Combinatorial Game Theory
who wins, and by how much
Generator

A star with one empty place

A star with one empty place
A star with one empty place. The Mū tōrere board at the start: eight points on a circle joined to their neighbours and to an empty centre, Black's four counters on neighbouring points and White's on the other four. Black's two end counters, each beside a White counter, may move into the centre; the two middle counters may not. The start is a draw with best play.

The Mū tōrere board at the start: eight points on a circle joined to their neighbours and to an empty centre, Black's four counters on neighbouring points and White's on the other four. Black's two end counters, each beside a White counter, may move into the centre; the two middle counters may not. The start is a draw with best play.

1 essay calls mutorere-board. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

Where it is called

Every one of these figures is a drawing of the same construction, so a correction to it corrects them all.

A star with one empty place. The Mū tōrere board at the start: eight points on a circle joined to their neighbours and to an empty centre, Black's four counters on neighbouring points and White's on the other four. Black's two end counters, each beside a White counter, may move into the centre; the two middle counters may not. The start is a draw with best play. Out in the world

The same rule on a star

Kōnane turned out to hold the theory's whole vocabulary, and one old game is an anecdote. Mū tōrere, a Māori game on an eight-pointed star, has the same rule for losing — a player who cannot move loses — and is small enough to solve whole. Of its 630 arrangements, not one is a win for whoever moves first or a loss for whoever must move, sixteen go to each side whoever starts, and most are drawn. A random player still loses it every time. The vocabulary was never in the rule for losing; it was in the captures.

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