Chaturanga (Sanskrit: चतुरङ्ग; caturaṅga), or catur for short, which means 'Four Divisions' (referring to ancient army divisions of infantry Pawn (che...
Chaturanga (Sanskrit: चतुरङ्ग; caturaṅga), or catur for short, which means 'Four Divisions' (referring to ancient army divisions of infantry Pawn (chess), cavalry Knight (chess), elephantry Alfil (chess), and chariotry Rook (chess)), is an ancient Indian strategy game that is commonly theorized to be the common ancestor of the board games chess, xiangqi, shogi, sittuyin, and makruk.
Chaturanga is first known from the Gupta Empire in India around the 6th century AD. In the 7th century, it was adopted as chatrang (shatranj) in Sassanid Persia, which in turn was the form of chess brought to late-medieval Europe.
According to Stewart Culin, chaturanga was first described in the Hindu text Bhavishya Purana.
The exact rules of chaturanga are unknown. Chess historians suppose that the game had similar rules to those of its successor, shatranj. In particular, there is uncertainty as to the moves of the Gaja (elephant).
The origin of chaturanga has been a puzzle for centuries. It has its origins in the Gupta Empire, with the earliest clear reference dating from the sixth century of the common era, and from north India. The first substantial argument that chaturanga is much older than this is the fact that the chariot is the most powerful piece on the board, although chariots appear to have been obsolete in warfare for at least five or six centuries. The counter-argument is that they remained prominent in literature. Several more recent scholars have proposed a gradual evolution in the centuries B.C. in the northern or northwestern border areas of Indian culture, where it was in contact with Greek culture brought by the Macedonian-Greek army, and where some rulers issued coins with fused Greek-Indian imagery. Myron Samsin argues that chaturanga originated in the kingdom of Bactria, ca. 255–55 B.C., in a fusion of the many short-moving men of the Greek game petteia, or poleis, with men derived from the various moves of an Indian race game, perhaps Seega or Chaupur, on the ashtapada, the board of another race game.
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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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