Mike Gunn wrote:
The non-W method is sometimes called the Russian method of mating with B and N. It's described in "A Pocket Guide to Chess Endgames" by David Hooper which is out of print but available quite cheaply e.g. via http://www.adebooks.co.uk
Hooper's cordon method is the way I learned it, too, and Alex's youtube reference is similar. As a coach I used to get students to take a step backwards from the final mating position and play for the mate, step by step, going just a bit further, making it a bit more difficult each time. That way the student was always reinforced with the picture of the final objective, and quickly gained confidence because of the simplicity. Starting from the worst case scenario is a bit daunting and particularly off putting for juniors.
Mike Gunn wrote:
Every few years there is a story in a chess magazine about some strong player who has failed to mate with B+N and the most recent one I saw featured a Russian master who demonstrated the non-W technique not by moving the pieces but by demonstrating how the defending king can be fenced in the corner by a series of decreasing cordons created by placing K+B+N on apprpriate squares. This player is supposed to have just said (imagine heavy Russian accent): "Put king in cage!".
I've seen a player (about 200 BCF) fail to do it in a tournament game back in the 80s, and it was obvious that he'd never looked at it, not even knowing about the bishop needing to control the corner square. That's fine, since most chessplayers will have gaps of some kind or another in their basic technical knowledge; I just hope the player looked it up when he got home, unlike IGM Lilienthal, who got K & two knights v K & P, twice, and failed each time. There's a famous criticism by Botvinnik on Lilienthal's "unprofessionalism" and I asked Bob Wade how could such a strong GM not learn from his first failure. Bob simply said that Lilienthal was lazy and probably didn't expect to see that ending again.
Then today I found this in Wikipedia and could hardly believe that people like Howell and Silman would have such opinions.Opinions differ as to whether or not or not a player should learn this checkmate procedure. James Howell omits the checkmate with two bishops in his book because it rarely occurs but includes the bishop and knight checkmate. Howell says that he has had it three times (always on the defending side) and that it occurs more often than the checkmate with two bishops (Howell 1997:138). On the other hand, Jeremy Silman includes the checkmate with two bishops but not the bishop plus knight checkmate because he has had it only once and his friend John Watson has never had it (Silman 2007:33,188). Silman says
"...mastering it would take a significant chunk of time. Should the chess hopeful really spend many of his precious hours he's put aside for chess study learning an endgame he will achieve (at most) only once or twice in his lifetime?"
Perhaps I'm just "old school" in the belief that the study of these basic endgames teaches the aspiring player not only essential technique, but also provides a superb exercise and insight in how to coordinate the pieces. It is also a good idea to quickly remind oneself now and again how to do these endings... it is possible to get a bit rusty and forgetful.