: Kalah(6,4) is a proven win by 8 for the first player and Kalah(6,5) is a proven win by 10 for the first player. In addition, Kalah(6,6) with the standard rules has been proven to be at least a win by 4. Further analysis of Kalah(6,6) with the standard rules is ongoing.
For the "empty capture" version, Geoffrey Irving and Jeroen Donkers (2000) proved that Kalah(6,4) is a win by 10 for the first player with perfect play, and Kalah(6,5) is a win by 12 for the first player with perfect play. Anders Carstensen (2011) proved that Kalah(6,6) was a win for the first player. Mark Rawlings (2015) has extended these "empty capture" results by fully quantifying the initial moves for Kalah(6,4), Kalah(6,5), and Kalah(6,6). With searches totaling 106 days and over 55 trillion nodes, he has proven that Kalah(6,6) is a win by 2 for the first player with perfect play. This was a surprising result, given that the "4-seed" and "5-seed" variations are wins by 10 and 12, respectively. Kalah(6,6) is extremely deep and complex when compared to the 4-seed and 5-seed variations, which can now be solved in a fraction of a second and less than a minute, respectively.
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