Let’s examine a particular corner defense in the queen-vs-rook chess end game. We are indebted to Derek Grimmell for his studies and his videos that explain how this kind of endgame works.
Diagram-1: Black to move (White threatens to win the rook soon after Qa4+)
With black to move, in the above position, there is no reasonable way for the rook to attack either the white king or the queen. Moving the rook to be a knight’s move away from the defending king is often good, so black plays Rb5.
Notice that any king move, in Diagram-1, loses quickly. Ka8 allows the pin Qe4, with mate on the next move. Kb6 loses the rook to a skewer: Qb4+. Ka6 loses the rook almost as quickly after Qa4+. Black is better off playing Rb5 instead a king move.
Diagram-2: White to move
After black moves the rook, we have the position in Diagram-2. What can white do? If Qa4+, then the black king escapes to b6, towards the center. If Qc7+, then Ka6 leaves the white king almost trapped on the edge.
White has two moves worth looking at in Diagram-2: Put the queen on the long diagonal with Qe4 or make a rosette, for a rosette is often challenging for the player with the move. But in this position Qe4 allows Rc5+, followed by Kb7, getting the defending pieces further away from the corner.
Let’s look at Qd6, creating a rosette pattern, as Mr. Grimmell calls it.
Diagram-3: Black to move
In this particular rosette, black cannot move Rb6 because the rook would be pinned by Qd4, and black would quickly lose (Ka8 would then fail to Qa4+ and Ka6 would allow White to play Kc7, threatening both mate and the rook). Black cannot move Rb7, in Diagram-3, without quickly losing the rook to Qa3+ and then Qb4+.
Diagram-4: Black just moved Rh5
White now has a way to prepare to shield the white king and to threaten mate at the same time. Do you see it? It’s Kc7!
Diagram-5: White moved Kc7!
White now threaten a mate-in-two beginning with Qa3+ and another one beginning with Qb6+. Black has not reasonable choice except to check the white king with Rh7+.
Diagram-6: Black moved Rh7+ and white then moved Kc6
We now see what Grimmell calls the Javelin position, in Diagram-6. Black has the move but what could work better than Rb7, which allows the Philidor position after Qa3+, Kb8, and Qa5? The Philidor is well known in the winning technique. Look instead at Rh1.
Diagram-7: The black rook now appears safe (white’s move), but is the king safe?
In Diagram-7, black has just moved the rook to h1, apparently putting it on a safe square. But what about the black king? What is that rook doing, other than keeping far away in a safe place? Notice that the defending king is hemmed in at the upper left corner. How many ways does the queen have to make a check while preparing to checkmate? More than one, including Qc7+ and mate next move.
The Philidor position is covered elsewhere, so that’s it for now, for this particular corner defense of the queen versus rook end game.
Moving Rc8 soon results in a fatal back-rank prison for the black king
How do you draw when you have only a rook and king and your opponent has only a queen and king?
Video by Derek Grimmell