Chess is a recreational and competitive board game played between two players. It is sometimes called Western or international chess to distinguish it...
Chess is a recreational and competitive board game played between two players. It is sometimes called Western or international chess to distinguish it from related games such as xiangqi. The current form of the game emerged in Southern Europe during the second half of the 15th century after evolving from similar, much older games of Indian and Persian origin. Today, chess is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.
Chess is an abstract strategy game and involves no hidden information. It is played on a square chessboard with 64 squares arranged in an eight-by-eight grid. At the start, each player (one controlling the white pieces, the other controlling the black pieces) controls sixteen pieces: one king, one queen, two rooks, two knights, two bishops, and eight pawns. The object of the game is to checkmate the opponent's king, whereby the king is under immediate attack (in "check") and there is no way to remove it from attack on the next move. There are also several ways a game can end in a draw.
Organized chess arose in the 19th century. Chess competition today is governed internationally by FIDE (International Chess Federation). The first universally recognized World Chess Champion, Wilhelm Steinitz, claimed his title in 1886; Magnus Carlsen is the current World Champion. A huge body of chess theory has developed since the game's inception. Aspects of art are found in chess composition; and chess in its turn influenced Western culture and art and has connections with other fields such as mathematics, computer science, and psychology.
One of the goals of early computer scientists was to create a chess-playing machine. In 1997, Deep Blue became the first computer to beat the reigning World Champion in a match when it defeated Garry Kasparov. Today's chess engines are significantly stronger than even the best human players, and have deeply influenced the development of chess theory.
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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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