The key pattern called diagonal (named by Derek Grimmell) appears to have these characteristics, in the queen-versus-rook end game of chess:
- Defending king is on the edge of the board or in a corner
- Immediately along a diagonal from the defending king are the other three pieces
- The order is this: defending-king, rook, attacking-king, queen
- Black is to move
When the defending king is on a corner square, the win is too easy for the attacker, at least for the player who knows about the Philidor position of the queen-versus-rook. Let’s examine a more challenging example: when the defending king is not in a corner.
From Diagram-1, we’ll first look at what happens when the defending king moves off the edge of the board. That defense does not hold up for long.
Diagram-2 (Black just moved Kb2)
The problem with moving the black king to b2, as shown in Diagram-2, is that the rook is still under attack. This restricts how the defender can respond, especially to the queen now moving to b4, with check.
Diagram-3 (White just moved Qb4+)
Notice the defending king has only one reasonable way to move out of check: Kc1, for the other two king-moves immediately lose the rook. Also notice that there is no stalemate defense available to the defender here. The queen is just a bit too far away to make a stalemate, and that is the point of some of these positions: The queen is ideally placed.
Diagram-4 (Black just moved Kc1)
Now it’s white’s turn in Diagram-4. What would you do, as the attacker?
Be careful here. The defending king is where you want him, on the edge. Checking him with Qe1+ or Qf4+ would just drive him off the edge with Kb2. The key to winning quickly in this position is in creating what Grimmell calls a cage. Observe what happens when the queen now moves to a4.
Diagram-5 (White just moved Qa4)
This is a cage, with both queen and attacking-king pointing to a square immediately next to the defending king. (If I understand the terminology, a thorn is similar but the square in question is a diagonal move away from the defending king.) Be aware that a cage need not have the defending rook on that square: If the rook in Diagram-5 were on b2, white would still have a cage against the defender (although in that case black would be able to move Rb3+, for Qxb3 would make a stalemate, so the cage would not then be helping white).
Notice the critical problem for the defender in Diagram-5. White has two threats, two checkmates: Qxc2# and Qa1#. If black now moves Rb2, white has a mate in three: Qa1+, with Qc3+ and Qd2# following.
Diagram-6 (Black just moved Rd2+)
Two misconceptions need to be avoided for the attacker in many queen-versus-rook end games: You don’t need to be constantly checking, and you don’t need to always prevent the defender from checking your own king.
In Diagram-6, the defender gets to check the attacking king. Great . . . or is it so good for the defender in this position? I give this Rd2+ move suggestion for black (resulting in the position shown in Diagram-6) not because it saves the defender but because, from the previous diagram, no other move does much better.
Diagram-7 (White just moved Kc3)
That was an obvious choice for white, getting to the position shown above: Kc3. How can black continue? The king has only one move, to b1, resulting in the immediate loss of the rook. Again, there is no possibility of a stalemate, for the black king would be able to move to b2 after the rook is captured.
White threatens Qa1#, and the only rook move that appears reasonable is Rb2, preventing that immediate mate. Shall we look at that?
Diagram-8 (black just moved Rb2)
What would you do, with the white pieces? I see more than one way to win, for white in this position of a queen-versus-rook end game. Let’s look at the simplest procedure.
Diagram-9 (White just moved Qa3)
This appears to be the easiest way for white to win, moving the queen to a3 to pin the rook and win it. Notice that there is no stalemate resource for the defender, for after the black king moves to d1, white may capture the rook with either the queen or king, and the defending king temporarily escapes towards the right.
We can look at other defensive attempts, from the position in Diagram-1, but for the here-and-now this will do.
A key point to remember in this chess end game is that the defender has the move, otherwise the attacker can just move the king to the key square and make it an orthodox Philidor position.
A sequence of moves that confine what the opponent can do and which can lead to gaining a material advantage or checkmating the opponent’s king—that is the tactical side to chess.
Clear thinking may help solve this puzzle, but clear understanding of the influences of chess pieces can here make an apparently difficult problem easy to solve.
Two books: Beat That Kid in Chess and How to Beat Your Dad at Chess