Bishop Knight mate on Chess.com

This reminds me of a story I read about a master who was struggling to effect this mate and asked some colleagues in the rest room:

How do you mate with a bishop and knight?

You push his king into a corner of the same colour as your bishop.

What if he doesn't want to go? 

I think it's that last question which usually causes people difficulty.

Well I watched your video and was not impressed. Having said that I looked at a bunch of others by various grandmasters linked to on the same page and was even less impressed. At least the one you recommended gave an explanation of some of the ideas but sadly nowhere near enough.

To start with, all the videos were agreed that the first thing to do is to look at what colour your bishop is. So far so good. That's what I do first too. The next thing is to decide what phase you're in. Nobody mentions that. For instance what is the viewer supposed to make of the following position?

After working out what colour my bishop was I would next decide which is the smallest diagonal of the same colour as the bishop and orthogonal to the main diagonal of that colour behind which the black king can be trapped. If the answer is none I start with phase 1. Here the answer is obviously the a2-g8 diagonal so I would skip phase 1 and play it as shown. (Hope you like the last dozen moves - I call it the hopalong.)

But which step should the viewer start with? It doesn't seem to correspond with any positions in steps 2-6, so he may be forgiven for assuming step 1. So I tried that as well and reached the prescribed position in 9 moves, which is supposed to be about right, but the black king was nowhere near g7. Of course I could switch the positions of the bishop and knight and move my king through the gap, but that would take four moves even assuming no interference from Black. Where would the black king be then and how do I get to step 2?

To clarify some of my objections I've played the game in the video and reproduced it as played in the video.

 The first thing to notice is the disparity in the number of moves. It should take under 30, but takes over 40. There is an accumulation of causes.

Firstly the video recommends collecting all your pieces in the centre. There is no good reason given. I think this just makes it harder to coordinate them and renders them subject to attack.  In particular a knight in the centre (which is actually just the two squares in the middle of the opposite coloured main diagonal in this endgame) doesn't cover any central squares so doesn't directly  exclude the enemy king from those squares while tying up pieces defending it.

I recommend, if the knight is in a safe position (as obviously here) to move it only when a waiting move is required and only along a shortest path to the squares that attack the far corner of the wrong diagonal and only if it remains safe, but given that to move it in preference to the bishop. This is not always the most efficient but usually is and should never lose you more than two or three moves. If it's not in a safe position just move it to one. Sometimes you don't even need the bishop (see the last example in my post #114 here https://www.chess.com/forum/view/endgames/bishop-knight-amp-king-versus-king?page=6). 

The video says never make a waiting move with a knight but gives no reason. 

If your king walks toward the key square (f6 in this case) up the opposite coloured main diagonal and the two adjacent same coloured diagonal the black king has no option but to follow you in front on pain of lapsing into a subsequent phase. The best he can do is give you opposition on the forward orthogonal diagonals, but this can be broken by the bishop. (This assumes of course that your pieces are not blocking each other or subject to attack.)

Often you can also stray from the threefold path as in move 5 of my example. (Edit: Just noticed  from Nalimov's mate calls that it was a blunder in this instance. Correct is (only) 5.Nh3 which gives mate in 28.)

The author tacitly admits that the method is inferior by saying it takes about 10 moves to reach the position with the pieces in the centre. It takes another four moves to reach a position equivalent to the final one in my variation from where it would take 20 moves with accurate play, giving an average mate length with no further slips of 34. But the average mate depth is between 26 and 27, therefore he expect to lose 7 or 8 moves in getting the king to the wrong corner.

He then gives a move sequence for getting into Delétang's first net, but there's a much better wall to be built and apropos Delétang's method he doesn't explain why and when it's important to place the bishop on the penultimate squares of the diagonal or the significance of what I've called the "awkward squares".

Having said that the video is obviously popular as you may see be scrolling down to post #120 on the page I gave a link to a couple of paragraphs back.

@hermanstinkt

It all sounded reasonable, but I thought the assertion that the black king would be on g7 was a bit dubious.

The first diagram in my post was actually a bit tongue in cheek, because I set up the pieces exactly as specified when the direction was obviously opposite to that in the video. However I just tried it forcing the same direction and look what happened.

There has to be something seriously flawed with a six step system where there's no linkage between the first and second steps.  I imagine the viewer would be able to see that relocating his knight to d3 in the position reached above will take him back into the video, but in my original example it's back in the first phase.

The problem of course is that the initial position is effectively already in the fourth step. That's why I say there should be something in the videos about recognising the phase of the initial position.

The games must have been more distant in the past than I remember, since I don't see them in any recent games (and have little interest in manually going through hundreds, or thousands of games to find one or two). I would still like to see games from others though, if they have any personal examples they have played and are more easily accessible.

I totally agree with that, the king can go where ever he wants and he doesn't have to go to g7. And you're also right that always relocating your pieces to the center first will probably not lead to the fastest mate. The reason I think it's still a good video is because before the B + N endgame starts the 50-move rule is reset, so there is always time to get your pieces organized first. And if you practice this enough you'll be more likely to at some point recognize: "Hey, I don't have to put my pieces in the center first I'm already in phase #x." 

@KeSetoKaiba

I wanted to go into a B + N endgame, but my opponent didn't want to, which resulted in quite a funny ending: 

 Funny ending. Yes, of course anyone could be checkmated in the "wrong corner" (for B+N endgame). It is just that checkmate in the wrong corner can't be forced.

Checkmate can strictly speaking be forced on the squares adjacent to the wrong corner, but the mates are of limited use because they have maximum depth of three ply. They could sometimes be useful  if you want to extract the enemy king from the corner and you've learned only the Delétang triangle method. E.g.

 I imagine Tazo10 must have seen some explanation of the endgame that asserted the lone king should always run to the wrong corner.

All of what you say is true and I thought the video was better than the others I looked at, but I think if you practise it enough you would more probably come to the conclusion:

Hey, I don't have to put my pieces in the center first.

Indeed:

It's easier if I don't put my pieces in the centre first.

I've studied this, and forgotten it twice now.

After I watched an online game between Finegold and Williams (both GMs) and Williams was up a knight and bishop and pawn against, I think a rook, he said something like  "I'm gonna be left with a knight and bishop aren't I? I have no idea how to mate with a knight and bishop. I mean, I should, but I don't."

It's not that I don't think it's important, but I think it can go pretty low in my priorities.

I've been playing chess OTB for over forty years. I've seen it twice. The last time was about five years ago. On chess.com a couple of times when the opponent has been reluctant to resign I've sub promoted just in order to practice - and partly to "teach them a lesson" :-)

I've spent hours and hours on this in the past. As a matter of "chess honour" I like to think I could carry this out. It would quite humiliating to get to this endgame and not convert. WRT the Women's World Championship, there is a very subtle knight manoeuvre to be carried out if when the king is being driven along the edge, and "goes in the wrong direction" WRT his strategy of staying as far away from the corner opposite to the bishop and tries to cut for the centre - this is what happened in that game.

I've only encountered it once, when I played a fellow rated 500 pts. higher than I was. He had the bishop and knight (a casual game), and I said, "Well, here it is. Can you?" 

He tried valiantly, but to no avail. In practical terms, I'd say it's useless. Silman doesn't even address it in his "Complete Endgame Course," although Pandolfini does. However, in terms of really understanding how to coordinate your pieces and having a great vision of the board, I'd say it's a wonderful ending to master. 

That said, I haven't mastered it. And I'm not going to.

Most simple endgames occur much more frequently than they occur! Paradox? Yeah. They occur in the brain of the players calculating ahead and avoiding a common lost endgame at all cost. They'd either resign or choose a less standard line for the slim chance the opponent fails.

So you don't see this endgame but it's there. It only manifests when time controls are an issue or the players are very weak.

By the way, it's the same reason why you don't see many checkmates though they are the goal of the game.

I worked it out in a weekend on the back of three or four inches of pyjama stripe computer paper (no chess board). The majority of the time was spent on proving (wrongly I now think) that there were draws by repetition on large enough boards.

What probably is useless is trying to mate across the board if you haven't previously looked at the ending. Witness failures by Epishin (Karpov's second) and Ushenina (ex women's world champion). In the latter case I would say she had looked at the ending before to the point of remembering move sequences, but the memory unfortunately lost some moves.

I always maintain that the strength of a player bears very little correlation to how well they play these "simple" endgames. I don't think even strong players play any "simple" endgames well that are much more difficult than KBBK without first spending at least some time looking at them. This ending is commonly not resigned even against strong opposition. See the examples I mentioned in my previous post. Another example is probably KNNKP. Topolov and Karpov reached a drawn version of this in 2000 and between them threw away three half points in the first nine moves (Topolov was ranked number one in the world at the time and Karpov was, well. Karpov).

We have a different definition of "simple" endgames. I do not mean endgames with scarce material but endgames which are practically and theroretically simple - given the conditions of play.

As a (former) 2200+ player I know that the endgame K+B+N vs K is "simple" for most players on that level today (may be not in 1900) and that the complications mainly arise by clock pressure - which I excluded in my post. Occasionally the 50M line may be close but commonly this endgame does not start from the worst theoretical position (kings are mostly active) and there is plenty of room for correcting mistakes.

More important for "avoiding this endgame" is not how well your opponent plays it but how well you believe he plays it. Once the percentage winners is high enough, nobody will risk choosing it. Ms and GMs will absolutely not play this endgame against an equal opponent except in a psychological battle - or under forementioned clock pressure. Most players feel it is discourteous to interrogate your opponent on something he is 99% certain to know and good relations count, especially in OTB games. There is always the press which reports just the incidents. If you take that for a statistical base, you might believe that 99% of all GMs play this endgame to torture their hated opponents and only 1% kindly resigns on foresight.

Note that endgames like K+R+B vs K+R should not be considered simple and K+Q vs K+R is borderline. Some will play them, some will not.

On a separate note: 

Strong chess players do not learn the standard endgames in the same way weak players learn because their calculaton skills and space control are much better. The only really important thing you must know about the K+B+N vs K endgame is in which corner to checkmate. The rest is "shrinking the accessible space of the king until it suffocates" which is a principle for all basic endgames. A 2000+ player is always capable of keeping the net around the king closed and slowly shrinking its size - simply by calculation. The process won't be accurate but it will be good enough. Weak players can't do that and see their opponents monarch escape again and again. To get this endgame under control they need to memorize specific piece positions and specific moves to advance from it. And exercise it every week because they are dead meat when they forget it.

That is why K+B+N vs K s basically a simple endgame. much simpler than the others I mentioned. You need not learn any patterns. There is the 50M threat though and if you find your calculation skills are not sufficiently efficient to avoid it you will study to improve some part of your personal checkmating procedure - e.g. the best use of the knight to eliminate king flight squares along the 1st rank. And still do the rest by pure calculation.

Thus, all strong players can win this endgame in a fair amount of moves. Unfortunately, calculations consume time and that confuses the issue. With fixed patterns in your head you can win this endgame much faster and that will make a big difference under time pressure. It explains why top players will occasionally play on and might get a draw. And it explains why top players will try to learn the effcient patterns of this ending. They wouldn't need them with an extra hour on the clock or without 50M.

Btw, I don't how SF performs on this endgame but if it fails it is because it has no sense of space domination and shrinking spaces - not because its reading depth falls short!