Bishop, Knight & King versus King.

I studied the technique in Fine's Endings book and then demonstrated it on occasion against my typically-1300's-rated students/players on the high school team I coached.  I was able to do it in under 40 moves starting from the worst position.  I never encountered it in a real game.

I think it's worth practicing even if you never see it in a game. You learn a lot about coordinating your minor pieces. The old chess manuals always encouraged this as a basic part of chess mastery.

Arisktotle you are making things more complicated and sometimes simpler if you add a pawn for the defender.  The basic discussion is about king and two minor pieces against a king. This as I now know is actually a simple win for the side with the two minor pieces. Keeping a pawn on the board sends this into the realm of pawn Endings, which is a different discussion. See WFM Anna Rudolph's very helpful video.

I agree. It is all about the slow art of piece coordination and patience. Failure comes from hurried attempts to chase the king across the board while neglecting to guard the escape routes!

Remember though that two knights cannot force mate against a king. This is caused by the fact that they have to switch color ever move. You need at least one bishop.

Yes agreed you need three gallant knights to mate a lone king! Or at least a pawn with promotion prospects and two knights😃 usually however you will probably find the the lone pawn can hamper the opposing king enough to make this easy. However I would argue this again makes it a pawn ending!

Bravo 😃 but definitely a pawn ending until it transposes into KNBvK it would be very rare to encounter this over the board!

If you consult a large number of endgame books, you'll find that "pawn ending" refers to an ending with kings and pawns. Adding a pawn to K+B+N vs. K makes it a minor piece ending with pawn(s), rather than a pawn ending. Of course there's no law against creating your own terminology, but it can lead to confusion.

Ok I concede that the books call pawn endings endings where there are nothing but pawns on the board. However there is a big difference I feel between minor piece Endings and minor piece and pawn. I thought that this forum was about the least material with which you can force checkmate I.e. KBNvK  and how easy or otherwise it is to do it. I am now satisfied that I can do the checkmate so I am going to go to another end game forum!

Great example, Ruben! It's simpler than the famous composed problem where underpromotion to bishop is necessary (http://www.edcollins.com/chess/under-promote.htm).

I have had a K, B, B v K but only because the player did not resign and I under promoted the eighth rank pawn for the fun of it.

Not very easy 

Most basic piece endings only occur in blitz/bullet games. When people have time to think about it why would anyone play K+R vs K?. The game will be resigned even before the endgame is there.

"Learning endings" is just like "having an army". You have an army to prevent a war, not to fight one. You learn endings to scare your opponent from ever playing you in a lost ending.

So the general rule is: "all known endings are rare" even the most obvious ones. The exception is probably the K+N+B vs K endings since players are not convinced their opponents know it well. They might get away with the 50M-rule and therefore play it!

I was discussing this with a Master.  He said there's a triangle involved -
and he got that idea from Pandolfini.
But on reading here - I saw "Deletang's Triangle".
So its time to look that up.

A big problem with the process seems to be the counter-intuitiveness.
Which takes this form:
Drive the target King to edge of the board (easy) -
Then let him off the edge again (irksome).
You know you want him driven -
towards one of the two correct corners - (hard)
so you can mate him there in a few moves (easy).

But to get him to that correct corner -
you have to let him off the edge.   

Here's a better thread on the topic of bishop-knight mate:

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

That "letting him off the edge" happens only in The W Method, I believe; in Deletang's Triangles Method, the king never escapes the big triangle outlined by two sides of the board and the long diagonal. "The Lock" position of The W Method is where the opponent starts to escape and you're barely able to catch him in time via a clever piece arrangement. This is the part of the process where would-be maters tend to go wrong. My hypothesis is that if the chessboard were just two squares longer in both directions (i.e., a 10x10 board), then a bishop-knight mate would be impossible on it since the defending king would be able to escape at that time. I never tried to prove this, however.

Yes, they're the same, despite a slightly confusing Wikipedia page that doesn't make that equivalence clear.