ChessKing and queen against a bare king is always a win, and it doesn't take many moves. First you use the queen to shut the enemy king into a smaller and smaller "box", then you bring your own king up to help deliver mate. The only thing that can go wrong is stalemate. This is the first endgame everyone should learn, and when you play chess online against the computer, it's often how the game ends.
Key position
How to play it
Step 1: put the queen a knight's move away and shrink the box
The best spot for the queen is a knight's move away from the enemy king. From there, the queen's two lines form a box around the king: it can't get out, and it can't attack the queen either. Every time the black king moves, the queen follows to the new knight's-move square, and the box gets one size smaller.
White's king didn't move once here. The queen drove the black king into the corner all by herself.
Step 2: bring the king up and mate
Once the black king is stuck on h7 and h8, leave the queen where she is and walk your king over. When the white king reaches f6, the queen can mate on g7, protected by the king.
There are two common mating patterns: the queen right next to the enemy king, protected by your own king (like Qg7 above), or your king pins the enemy king against the edge and the queen checks along the back rank.
Common mistakes
As the box gets smaller, the easy mistake is to take away the king's last square without giving check. That's stalemate, and it throws away the win.
The other mistake is checking too soon. In the same position, Qg7+?? leaves the queen unprotected and the black king simply takes it, which is also a draw. Before your queen goes near the enemy king, ask yourself two questions: Does the king still have a square? Is my queen protected?
Practice puzzles
Show answer
1. Qd8# The queen goes to d8 and checks along the back rank. The white king covers a7 and b7, so the black king has nowhere to go.
Show answer
1. Qd7 For example, pull the queen back to d7 and give the king b8 (Qe7 and Qf7 work too). The black king has to go to b8, the white king comes closer, and mate follows. Any king move by White, or Qb6, is stalemate.
Show answer
1. Qe8# The queen goes to e8 and checks along the back rank. The white king covers f7, g7 and h7, so there is no escape.
FAQ
How many moves does the queen mate take?
According to the tablebase, it never takes more than 10 moves, even from the worst starting position. The box method may take a few more, and that's fine as long as you finish within the 50-move rule.
Why do I have to bring my king?
A queen alone can't checkmate a king. She can trap it, but the final move needs something to protect the queen or to block the king's escape. When you mate a lone king, your own king is an essential helper.
Can I just keep giving check?
Better not. Endless checks often chase the king back toward the center. Boxing it in with the queen first works much better than random checks.
Try it yourself
Once you know the queen mate, look at the rook mate next. The idea is similar, but the king has to help even more. All the endgames are collected in Chess endgames. To practice for real, go to free online chess, get down to king and queen against king, and play on until you mate.