Two answers, and a game with four

Every ending of three files in range, sorted by its computed outcome class. The upper bar of each pair counts endings of plain files, where the tempo-counting rule is exactly right; the lower counts endings where one pawn still has its double step. Two whole outcome classes — a win for one side whoever moves — appear only in the second group, and the counting rule has no way to express them.

1 essay calls parity-audit. 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.