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New computer cluster solves 3500-year old game

August 29, 2002

Dutch computer scientists from the Vrije Universiteit Amsterdam have solved the game of awari. With optimal play from both players, the game ends in a draw. Awari (a mancala variant, that is also known as wari, owari, awalé, awélé, and ayo) is an ancient board game that originates from Africa, and is played worldwide now.

Both players own six pits, in which stones are kept. The stones, 48 in total, are sown around over the pits, and can be captured according to the rules of the game. The objective of the game is to capture more than 24 stones. Although the rules are simple, the game requires profound strategic insight to be played well.

Dr. John W. Romein and Prof. dr. ir. Henri E. Bal solved the game by developing a program that computes the best move and eventual outcome for all 889,063,398,406 positions that can possibly occur in a game. The results are stored in a database that is 778 gigabyte large. The database was computed on a large computer cluster with 144 processors. A new and fast, parallel algorithm managed to compute the database in only 51 hours. Each processor accounted for part of the postitions, but the processors closely co-operated to determine the best moves. One complication was that the available main memory, 72 gigabyte, was by far not large enough to hold the entire database. Another problem was the heavy communication between the processors; a total of 1.0 petabit (= 10^{15} bits) was sent over the interconnection network.

The researchers are currently developing an invincible awari program, that uses the database to play perfectly. The game can be played online via http://awari.cs.vu.nl/. By default, the program plays at a weaker level, so that the human can actually win. The web interface can also be used to look up any position, to ask for the best move. The research is an important step forward in a research area within Artificial Intelligence, to solve games with increasing complexity. For example, Connect-4 was solved a decade ago, and some chess endgames are solved as well. Although solving checkers seems feasible, chess and go are not solvable in the foreseeable future.

Vrije Universiteit

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