Endings – Bishop & Knight mate the king

How to Mate with Bishop, Knight and King

TaskRatingComments
DifficultyThis is a difficult ending to learn
FrequencyThis ending comes up very rarely!
DetailThere is a lot of material to learn

This is a notoriously difficult ending. At the very top level, GMs will convert this ending with ease, because they practice it a lot - just in case it comes up.

There are stories of very good players (even IMs and FMs) being unable to win this "over the board". This is a harder ending to win and requires knowledge of the technique. Players tend to find this a hard ending to get to grips with.

I would speculate (from personal experience) this has something to do with the human mind and our innate inability to multitask.

Multitask

A man trying to multitask - it's not going well

Two bishops are easy to get to grips with - one covers one colour, the other bishop, the other colour. We can basically frog-march the king across the board, creating a diagonal wall as we go. Similarly, rooks can close off and box the king. It's easy to limit options for the defender with rooks and bishops; they are geometrically easy.

Bishops and knights don't tend to work so well together but they can mate the defender with the help of the king. In this section, we'll show you how.

Three things you will learn today

  1. This is a technically won position from any start, unless either the knight or bishop can be captured by force.
  2. How to push the king on to one side
  3. Pushing the king across to the right corner.

Part 1 of 3 - A won position

Your Turn! White to play

More detail on the study position

Black is stuck wobbling between g8 and h8 - we start by restricting him further - 1. Nh6+! leaves only one square 1...Kh8 when Bd4 finishes black off!

(BE CAREFUL)! White to play

More detail on the study position

Unlike the previous position, white cannot mate in two and must be very careful.

The natural 1.Nh6?? is a disaster. Black cannot move but he is also NOT in check - STALEMATE!

We make use of a waiting move, so black will stumble into our first study

1. Bb4 (any bishop move along the a3-e7 diagonal works) 1..Kg8 and now we're back to the position above!

2. Nh6+ Kh8 3. Bc3#

Summary of part 1

The king being blocked by a king on g6 and bishop controlling f8 means we have all the time we need to re-route our knight to h6 to finish the game off.

Note: The Geometry of the chessboard means the same bishop and king combo can restrict to h8 by the bishop controlling h6 and the king on f7 with the defending king on h7/h8 also. This also works with Kb3, Ka1-b1, Bishop controlling c1 and Kc2, Ka1-a2, Bishop controlling a3.

This is the position we are aiming for (since we know how to win from here, if we can reach this position).

Let's look at how to get here!

Part 2 of 3 - Pushing the king to the side of the board

A quick aside

An ideal position but not a realistic one!

More detail on the study position

[Event "Study of Bishop v Knight"] [Site "Chess Toolkit (Author = Ed.)"] [Date "2017.02.04"] [Round ""] [White "Bishop and Knight Owner"] [Black "Owner of a Fearless King"] [Result "1/2-1/2"] [ECO "N/A"] [Annotator "Ed."] [SetUp "1"] [FEN "1k6/8/K7/4B3/2N5/8/8/8 b"] [PlyCount "44"] [EventDate "2017.02.04"] [EventType "Endgame Study"] [EventCountry "GB"] 1...Ka8?? {suicide!} (1...Kc8 {not only gets the black king out of the corner but he's running to freedom via d7 and into the middle of the board! Mindful we have 50 moves to win, this could be a challenge if the king gets out!}) 2. Nb6 {This is what we would love to happen!}
What we've learned is that although there is a theoretical mate in the "other corner", we cannot force it.

As we know the technique to mate the king once we get to the Kg6, Kh8-g8, Bishop covering f8 set up, we should aim for this.

Getting the king to the side of the board

This is actually not too tricky but it's all about co-ordination of the attacking forces.

If the defender knows the winning technique, as well as running to the wrong corner, they will also try and stay in the middle of the board as long as possible.

Let's take the following starting position and show a key method to push the king back:

    1. Get all our attacking units together
    2. Push the king to one side where our king initially blocks the exit (e.g. Kd6 and Kd8)
    3. We will then look in section 3 how to finish the king off!
[Event "Study of Bishop v Knight"] [Site "Chess Toolkit (Author = Ed.)"] [Date "2017.02.04"] [Round ""] [White "Bishop and Knight Owner"] [Black "Owner of a Fearless King"] [Result "1-0"] [ECO "N/A"] [Annotator "Ed."] [SetUp "1"] [FEN "8/8/6B1/8/8/2k5/8/2K4N"] [PlyCount "44"] [EventDate "2017.02.04"] [EventType "Endgame Study"] [EventCountry "GB"] 1. Bc2 {This is already a key dynamic. Placing the bishop next to our king and theirs kills off b3 and d3. Since our own king covers b2 and d2, the defending king is pushed back} 1...Kd4 2. Nf2 {bringing our knight closer to the action - we need everyone taking part!} 2...Kc3 (2...Ke3 3. Nd1 Ke2 4. Nc3 Ke1 (4...Ke3 5. Kd1 Kd4 6. Kd2 {and we continue with the plan in the mainline}) {and we are just running the king to the h file instead!}5.Bd1!{using the theme we saw on move 1!} 5...Kf2 6. Kd2 {and we are again doing well!}) 3. Nd1 {all our units are together, so we've achieved our first aim - now to push the king to one side} 3...Kc4 4.Kd2 {the defending king can now run to the side with Kb4 but as we want him near a side, this isn't a big concern!} 4...Kd4 5.Bd3 {the same idea as before - we are making good progress! Note how having the king bishop and knight in close proximity make this much easier - of course we still have flexibility if we work with the bishop from distance but the king and knight in particular are close range pieces.} 5...Ke5 6. Ke3 Kd5 7. Nc3 {again not worrying too much, the king can only run to one side so we concentrate on keeping our pieces close and limiting squares near the king.} 7...Kc5 8. Ke4 {Bishop and knight are on good squares so we use the king to push black to either the b file or 8th rank} 8...Kb4 9. Kd4 Kb3 10. Nd1! {cutting off b2 so the king can either go back to b4 and our bishop trick pushes again or go to the a file directly!} 10...Kb4 11. Bc4 Ka4 12.Kc5 {we have b3 and b2 covered so the king is left to wonder lonely along the a file} 12...Ka3 13. Bd5 {our pieces are placed beautifully so we waste a move} 13...Ka4 14. Nb2 Ka3 15. Nd3 {this may look mysterious but we have now got our king on a thumpingly good square and all our pieces are again in the action! Our bishop is covering b3 and b7 so we have used our knight to limit the king more!} 15...Ka4 16. Be6! {we waste one more move to let the king choose his fate} 16...Ka3 (16...Ka5 {and we have an improved version of section 3, after} 17. Bd7) 17. Kc4 Ka2 {17...Ka4 and we are ready to go to section 3} 18. Kc3 Ka1 {now we are ready to look at section 3!})

Summary of part 2

We have learned there is really only one corner we can hope to mate the defending king in.
That's the corner of our bishop.

We also saw that it is possible to push the king to one side of the board and that will help us!

The Geometry of the chessboard means our plan is flexible and if the king goes left, we can press him to the a file or up and we go for the 8th rank.

We now see how to move from the wrong corner to the right one!

Part 3 of 3 - Getting the king into the RIGHT corner

This is the famous bit of the technique but hopefully we now know 1. Why it's important and 2. How to get there!

[Event "Study of Bishop v Knight"] [Site "Chess Toolkit (Author = Ed.)"] [Date "2017.02.04"] [Round ""] [White "Bishop and Knight Owner"] [Black "Owner of a Fearless King"] [Result "1-0"] [ECO "N/A"] [Annotator "Ed."] [SetUp "1"] [FEN "8/8/4B3/8/8/2KN4/8/k7"] [PlyCount "44"] [EventDate "2017.02.04"] [EventType "Endgame Study"] [EventCountry "GB"] 1. Nb4 {the knight is moving to c2 to stop the king going back to a1 - our technique will take the white king from a1 to h1 where he will be mated!} 1...Kb1 2. Nc2 Kc1 3. Ba2 Kd1 {Now is the critical bit! Our king shouldn't move and there's no value in moving the bishop either} 4. Nd4 {this is the start of the W manoeuvre - it looks like black can wriggle out but it's covered - trust me!} 4...Ke1 {hoping to run with Kf2 etc.} (4...Kc1 5. Ne2 {and we continue the march} 5...Kd1 6. Kd3 Ke1 7. Ke3 Kd1{hoping to scurry back} 8. Bb3 Ke1 9. Nf4 Kf1 {Now everything is well placed so the bishop swaps duties with the knight} 10.Bd1 Ke1 11. Bf3! Kf1 12. Ng2 {stopping the king returning to e1}12...Kg1 13.Be4 {not the fastest but the idea is clearest - we play a waiting move so black chooses his own fate} 13...Kf1 14. Kf3 Kg1 15. Bd3 {denying f1} 15...Kh2 16. Nf4 {now this should be familiar from part 1 - the king is in the ideal box and his days are numbered!!} 16...Kg1 17. Kg3 {Now we know it!} 17...Kh1 18. Bc4 {to waste a move - of course not 18. Nh3 (draw!!)} 18...Kg1 19. Nh3 Kh1 20. Bd5) 5. Kd3 Kf2 {The king has escaped! Or has he?!} (5...Kf1 6. Ne2 {and it's the same plan but easier} 6...Kg2 7. Be6) 6. Ne2! Kf3 7. Be6!! {what a picture! The king can only hobble lamely back towards the end of the board} 7...Kf2 8.Bg4! {another great move - the king can't go back to the 3rd rank now either} 8...Kg2 9. Ke3 Kf1 10. Nf4 Ke1 11. Ng2 Kf1 12. Kf3 Kg1 13. Ne3 Kh2 14. Kf2 {and now we are familiar...} 14...Kh1 15. Bf5 Kh2 16. Nf1 Kh1 17. Be4

Summary and Recommended Next Reading

  • This is a won position
  • We need to mate in the bishop's corner which involves: 1. Pushing to the edge of the board and 2. Getting the king into the right corner!
  • This is tricky and doesn't come up often.