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Mū Tōrere is a traditional Maōri blocking game from New Zealand.
The game was first described in print by Best (1917), and this description is based upon his.
It is said that the Ngāti Haua chief Wiremu Tamihana Te Waharoa once offered to play Mū Tōrere with Governor Grey, with the whole country as a stake — Grey apparently declined.B[p. 54]
The board used in the game has a central spot (putahi ‘centre’) as well as eight arms or ‘tentacles’ (kāwai) arranged around the central spot. In this way, the board resembles an octopus, and modern commercial versions of the game are often octopus-themed.
Each player has four pieces in a different colour from their opponent, which begin the game placed in a single cluster at the end of four of the eight arms.
On each player’s turn they must move one piece either from one arm to an adjacent arm which does not have a piece on it, from an arm to the central spot if it is empty, or from the central spot to any empty arm. The goal is to block the other player so that they are unable to move; if this is done, the blocking player wins.
To start the game, the first player must move one of the two pieces at the end of their cluster, as moving one of the central two pieces would result in an instant victory.
For analysis, see Ascher (1987); Straffin (1995); Straffin (1996). With perfect play, the game is a draw.
Some general references are: The Oxford History of Board Games, Math Games & Activities from Around the World (p. 34).
Best, Elsdon (). ‘Notes on a Peculiar Game Resembling Draughts Played by the Maori Folk of New Zealand’. Man vol. 17, : pages 14–15.
Reed, Alexander Wyclif and Buddy Mikaere (). Taonga Tuku Iho: Illustrated Encyclopedia of Traditional Māori Life. New Holland: London, England, UK. ISBN: 978-1-877246-90-6.
Ascher, Marcia (). ‘Mu Torere: An Analysis of a Maori Game’. Mathematics Magazine vol. 60 (2), : pages 90–100.
Straffin, Philip D. (). ‘Position Graphs for Pong Hau K’i and Mu Torere’. Mathematics Magazine vol. 68 (5), : pages 382–386.
Straffin, Philip D. (). ‘Corrected Figure for Position Graphs for Pong Hau K’i and Mu Torere’. Mathematics Magazine vol. 69 (1), : page 65.
Parlett, David (). The Oxford History of Board Games. Oxford University Press: Oxford, England, UK. ISBN: 978-0-19-212998-7.
Zaslavsky, Claudia (). Math Games & Activities from Around the World. Chicago Review Press: Chicago, IL, USA. ISBN: 1-55652-287-8.