Kōnane rows, and what the recursion says they are worth
Rows of a Kōnane board with the value the game recursion computes for each. Black stones move as Left and White as Right; every move hops a stone over an adjacent enemy into the empty square beyond, taking it, and a player with no capture available loses. The values are the ordinary values of this site — numbers, stars, switches and infinitesimals — computed for a game that was played on lava rock for centuries before any of that vocabulary existed.
4 essays call
konane-row. 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
50 distinct positions, harvested by running this generator again at the options each essay passed it.
Where it is called
Changing this generator changes every one of these figures.
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.
Sums and comparison
Independence is a claim
Splitting a position into parts and adding the values is the whole method of this subject, and the splitting step is a claim about the position rather than a fact about the drawing. Where it is false the two answers differ — and the failures that matter are the ones that keep the same winner and change the value, because nothing reports those.
Out in the world
The second dimension is not the deep end
The rung below says a row of eight reaches every corner of the vocabulary and goes far into none of them, and that the narrowness is a fact about the board. So the obvious next move is a rectangle — and nine squares in a square hold twenty-five values where nine squares in a line hold fifty-eight. The geometry says why before any stone is placed.
Out in the world
The two moves that are not captures
Kōnane begins from a full board and the first two moves lift stones rather than take them, which is the only time in the whole game anybody does. Nothing on this site applies to them, and the choice is not free — on a 3 × 5 board two of Black's eight openings leave a position a whole move worse than the other six, and on a 3 × 3 board none of the five does.
The whole library · The position index · The figures that play back