Phase 1 of Knight Bishop Checkmate

Question

I am working on my basic endgames and I am aware that knowing the Knight and Bishop Mate is unlikely to come up anytime soon, but I still want to know this better.

Once we reach a position like the one immediately below this paragraph, I know what to do to win (with common variations omitted):

[Title "SetUp 1"]
[FEN "7k/8/5K2/4N3/2B5/8/8/8 w - - 0 1"]

1. Ng6+ Kh7 2. Be6 Kh6 3. Bg8 Kh5 4. Ne5 Kh4 5. Kf5 Kg3 6. Ng4 Kf3 7. Bc4 Kg2 8. Bb5 Kg3 9. Bc6 Kh4 10. Kf4 Kh5 11. Be8+ Kh4 12. Bf7 Kh3 13. Ne3 Kh4 14. Ng2+ Kh3 15. Kf3 Kh2 16. Be6 Kg1 17. Ne3 Kh2 18. Kf2 Kh1 19. Bf5 Kh2 20. Nf1+ Kh1 21. Be4# 1-0

However:

What I am struggling with is how to go from some arbitrary position to something like the setup above. It seems like most books/articles/lessons just take it as a given that you can get the king stuck in the "bad" corner. So, as nice as it is to practice from that position or standard starting positions, no one has explained a technique to go from some arbitrary board position to that checkmating pattern.

From an actual game (where I admitted sacked pieces because I wanted to actually get a knight-bishop mate on the board for style), black to move:

[Title "From an actual game"]
[fen "8/8/8/7K/3n4/5k2/8/6b1 w - - 0 1"]

Or this, just to be obnoxious:

[Title "Obnoxious case"]
[fen "B6N/8/8/4k3/8/8/8/7K w - - 1 0"]

And yes, I know that we can analyze and come up with The Answer™ to checkmate most efficiently, but what I need is a replicable technique I can use in an arbitrary position with this material (especially in time trouble) like I have for queen, rook, and two bishops.

Answer 1

As Brian Towers already said – he finished his post earlier than I did, I was busy right-clicking squares – it is about building a barrier with king, bishop and knight. Consider this example from Dworetzky's endgame manual (can be found as PDF on the internet). White narrows the barrier step by step until it is mate.

Such barriers happen earlier too, usually as soon as the knight & bishop party have centralized their pieces. In your game, the barrier is already perfect after the bishop has moved to g3 and the knight to c5. The black king is only needed for the square g4, the rest is controlled by the two other pieces. Black then, again, slowly narrows the barrier. Notice the maneuver 7...Bc7! and 9...Bd8, which reduces the barrier along the diagonal. Later the trick 17...Be7+ further narrows the barrier.

In your second example it is first about not losing one of the pieces, then centralizing the king and knight, but a barrier already happens after 6...Ke3 7.Nf3 (the bishop will take care of the orange squares).

Some general hints:

• King and bishop alone can prevent that the other king can cross the diagonal barrier which the bishop creates. E.g. Be4, Kf5 vs. Kd4 – the Kd4 can not enter the upper triangle of the board. These two pieces do the main work, the knight adapts to their barrier. Examples: 1, 2, 3, 4 (in the following subline).
• The knight and bishop work well together when they are placed on squares of the same color. The knight controls the squares which the bishop does not. Examples: 1, 2, 3, 4.
• The king and bishop make waiting moves. Examples: 1, 2.
• The bishop is good at narrowing the barrier. Examples: 1, 2, 3.
• There can be zugzwang situations comparable to pawn endgames, where it makes sense to lose a tempo. Examples: 1, 2.
• The barrier does not have to be complete, as long as it can be closed when the king approaches. Example in the following subline.
• The king can also be mated when not in the corner, and this can be used to restrict him further. Examples: 1, 2.
• Look out for stalemates! Example in the following subline.

You also asked for a premovable mechanism to mate with them in time trouble. It is not as simple as with two queens, but you have a quite good scheme-f method starting with a centralized knight and bishop.

Answer 2

Let's start by reminding ourselves of what the checkmate process involves in general terms and then deduce guiding principles for both black and white.

The checkmating process basically consists of trying to build prison walls around the black king, gradually making the prison cell smaller and smaller until eventually we can kill the king.

Inevitably with just king, knight and bishop our prison walls are going to have holes in them which the enemy king will try and escape through. Only the queen can build a wall with no holes in it. Even the wall built by a rook has a hole in it where the rook stands.

The principles for black are very simple:

1. Stay in the center of the board as long as possible
2. When that fails then head for the corner of the opposite colour to the bishop because you can't be checkmated there.

The principles for white come from the building prison walls task. The king can build a 3-brick wall (the opposition), the bishop and knight can only build 2-brick imitation walls. If it's on the right diagonal then the bishop can also check the enemy king meaning it controls 3 squares.

Also the king can only control squares (build prison wall bricks) one square away from the itself. The knight is slightly better, it can manage 2 squares away.

Hence:

1. All 3 pieces have to work closely together if they are going to herd the enemy king in the right direction.
2. The king and knight have to be close to each other and close to the enemy king to make any kind of progress.
3. The bishop can work both close up and from a distance.

Now let's try and apply that to your "obnoxious case". I will only show driving the enemy king into the wrong corner because you already know what to do then.

The first task is to coordinate the king and knight, i.e. get them close to each other and close to the enemy king.

[Title "Obnoxious Case"]
[fen "B6N/8/8/4k3/8/8/8/7K w - - 1 0"]

1. Ng6+ Kf5 {attacking the knight but staying close to the center} 2. Nh4+ Ke5 {principle 1. stay close to the center} 3. Kg2 {The king is the slowest moving piece. It needs to get close to the enemy king} Kd4 {Stay close to the center} 4. Kf2 {bring the king closer, now we have diagonal opposition} Ke5 {stay in the center} 5. Ke3 {Oy! You! Get out of the center! Notice how the bishop and knight are now coordinating with the king to force the black king back} Kf6 {head for the opposite coloured corner} 6. Kf4 Ke6 7. Nf5 {Not the knee-jerk Ke4. We mustn't leave the knight behind and it now controls d6} Kf6 8. Bd5 {notice the bishop and knight controlling squares around the king forcing black's next} Kg6 9. Ke5 {restricting the black king to 2 files} Kg5 10. Ne7 {trying to keep the black king away from the "wrong" corner} Kh6 {moving toward the corner but giving up another file} 11. Kf6 {taking the opposition and not allowing the black king to gain a file} Kh7 12. Ng6 Kh6 13. Bg8 {you're not going back into THAT corner!}

And from there you know what to do.