Mancala

Abstract

Mancala is a generic term for a group of board games that commonly consist of two or four rows of cup-shaped holes using a proportionate number of counters, often seeds, stones, or shells. There are usually two players who take turns spreading counters one by one in consecutive holes around the rows of holes. In most cases the object of the game is to capture the majority of the counters. The wide variety of rules and boards complicates a comprehensive descriptive definition of the game. Some variations, in particular the games known as Bao in East Africa and Wari in West Africa and the Caribbean (also known a Warri, Awari, Awélé, Oware), are played in competition. They have been instrumental in cognitive psychological research where they allow a contrast with studies on chess. In 1990, Retschitzki conducted research on players of Awélé in the Ivory Coast as part of his studies in developmental psychology. de Voogt (1995) completed a study on expertise with tournament players of Bao in Zanzibar, Tanzania. Both researchers collaborated with Fernand Gobet to show the influence of board game research in the field of psychology in their Gobet et al. 2004 publication. In computer science a series of studies on mancala variations known as Awari (e.g., Allis, van der Meulen, & van den Herik, 1991), Tchuka Ruma solitaire (Campbell & Chavey, 1995), and Kalah (Russel, 1964) were conducted. More recent studies by Donkers and Uiterwijk (2002) as well as Kronenburg, Donkers, and de Voogt (2006) on Bao and Irving, Donkers, and Uiterwijk (2000) on Kalah show a continued interest in using and exploring mancala variations in computer science. This interest overlaps with studies in the field of Artificial Intelligence and even mathematics as Donkers, Uiterwijk, and de Voogt (2002) have shown in an overview of the use of mancala in these fields. These studies are mainly interested in optimal search functions and strategies that can be tested using individual mancala games. The interest in mathematics dates back to the work of Zaslavky (1973) and Deledicq and Popova (1977) whose interest was grounded in the cultural aspects of these games. Manansala (1995) added a mathematical study of a Philippine variation. This was followed by a similar study by Donkers, de Voogt, and Uiterwijk (2000) on Dakon found in Indonesia. Zaslavsky emphasized African mancala games while Deledicq and Popova included Asian variants, which have now gained as much attention as the African ones. The results of these studies emphasize the ethnomathematical aspects of mancala play, identifying mathematical and computational abilities of players. Historical and anthropological studies of mancala games go back to the first mention of a mancala game, closely resembling today's game of Bao, by Flacourt in his history of Madagascar (1661). More influential was the work of Culin (1896) and later the seminal work by Murray (1952) who provided one of the first overviews of known mancala variations. They are at the basis of questions concerning the history and distribution of mancala games. In archaeology Schädler (1998) has shown the likely confusion of mancala with the game of five lines for rows of holes dating to the Roman period. Similarly, four rows of holes may be confused with the Middle Eastern game of Tab (Depaulis, 2001). A series of finds in Sudan (de Voogt, 2012), Syria (de Voogt, 2010), and the Balkans (Bikić & Vuković, 2010) strongly suggest that rows of holes