Generator

Depth is not material

Endings of a lone king against a queen, rook, two bishops, bishop and knight and two knights, each solved by backward labelling. Longest forced mates are 10, 16, 19 and 33 moves, and two knights force nothing from any position where black has a choice.

1 essay calls endgame-table. 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.

The same table, read two ways. Two games of king and rook against king from a position 16 moves from mate. A white who reads the distance descends one move at a time to mate. A white who reads only whether a move keeps the win wanders and is still 13 moves from mate after 80 moves.

Out in the world

A win is not a way of winning

Solve a lone king against a rook completely and every one of 175,168 positions with white to move is won. Now let white play any move the table says keeps the win, and black resist as long as it can: in 400 games of up to 2,000 moves, white never mates. On a graph that loops, staying won is not progress. From every won position in the queen and rook endings white can stay inside the won set for ever, and what wins is a second number, the distance, which the theory of finite games never had to ask for.

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