Resolves to all answers indicating the size, in number of nodes, of the smallest DAG (directed acyclic graph) node-labeled with chess positions that proves a win for black, in a game of chess where white starts without its queen.

A chess position here includes data on whose turn it is, location of all pieces, castling rights, and en passant squares, but not data on 50-move rule timeouts. A DAG of positions proves a win for black if:

Answers resolve either when the exact number is known, or when the intended resolution is provable to be more/less than the value in the answer. If the game is not a win for Black, resolves to infinity.