Size of the smallest number of positions proving a win for black in Queen-odds chess

Question

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:

The collection includes the initial position

In every position with white to move, all possible subsequent positions after a move by white are also included, with an edge from the former to the latter.

In every position with black to move, either there is a mate-in-one, or there is a unique edge from the position to another position, indicating the state after a legal move from black.

There are no cycles (as the definition of DAG requires)

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.

Manifold Markets · Answer

Per Manifold Markets prediction market, <=10^50, followed by <=10^30 and <=10^10 are most likely. See the market for live updates (2 traders, as of Dec 4, 2025).