I think the mere act of being able to learn this endgame opens the doors for learning a ton of other ones. If you have some sort of system to learn this stuff (I just figured mine out - a mix of reviewing the games/solutions and playing against the computer), the world of more complex endgames suddenly opens up!
Good point! It also teaches you to coordinate your pieces to the max.
I periodically practice this endgame by randomly placing the pieces on the board. I think that it is fascinating the amount of space that can be controlled by the bishop and the knight working together, and I enjoy trying to complete the mate within 50 moves. Additionally, I have had four or five games where this endgame occurred.
Below is a link to a game where knowing the technique came in handy. My opponent wanted to play to checkmate, and my first thought was to promote a pawn, but the K+N+B technique was faster.
https://www.chess.com/forum/view/endgames/kbn-vs-k2
I learned it. The very next day in rapid tournament in endgame my opponent sees that he can sacrifice a piece and a pawn, so to be left only with bishop and knight vs his King. Boy i was so happy can't believe it. I pushed his king to the wrong corner , then with W shape maneuver almost to correct corner and it was mate in 8 or something. Problem was i was left with 2 minutes with no increment. And basically i was moving instantly becouse i memorized the pattern and my opp wanted to flag me. But.. i noticed my position was litle different and my opponent made a move that i havent study.. after the game i saw that it allows me to checkmate him in middle of board on 8 rank. But in game i almost premoved and made normal move that.. hangs my knight for free... I was so frustrated... How the heck.. but i never never saw this in any teaching video. No master or teacher showed that you can checkmate him that way.
here: https://www.chess.com/analysis-board-editor?diagram_id=2782076
Two additional variations. As I said earlier, I enjoy experimenting with this ending.
The position after 6. Ba7 is a starting position in many endgame books. From that point, it's purely mechanical. Only a small amount of thinking required.
Great clip from the blitz world championship a couple months ago. Glad someone put this on youtube. The trade down to knight and bishop is around 1:20
https://www.youtube.com/watch?v=ePyx5rLxnb4
Too bad, but with no time on the clock it is very difficult. So don't be too hard on yourself. I think on move 34 you needed to play a waiting move with the bishop, e.g. ...Ba4. One line would go like 34...Ba4 35. Kg1 Kf3 36. Kh2 Bb5 37. Kh1 Kg3 38. Kg1 Nh3+ 39. Kh1 Bc6#
My brother once managed this OTB in a competitive game, though not having learnt it. He was rated around 2000 at the time I think (40 years ago). One of his proudest achievements. I learnt it a while back, but couldn't do it now I think. there is a point where it seems counter-intuitive as it looks like the king is getting away.
My favorite video on this mate is:
How to Checkmate with Knight and Bishop | Chess Endgame Basics #1
https://www.youtube.com/watch?v=hWwuy-aiK1M
This is an ending I forget if I don't practice it about once a year. My goal is to find an easier way to remember it. I definitely believe it's worth learning. Polgar knows how to do it even blindfold, and men should know how to do everything a woman can do, right? 
http://www.chessgames.com/perl/chessgame?gid=1092636
woton, in your first diagram you can play 13. Nc6.
13...Kf7 seems to be escaping, but 14.Ne5+ keeps the black K in his cage. It looks so cool.
woton, in your first diagram you can play 13. Nc6.
13...Kf7 seems to be escaping, but 14.Ne5+ keeps the black K in his cage. It looks so cool.
Thanks. I didn't know about that one. I got the one that I used from a book several years ago. I've found some complex ways of playing this out, but one mistake and it will take >50 moves. Eventually, I opted for the simple-minded mechanical method.
The hard part is forcing the king into one of the corners (It's no big deal if the king goes to the opposite color corner, it just takes longer). After that, it's fairly simple.
I think the mere act of being able to learn this endgame opens the doors for learning a ton of other ones. If you have some sort of system to learn this stuff (I just figured mine out - a mix of reviewing the games/solutions and playing against the computer), the world of more complex endgames suddenly opens up!