Bul (also called Buul, Boolik or Puluc) is a running-fight board game originating in Mesoamerica, and is known particularly among several of the Maya...
Bul (also called Buul, Boolik or Puluc) is a running-fight board game originating in Mesoamerica, and is known particularly among several of the Maya peoples of Belize and the Guatemalan highlands. It is uncertain whether this game dates back to the pre-Columbian Maya civilization, or whether it developed in the post-colonial era after the arrival of the Spanish conquistadores.
Stewart Culin described the game in the 24th Annual Report of the Bureau of American Ethnology: Games of North American Indians published in 1907. R. C. Bell referred to the game in Board and Table Games from Many Civilizations. Both of these descriptions were based on the eyewitness accounts of others.
Lieve Verbeeck, a linguist studying Mayan language, witnessed the modern version of the game being played by Mopan and Kekchi Maya in Belize
It is not known exactly when the game was developed or what the original rules were as very few records survived the invasion by the conquistadors between the 15th and 17th centuries. Stewart Culin organised the games in his anthology into those he thought had an influence from Europe in their creation. Bul is not listed among these, and in his opinion the game must have developed before Europeans arrived in Central America.
There are a variety of ways to play the game, as Verbeeck's account shows. The game could be played by two people, or by two equal-sized teams. The overall objective is to capture and subsequently kill the playing pieces of the opposition, so the game is in essence a war game.
The playing area is divided into equal spaces using rods placed parallel to each other. The two players have control of a base at either end of the play area. The players take an even number of stones or figurines (or any suitable playing piece) and place them in their respective bases.
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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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