Mighty Queen, Lowly Rook

A friend sent me a game that reached the position shown in the diagram and asked me what I thought about it. My first reaction was that White has winning chances, but after some analysis it appears to be a solid draw. Once the Black King moves out of checking range, the Black Queen has no problem creating constant threats to win a Pawn or worse. The Queen's movements on the diagonals allow it to switch rapidly from one section of the board to another while the Rook remains huddled close to its Pawns. The Queen dominates the Rook in a way that the Rook can't match when faced with a minor piece alone.

White to move

I started to wonder what theory said about the position. Averbakh (see Averbakh's Convekta for a previous post on his work) only looks at Rook and two Pawns vs. Queen. He divides the positions into those with doubled Pawns, disconnected Pawns, and connected Pawns. In the first two cases, the side with the Rook looks to sacrifice one of the Pawns, leaving a theoretically drawn fortress. The third case breaks down into positions where the weaker King is either separated from its Pawns or close to them. In positions like the diagram, the White King behind its two Pawns has good drawing chances.

I also looked at positions like the diagram where I added a White Pawn on the e-file, i.e. Rook and four Pawns vs. Queen. Here the Queen also manages to hold the position. I tried to invent positions where the Queen finally loses, but they are not easy to find.