Why native birds?

Mū tōrere is a small game. Each side has four counters and there is only ever one empty spot. With perfect play from the start, neither side can force a win. So the fun is in who you play, and here that is four birds of Aotearoa New Zealand, from an easy one to one that never loses.

The board stays plain on purpose: the eight-pointed star the game is played on, a sand-coloured mat, green counters for you and orange for the bird. We have not added any patterns or symbols.

A bit of real mū tōrere history

Mū tōrere is a traditional Māori board game. Te Ara, the encyclopedia of New Zealand, says it was popular with some Māori from the early years of European contact, especially on the East Coast of the North Island. The points of the star are called kewai (some sources write kawai) and the centre is the pūtahi.

How old the game is, nobody knows for sure. The ethnographer Elsdon Best, who wrote about it in the early 1900s, thought it came after contact with Europeans and may have grown out of draughts. Others think it is older. The question is still open.

In 1987 the mathematician Marcia Ascher published a study of the game, and later work confirmed that the starting position is a draw. Te Ara notes that in the 2000s the game was used to teach mathematics at several universities in the United States.

One rule, written down different ways

The rule that matters most is the one about the middle. Most rule write-ups, following Ascher, say a counter may move into the pūtahi only if at least one counter next to it belongs to the other side. Some put it the other way round: a counter sitting between two of its own may not go in. On this board those two say the same thing, because the middle can only be empty when every point is full.

Other versions use the rule only for the opening moves. Without some form of it, the first player can block the other side on the very first move. This game uses the rule for the whole game, which is the version Ascher analysed.

The birds

• Pūkeko: moves at random. It spots a finishing block only about half the time.
• Tūī: checks your reply to each move it could make, so it will not walk into a block one move away.
• Kererū: looks four moves ahead most of the time. Once in a while it only checks your next reply.
• Kea: the mountain parrot has every position worked out and never loses. Your goal is a draw: hold out for 30 moves each.

How to play

• You are green and go first. Your four counters start on the bottom half of the star, and the middle is empty.
• There is always one empty spot. On your turn, move one counter into it: along the star to the point next door, into the middle, or out of the middle.
• A counter can only move into the middle when at least one counter beside it is orange.
• No jumping and no capturing. If the other side has no move on its turn, you win.
• If 30 moves each go by and nobody is blocked, it is a draw. The old sources give no limit. This one is ours, to keep games short.
• Stars for a win: 1 for any win, 2 in 20 of your moves or fewer, 3 in 10 or fewer. Using undo takes one star off. Against the Kea, a draw earns the stars.
• Pick 2 players to share one device. Earn 3 stickers for your QuickBOP sticker book.

Tips

Blocks need the middle. With this rule, a side can only be blocked when the other side holds the pūtahi and slides a counter along the star. While the middle is empty, everyone has a move.

Watch the gap they leave. When the other side holds the middle, look at the point each of their counters would leave behind. If both points beside it and the middle are theirs, that slide blocks you. Move so it can’t happen.

Think like the Tūī. Before each move, picture every answer the other side has.

Your turn

Four green counters are waiting on the star at the top of this page. Start with the Pūkeko, work up to the Kea, and play.