King and Queen vs King: how to mate without stalemating

King and queen against a lone king is the first checkmate every player has to own, and the technique fits in three phases: use the queen to shrink the box the enemy king lives in, walk your own king up, then deliver mate on the edge of the board. A queen up you cannot lose, but you can very easily draw, because the one real mistake here is stalemate. The knight move rule below removes that risk.

The box and the knight move

The core idea is the box: the queen’s lines act as walls and the enemy king is locked inside whatever rectangle is left, and that rectangle has to shrink on every move. The safest way to do it is to put the queen a knight’s move away from the enemy king. From e5 those squares are c4, c6, d3, d7, f3, f7, g4 and g6. The queen on c2 can reach c4, so the move is 1.Qc4: the c file and the fourth rank become walls and the black king is trapped in the rectangle from d5 to h8, twenty squares.

From here you repeat. The king runs, you place the queen a knight’s move from his new square, and the box shrinks on its own: 1...Kd6 2.Qb5 Kc7 3.Qa6. Two queen moves have cut the box from twenty squares to fourteen, and the black king is confined to the last two ranks with only b8, d7 and d8 available. The white king has not left g1. If the enemy king walks toward your queen, so much the better: the box shrinks faster.

The stalemate trap

Stalemate is a draw: the side to move is not in check and has no legal move at all. A queen up, it is the only way to throw half a point away. With the queen working alone, the knight move rule fails in exactly one case: when the enemy king is already in one of the four corners. Black king on a8 with the queen on b6 is stalemate, and with the queen on c7 it is stalemate too. The same happens, mirrored, on a1, h1 and h8. Away from the corners, the queen on her own can never take his last flight square. Once your king joins in the count changes, which is what the next section is about.

Bring your king up

The queen cannot mate on her own: as long as nobody covers the squares next to the enemy king, he always has somewhere to run. Once the box is small, stop moving the queen, since she already holds the black king on the back rank, and march your own king toward him. This is where stalemate comes back: your king starts covering squares the queen already covered, and that overlap works against you.

The concrete case is in the line from the first section: after 3.Qa6 Black replies Kb8, queen on a6 against king on b8. The queen already controls a7, b7, a8 and c8, so the black king’s only free square is c7. If your king steps onto b6, c6 or d6, it takes c7 away and the game is drawn. With your king on c5 instead, the black king still has c7 and you keep making progress.

• Split the work: the queen holds the edge line, your king takes the squares the queen does not already cover.
• Approach one rank short: if the queen sits on the sixth rank, bring your king to the fifth, not to the sixth.
• Count before every step: one free square for the enemy king is enough, zero is a draw.
• Do not rush: the 50 move rule will not catch you. With accurate play, king and queen against king mates in at most ten moves from any position.

Delivering mate

The final mate always has the same shape: enemy king on the edge, queen right next to him, your king defending the queen. With the black king on d8 and your king on d6, the queen goes to d7 and it is over. She checks from close range, she is protected (which is why the king cannot take her), and c7, c8, e7 and e8 are all covered by her or by the king. The pattern repeats along the whole edge: with the white king on d6, a black king on c8 is mated by Qc7 and a black king on e8 by Qe7.

There is a second version, for when your king stands directly in front of his with one square between them: white king on d6, black king on d8. Then the queen mates from a distance along the eighth rank, with Qa8. The white king covers c7, d7 and e7, the queen covers the rest of the rank. Any eighth rank square works as long as it is not next to the black king, because an unprotected queen beside him would be captured.

The routine for the clock

With ten seconds left nobody calculates variations. What saves you is a routine your hand can run on its own, always in the same order:

1. Queen a knight’s move from the enemy king, move after move, until he reaches the edge.
2. Stop the queen and bring your king, counting his free squares before each move.
3. Either king beside him with the queen adjacent and defended, or king in front of him with the queen mating from a distance along the edge.