Have you ever played this endgame?
Then you may know it should be an easy win for white.
But have you ever let this endgame come to an end of stalemate? Perhaps while in timetrouble? Or while playing blitz?
In this case, you'll know there are some positions to handle with care.
So, for everyone who doesn't yet know how to handle this, let us examine the winning plan.
First, we have to confine the opposing King to the edge of the board.
Second, we bring our King to the place of the action. The place of the action in this case being the side of the board where we've trapped the opposing King.
Third, we drive the opposing King to a square where it can be mated.
Fourth, we mate the King.
As this may sound easy enough, it's still only a plan. We need to make moves at the board to implement this plan. So let's see which moves to play...
Let's assume black starts to play. He knows our winning plan and therefore plays 1...Kd7, trying to get away from the edge.
Now we have to confine the King as much to the edge of the board as possible. So we play Qa6. (Note that Qf6 accomplishes the same)
Now the King is locked in a (kind of) box. This is the time to bring our own King to this box to help the Queen. In the meantime the opposing King can do nothing else than move around in the box. So we play on 2...Kc7, 3. Kg2 Kd7 4. Kf3, Kc7 5. Ke4, Kd7 6. Ke5 hitting the edge of the box.
And here comes the tricky part. We have to drive the opposing King to a mating position, while at the same time avoiding stalemate.
Black knows this and his last hope is stalemate. So play goes on like 6... Kc7 7. Kd5, Kb8.
Look at this position. Black's only move here is ... Kc7. So black is hoping for white to play Kd6?? (or Kc6??) stalemate! This last move covers c7, so black has no more moves available, as you can see for yourself in the next diagram.
Ofcourse we recognize this, don't we? So we play something like ...
8. Kc5 allowing black to play 8...Kc7.
And only now we start the third part of our plan: chasing the King to a square where it can (and will) be mated.
We play 9.Qc6, forcing the King to the edge.
Now black has to choose between9... Kb8 and Kd8. We'll take a look at Kb8.
We'll make the box as small as possible by playing 10. Qd7. (watch out for stalemate by Kb6).
Do you notice black only has two squares left?
Now we bring the King in to b6: 10...Ka8 11. Kb6, Kb8
And now we're ready to deliver mate. There are two mating patterns available.
The first is to play the queen to the backrank like this...
The second is to bring the Queen in contact with the King like this...
And now for another stalemate we had to avoid.... The stalemate after 9...Kb8
Here you could easily, without thinking, play Kb6.
This would be played to bring your King in to help mating. Only in this position it is stalemating! It takes away the a7-square and thus throws away half a point.
Could you imagine the same thing happen with the black King at d8?
The King and Queen vs King endgame is easily won for the superior side.
Superior side: If you're at the winning side... You know the winning plan, so win!
Inferior side: If your opponent has the extra Queen and lots of time, you might as well surrender.
On the other hand, you might just be able to trick him/her into delivering stalemate.
If you feel this might happen, due to time-trouble or just inferior play, just go for it.
You now know some positions that might help you succeed...