Winning in a KBBvKN endgame: possible or too hard for humans?

Question

Apparently, two bishops and a king can mate a king supported by a lone knight, according to endgame tablebases, but it generally takes more than 50 moves, which is why it seems that one is studying that endgame.

Watching optimal play of such a position looks inhuman. It seems that the bishops really dominate the knight and that there are some complicated maneuvers where the king can be forcibly separated from his knight or where he can be pushed towards an edge. In the end, the king and knight are trapped in a quadrant and their moves can be methodically restricted such that the knight is pinned against the black king. Then zugzwang leads to the capture of the knight. So it looks like the game can be seperated into phases but it is really hard to to quantify "progress" just by looking at a position.

Do there exist any analyses or resources on how to learn this endgame anywhere or is it too hard / irrelevant for humans? Do grandmasters have the skills to play this endgame (with or without 50-move rule)?

Answer 1

John Nunn discusses this endgame in the last chapter of his book titled Secrets of Minor-Piece Endings. His analysis includes the pre-tablebase history of the ending and philosophical musings about the use of tablebases. He also includes analysis of the endings based on tablebases, with an attempt to set forth general rules how to play the ending.

Answer 2

Too hard for Humans

Nobody really understand what happens in the very long manoeuvring phase that ultimately lead to the domination of the knight.

Of course, there is very little incensitive to work on this: it a very harduous task, you will probably never face this in practice, and even if you do you'll be limited by the 50-moves rule, and very few of the skills you develop might be useful in different positions.

If a grandmaster devoted half a year to study and practice this endgame, he would probably be able to win it against other humans in a match without the 50 moves rule. But even so, he still won't have any chance to win it against the tablebases.

I am flabbergasted to see a National Master (a title delivered by the US-federation title, not by FIDE) publish a video like this one were he certainly worked out one or two useful patterns but wrongly present them as a simple general solution to the BB vs N endgame.

Answer 3

I don't recall having that endgame, however, every time I saw GMs have it, it ended in a draw. So in that sense it is probably not worth learning. The GMs actually do make progress sometimes, however, they don't (usually) seem to manage to finish it off within the 50 moves rule. (I suspect some might manage it without the 50 move rule but that is just a guess of course)

It may be useful to know the defensive ideas though, as to make it likely that you yourself won't lose it if you get that endgame. The main idea is to keep the king and knight together, once they get separated the attacker should win. And then an important setup to know is Nb2 Kb3 (or some other adjacent square not on the edge of the board). This was for a long time thought to be a fortress. The tablebase shows that the two bishops can break this fortress, however, against a human this is a good defensive setup to fall back on when you get pushed back. Then if you get forced out of this setup you can try to reach it in another corner again.