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K+Q vs K+minor piece: Two endgames you should know

K+Q vs K+minor piece: Two endgames you should know

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Jpatrick
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Sometimes everything comes off the board, and you are left with a Queen vs your opponent's minor piece.  If you don't know what you are doing, the defender can put up stubborn and annoying resistance.  Let's take a look at how to win this kind of ending. 

 

The easier of these two is KQ vs KB  The main reason is that the Bishop can only cover one color of squares, which means that there are 32 squares that the Bishop cannot cover.  If the weak side has a dark squared Bishop, then that means the King and Queen should attack on the light squares.

 

 Consider the position below where the White King and Bishop occupy the center, while the Black King and Queen are temporarily in disarray.

I will demonstrate how to win this ending by playing it against a chess engine at full strength.  In theory, the starting position is mate in 15.  As usual, my play wasn't perfect.  Where better moves were possible, I noted it in the game score.

 

 
So, the strategy for this one is easy.  Attack on the squares that are opposite the Bishop's color.  With that in mind, it is easy to find good moves.
 
 
If I magically turn the Bishop into a Knight, things become more difficult.  The main reason for this is that the Knight can cover any square on the board.  What naturally follows from that observation is that the strong side has to always look out for game-prolonging checks and Knight forks.  In the position below, Tablebase tells me that Black can force mate in 20 with White to move.  

That's nice to know, but what is really needed here is a coherent strategy to bring home the full point. With that in mind, consider this.

  1. If you can do it immediately, get control of the center.  This will force the King and Knight
      toward the edge of the board.

  2. Restrict the defending King so that it has less and less room to operate.

When the King has little enough room, one of two things will happen.  Unstoppable mate threats will become possible or the Knight will be driven away.  If the Knight is driven away, then it's vulnerable to queen forks.

That's the strategy, and it will work, but I believe it helps to think using specific strategic tools. Observe that if the Queen or the King attack the Knight, the number of possible King moves becomes very limited. Either the King protects the Knight, or the Knight has to move somewhere.  This can ease the task of calculation during the process.  

Next, consider using the Queen to cut off a rank or file, restricting the King to one side of the board.  You can move your Queen anywhere along the rank or file you are using to restrict the King. The other side of the board is thus taken out of play.

With all of this in mind, let's look at an example where I replaced the Bishop in the earlier example with a Knight.
 
 
 
 
That was a pretty good example of what to do, but let's review.  Where does the Queen go in this process?  Its main job is to cut off the King along a rank or a file.  Okay, good.   Where does the King go?
 
That is a brilliant question.  Once you understand the answer, the process becomes easier.  Let's look at another example, and then maybe you can figure out where the King goes.  If not, I will explain it below.
 
 
 
That example involved cutting the King off along ranks.  Let's look at the same idea cutting off files instead.  Where the King belongs should be clear from the annotations.
 
 
So, to summarize, the King goes one rank (or file) over from the one that the Queen is using to cut off the defending King.  From there, it controls key squares, that allow the Queen to drive the King toward the edge of the board.
 
Here's hoping you find these demonstrations useful.  You might need to know this some day.