King and queen against a lone king is the first endgame most players learn, and the one they most often fumble when the clock is ticking. There is no secret to it, but there is an order of operations: shrink the board with your queen, walk your king up, and finish on the edge. Get the sequence right and the mate arrives almost on its own.
A queen by herself can never deliver checkmate. She can chase the lone king around forever, but the moment she gets close enough to check him, he simply steps aside or takes her if she is undefended. Every mate in this endgame needs your king involved, covering the squares the queen cannot.
That is not a problem, because you have time. The fifty-move rule gives you fifty moves to get the job done, and the technique below takes far fewer once you have played it a handful of times. The lone king cannot attack your queen at all unless he is standing next to her, so keeping your distance costs you nothing.
If you remember a single idea from this article, make it this one: put your queen a knight's move away from the enemy king.
A knight's move is far enough that the king can never capture your queen — he would need two moves to reach her — and close enough that the queen slices the board in two. The king is suddenly trapped inside a rectangle and cannot cross the lines your queen controls.
An example makes it clear. Black king on d5, white queen on e3. The queen covers the whole e-file and the whole third rank, so the black king is stuck in the rectangle from a4 to d8. He cannot cross to the e-file and he cannot drop below the third rank. He is not in check and he is not in danger — he is simply boxed in.
As soon as he moves, you repeat the trick. If he shuffles to c5, you play your queen to d3, a knight's move from his new square, and the box shrinks again. Each repetition costs you one move and buys you a smaller prison.
Do not chase the king with the queen from square to square, and do not rattle off pointless checks. Checks push the king away from where you want him and waste moves. The box does the work; the queen just holds the walls up.
While you are shrinking the box, your own king should be walking towards the action, not spectating in the corner. Move him a square or two at a time. He cannot help until he is close, and the closer he starts, the shorter the whole exercise becomes.
Once the enemy king is pinned against the edge, your job changes. Keep the queen a knight's move away to hold him in place — she no longer needs to advance — and march your king up until he stands a knight's move or two from the enemy king. He should be covering escape squares, not standing in front of the queen.
You are ready to mate when your king controls the squares next to the enemy king and the queen can step in to deliver a check that cannot be answered. With the black king on a8 and your king on b6, a queen move to b7 is checkmate: the queen is protected by your king, so the king cannot take her, and she covers a7 and b8. Every escape square is gone.
The edge does not have to be a corner. The same mate works anywhere along the side of the board, as long as your king is close enough to support the queen and there is no square left for the king to run to.
This is the mistake that costs players half a point, and it has nothing to do with the technique above. Stalemate happens when the enemy king is not in check but has no legal move at all — the game is drawn instantly.
The classic blunder looks like this. Black king on a8, your king on b6, your queen landing on c7. It looks like a natural finishing move and takes away a7 and b8. But c7 gives no check, the king on a8 has nowhere to go, and you have thrown away the win.
The safe habit is simple. When the enemy king is on the edge or in the corner, give check unless you can see the mate clearly. If you are not certain, check first, let him shuffle, and start the process again. A wasted check costs nothing; a stalemate costs everything.
Set the position up with the lone king starting near the centre and give yourself twenty moves to mate. Play it out slowly, counting the box each time you move the queen, and notice how much of the work the knight's-move rule does on its own. Find a training partner, a computer set to a low level, or play both sides yourself until the pattern feels automatic.
Then try it with fifteen moves, and finally with ten. When you can mate comfortably in ten, you will never worry about reaching this endgame again — and you will stop being the player who offers a draw with a queen on the board. Learn the box, keep the queen safe, bring the king, and watch the edge. That is the whole method.
