Bishop and knight vs king?

Is there a method behind this checkmate?  It took stockfish 28 moves to checkmate from a random position, so it must be pretty difficult and I can't seem to find any lessons on it, so is there a method behind it or is it just raw calculation?

Yeah, there are a couple of methods, though I'm no good at them 

You should be able to find Lessons, maybe a video, and Drills on the checkmate here. 

I believe the mate is 32 moves from the worst postion, with perfect play.

I know this...

The goal usually is to get this position with pieces near the corner with the same color as the same color as the bishop. Its 2-move checkate no matter whos move it is 

or this position (rotational symmetry doesn't matter)

This question returns every 4 weeks or so. The last one was:

https://www.chess.com/forum/view/endgames/bishop-knight-amp-king-versus-king

The forelast one was:

https://www.chess.com/forum/view/endgames/bishop-and-knight-mate-1

The pre-forelast one was:

https://www.chess.com/forum/view/endgames/why-not-win-with-kinght-bishop-1

The pre-pre-forelast one was:

https://www.chess.com/forum/view/endgames/bn-vs-king-simple-theory

A few more:

CHESS.COM

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http://www.chess.com/forum/view/endgames/checkmate-with-knight--bishop

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https://www.chess.com/forum/view/general/who-here-knows-out-to-mate-with-kbn-vs-k

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https://www.chess.com/forum/view/general/bishop-king-and-knight-checkmate

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https://www.chess.com/forum/view/general/how-do-i-learn-bishop-and-knight-checkmate

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https://www.chess.com/forum/view/general/rare-end-game-encountered

I have a tutorial on how to systematically do this mating pattern on chess.com if you take a look at my two blogs on this.

Karsten Muellers endgame manual will have you playing it with ease in less than a day

I just learned recently that there exist two main methods of bishop-knight mates: (Philidor's) "W" Method, and (Delétang's) Triangles Method. This makes a difference since if someone explains one method, it might be the opposite of a method you find in a textbook. This confused me at times since the learning material seemed to be contradictory--because it was! I'm learning both methods better now, though I mostly know the "W" Method. Different people prefer different methods, and no one method is superior in every way to the other.

I have been playing chess for 50 years and so far as I recall this ending came up once.

I was playing what I thought was an alcoholic derelict for a "big bottle of beer" who claimed to have done black belt karate and represented Hungary in an olympiad.  I though it was drunken ranting, until he started to play.

Anyway, I got into a winning position, with trouble, and wound up in N +B vs K.  I managed to find the win over the board, with a lot of trouble.  Just too weird.

If you have a score of that game, please post it! Per trivia I've found online regarding this mate, it occurs only once every 5,000-6,000 games, and when it happens at a chess club, you'll usually have people gathering around to watch it. The latter is reason enough to learn it.

Here is a game I lost recently that shows the method. My opponent didn't do it perfectly but completed mate 3 moves before the 50 move rule would have applied.

Awesome, Strangemover! Thanks. I'm saving all such games I find.

No worries. I think just remember to push the king to a corner the same colour as your bishop and don't let it out. Get your zugzwang on!

That is pretty much all you need to know for this endgame!

There is only one reason why players can't execute it. They simply can't calculate a few moves ahead. They are very, very weak on visualizations. Some will argue that even GMs failed but such is only under extreme time pressure; calculations require time. Most endings can be finished by following simple rules and patterns but these are not as simple in the K+B+N vs K ending. You either have to learn a number of patterns and conversions (into subsequent patterns) or you just calculate. Calculation enables you to shrink the space of the bare king until the checkmate is obvious. All other theory  for this ending only exists to compensate for poor calculation skills!

I'm working on a nice PDF document that will describe both methods. It will contain every game I've found with this ending (including Strangemover's), and will fill in the gaps of where typical learning material leaves off. For example, as Arisktotle mentioned, most such learning material leaves off with the king close to the right corner, and basically just says to figure it out from there. Pandolfini's Endgame Course book, which uses The W Method, does the same thing, but provides several examples spanning several pages of *typical* positions at that point, which you're supposed to memorize to help overcome visualization deficiencies. Another important omission in such learning material is the process of driving the lone king across the middle of the board. I used to think that there were patterns and an algorithm to follow there, but there aren't, as I recently realized, only *typical* positions again, which implies that no methods presentated for that phase of the mate are guaranteed to work! Also, there exist minor variations in the procedures in those two phases within The W Method, and different authors show different variations. I'll post my article online if/when I'm done, and I'll let people here know about it.

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(p. 37)

ENDGAME 19

W: Ke8, Bf8, Ne5 B: Kg8

White moves and wins

Another Mate in Four

Black's King is about to depart g8, leaving the way open for

White's King to enter f7. This means that the Knight can relin-

quish its coverage of g6 and reposition to control h7. Starting

from e5, the Knight has three equally good ways to begin

deployment: 1. Nd7, 1. Nf3, and 1. Ng4.

      A

1. Nd7 Kh7

2. Kf7 Kh8

3. Bg7+ Kh7

4. Nf8 mate

     (1-0)

      B

1. Nd7 Kh8

2. Kf7 Kh7

3. Nf6+ Kh8

4. Bg7 mate

      (1-0)

Pandolfini, Bruce. 1988. Pandolfini's Endgame Course. New York, New York: Fireside.

That position you mentioned at move 7 is called The Lock. It's funny but this mate is just complicated enough that it has its own terminology: The Drive, The Lock, Phase 1, Phase 2, The W Method, The Triangles Method, and I added a few more of my own: Bishop Sandwich, The Edging, Phase 0, etc.

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(p. 36)
ENDGAME 18
W: Kg6, Bb4, Ng7 B: Kg8
White moves and wins

Mate in Four

Interesting thanks. In the position given, I would do it differently. It takes one move more, but I try and head to what I think of as imprisoning the opposite king with the bishop on h6 as a mini goal.

This would be revolutionary for this endgame :-)

Interestingly I played in an English county chess match last year where a team mate was the defender and the bishop/knight/king player graded at about 2100 fide couldn't force the mate. He had limited time but sufficient. He would have kicked himself after.