KALAH VS LIUBO

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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Liubo (Chinese: 六博 or 陸博; pinyin: liù bó; Wade–Giles: liu po; lit. 'six sticks') is an ancient Chinese board game played by two players. For the rules, it is believed that each player had six game pieces that were moved around the points of a square game board that had a distinctive, symmetrical pattern. Moves were determined by the throw of six sticks, which performed the same function as dice in other race games. The game was invented no later than the middle of the 1st millennium BCE, and was popular during the Han dynasty (202 BCE – 220 CE). However, after the Han Dynasty it rapidly declined in popularity, possibly due to the rise in popularity of the game of Go, and it became totally forgotten. Knowledge of the game has increased in recent years with archeological discoveries of Liubo game boards and game equipment in ancient tombs, as well as discoveries of Han dynasty picture stones and picture bricks depicting Liubo players. It is not known when the game of Liubo originated, although according to legend it was invented by Wu Cao (烏曹, called Wu Zhou 烏胄 in the early 2nd century CE Shuowen Jiezi dictionary), a minister to King Jie, the last king of the Xia dynasty, who according to traditional chronology reigned 1728–1675 BCE. While there is no archeological or reliable documentary evidence to support the view that Liubo dates back to the Shang dynasty (1600–1046 BCE), early Chinese records do indicate that Liubo was already a popular game by the Warring States period (476–221 BCE). For example, the Records of the Grand Historian records a speech made during the reign of King Xuan of Qi (reigned 319–301 BCE) that claims that the capital city of Linzi was so wealthy that its citizens were all able to indulge in activities such as playing musical instruments, cockfighting, dog racing, playing Liubo and playing kick ball.

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