Combinatorial Game Theory
who wins, and by how much
Generator

Kōnane from oxo.oxo.oxo, and who wins

Kōnane from oxo.oxo.oxo, and who wins
Kōnane from oxo.oxo.oxo, and who winsA row of Kōnane with the outcome stated before anybody moves. Blue stones are the reader's and red are the machine's; a move hops one stone over an adjacent enemy stone into the empty square beyond, taking it. The reader moves first and cannot win: the reply to every move was worked out in advance from the game recursion, so the machine is following a theorem rather than searching.worth 0the player to move loses — and the reader moves firststated before a move is madea move hops a blue stone over an adjacent red one into the empty square beyond, taking itthe value is 0 and the outcome is P — computed before the figure was drawn,not after the gameevery reply was worked out in advance from the recursion; nothing heresearches when a stone is clickedwith the script running, the blue stones become clickable and this claim canbe tested

A row of Kōnane with the outcome stated before anybody moves. Blue stones are the reader's and red are the machine's; a move hops one stone over an adjacent enemy stone into the empty square beyond, taking it. The reader moves first and cannot win: the reply to every move was worked out in advance from the game recursion, so the machine is following a theorem rather than searching.

1 essay calls play-konane. 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.

The positions it draws

1 distinct position, harvested by drawing the figure again at the options each essay asked for.

PositionWorth OutcomeDrawn in
oxo.oxo.oxo 0 P A game older than the theory

It plays back

The winner is named before a move is made, and every reply was worked out in advance.

Where it is called

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

Every row of 8 squares, and the 36 values they hold. A census of Kōnane rows: how many arrangements of a row of squares carry each value, with the shortest row carrying that value printed beside it. Most arrangements are worth nothing at all; the rest spread over numbers, halves and quarters, stars, switches and infinitesimals — the whole vocabulary of the theory, from a game that predates it. Out in the world

A game older than the theory

Kōnane was played on carved lava boards in Hawai‘i long before anybody wrote a brace notation, and its rule for losing is the normal-play convention arrived at some centuries early. Evaluate a row of it and the answers are halves, quarters, stars and infinitesimals — the theory's whole vocabulary, out of a game that was not built to display any of it.

The whole library · The position index · The figures that play back