Around the World in Eighty Games by Marcus du Sautoy

Author:Marcus du Sautoy [Du, Marcus Sautoy]
Language: eng
Format: epub
Publisher: Basic Books
Published: 2023-11-07T00:00:00+00:00

38: Mu Torere

MU TORERE IS PLAYED ON AN eight-pointed star. The board might be drawn in the sand or carved into wood or bark or marked out with a piece of charcoal. Each player has four counters that are placed on the points of the star. Traditionally counters might be pebbles, bits of vegetables, or, after contact with European travelers, broken bits of china. All that really mattered was that it be clear which counters belonged to which player. This game was simple to make and easy to set up, like many African games we will explore later in our journey.

The players are allowed to move their counters either into the center of the star, called the putahi, or to an adjacent empty star point, called a kawai. Putahi has the association of streams meeting at a junction, while kawai refers to a tree branch or even the tentacles of an octopus. The game is won if you block your opponent from moving. They are then declared piro, meaning “out” or “defeated,” although it can also mean “putrid” or “foul smelling.” Interestingly, in modern games we often say a player stinks if he or she plays badly. In order to ensure that the first player can’t easily force a win, an additional rule demands that the first two moves by each player be made by stones marked with an asterisk.

The mathematical analysis of how to play this game was first investigated by Marcia Ascher, a pioneer in ethnomathematics who worked at Ithaca College in New York State.

The first question is whether the game actually can be won. Though the game’s complexity can make it difficult to know where to start, one clever move to answer this question is to simplify the setup. I often use this strategy to try to crack a puzzle. If we start with just a two-pointed star, rather than an eight-pointed star, and each player has one counter, then the game never stops because there is no way to block your opponent. Either the center or the adjacent star is free to move to. The same happens with a four-pointed star.

Once we start playing with a six-pointed star, things begin to get interesting. Now it is possible for either player to block their opponent. There are thirty different configurations that the board might assume described in the following table. The first entry tells you whose go it is, the second entry tells you whose stone is in the center or whether the center is unoccupied, and the last six entries indicate the arrangement of stones around the star. Configuration (1) or (25) is the starting position for the game according to whether A or B plays first.

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