Mū Tōrere▶Play

The board is an eight-pointed star. Its eight tips are the kāwai, joined one to the next around the outline of the star, and every tip is joined by a line to the centre, the pūtahi. You start with four pieces on the four bottom tips and the computer with four on the top tips; the centre is empty.

A piece may step along the outline to the next tip if that tip is empty, and a piece in the centre may move out to the empty tip. A piece may move from a tip into the centre only if one of the two tips beside it holds a rival piece. Some modern write-ups lift this rule after each player's first two moves; this version keeps it for the whole game, as it is usually given. If a piece you tap cannot move, the message says why.

If the same position, with the same player to move, comes up for the third time, the game is a draw; the small line under the board warns you when a position has been seen twice. You move first in the first game of every run, and after that the first move alternates between you and the computer.

Each win adds one to your streak and the computer climbs a level. It knows every position of the game, but at level 1, whenever it has a losing move on offer, it lets one slip 55% of the time; each win cuts that chance by a fifth, so it gets rarer and rarer but never reaches zero. A loss or a draw ends the run. Your saved score is wins × 1,000 plus a run bonus: each win adds 40 minus the number of moves you made in that game (at least 1), up to 999 in all, so of two runs with the same number of wins the one that won faster ranks higher. At level 1 the game also warns you once before a move that hands the computer a forced win; tap the same piece again to play it anyway.

Tips & strategy

Watch the single empty point. Every turn is decided by which of your pieces can reach it, and there are never more than three choices. You lose when none of them can: the empty point sits between two rival pieces while a rival holds the centre, or the centre is empty and none of your pieces stands next to a rival. Most losses are set up one or two moves earlier — once a position is lost, the end comes within the winner's next three moves.

Some moves are always safe. Working through every position of the game shows that, from a level position, moving a piece out of the centre never loses, and neither does entering the centre with a piece that still has one of your own pieces beside it. The risky centre entry is the lone piece wedged between two rival pieces: from a level position that entry loses about one time in five.

Rim slides are where most games are thrown away. When your rival holds the centre, be careful about sliding a piece that has a rival behind it onto a point next to one of your own pieces — from a level position that slide loses three times in five. Every other kind of slide along the rim is safe from a level position. If both of your choices look alike, pick the one that keeps your pieces mixed in among the rival's rather than bunched together.

With perfect play the game is a draw, so winning means giving the computer chances to go wrong: of the 844 level positions that can arise from the start, only 128 offer the side to move a losing choice. Steer for them — hold the centre yourself, and leave its lone pieces a way into the middle. Mū tōrere was a popular game among Māori, especially on the East Coast of the North Island, from the early years of European contact; its board has been likened to an octopus, with the pūtahi as the head and the kāwai as its arms. Players and communities tell the rules in slightly different ways, and this page follows one common telling.