Checkmate with Bishop and Knight Using the W Maneuver
In October, I was playing a long correspondence game against blas1985. I had a big material advantage in the endgame, but I stupidly traded off my last pawns, leaving myself with bishop and knight against a lone king and one of the hardest mates in chess. But after 56 moves I would not be undone by ignorance. It was late. We had both been moving quickly, making it a live game for a while. I had expected to queen a pawn and win easily. I had no idea how to mate with bishop and knight. I went to sleep determined to learn how the following day.
The next evening, after work, I sat down with a board and pieces and began trying to figure it out. I started by placing the pieces in a position where the defending king was in check and had no move. It seemed intuitive to me (maybe I read it somewhere) that this had to occur in a corner controlled by the bishop. And it seemed clear enough that the defending king would occupy that corner, and the bishop would give the final check, like this:
It seemed clear then that the defending king would try to stay off the side of the board and then head for the corner not controlled by the bishop once forced to the side. The question would be how to force the defender out of the safe corner and into the mating corner. But since the bishop doesn't control the safe corner, and a king cannot give check, clearly it was going to be up to the knight to flush the king out of the corner. And options are limited, so the process is fairly clear:
At this point I became discouraged. Now the black king can escape the side of the board and break out into the open via c7, which cannot be covered in time. This seemed like a failure. The rules of correspondence chess allow for consulting published materials (or you could not study while playing a correspondence game). I turned to this Wikipedia article. Of course there is a lot more to the matter, but it turns out that I already had the basics above. The second diagram is the beginning of the W maneuver, so called because of the knight's peregrination from f7-e5-d7-c5-b7, making a figure like the letter W.
The point I reached in my initial noodling represents the critical strategic choice for the defender. Black can now either play 4... Kf8, heading back toward the safe corner (for a single move), or 4... Kd8, heading out into the open, as I feared--but permanently into the mating corner as well, never to return.
I studied the W maneuver over and over until I was sure I could do it live from memory if need be. And then my opponent did not put me to the test. When the time came, he headed directly into the mating corner and was dispatched quickly.
But the W maneuver is pretty straightforward. We've already seen the central four moves above. This core sequence can repeat up to twice, moving over two files at a time. In fact, if Black plays 4... Kf8, it can repeat very quickly:
Whenever White plays Nc5 in each line, the white king and knight have moved over two files from the end of the previous diagram. The bishop, previously covering g8, is now covering e8. In each iteration of the core maneuver, the knight moves forward to the next stops on its journey to the queenside, never moving back. Whenever it is on the 7th rank, it covers dark squares on the 8th (h8, f8). When it is on the 5th rank, it cuts off pairs of light squares on the 7th (d7&f7, b7&d7).
Eventually, the black king will have the option to leave the side of the board, such as when Black plays 7... Kc7 in one of the lines above. In some cases, like that one, the bishop and knight can intervene to force the king immediately back to the side of the board. But in all cases, the king is easily trapped by the pieces in the mating corner once this happens. The situation after 4... Kd8 is not much different.
At the end, the white knight and king trap the black king in an L-shaped pen:
I skipped a lot of variations there, but the idea is the same in all lines. Nb7 followed by Kc6 confines the black king to five squares in the corner. The bishop blocks escape on a light square. Then the white king moves opposite the black king (to b6 or c7) and finally the bishop blocks the other outside light square. The black king is now restricted to moving back and forth between two squares (a7 and a8 here).
This position also demonstrates a critical tempo issue that can result in stalemate if you get it wrong here. The black king is now limited to two squares. But White no longer possesses a horizontal or vertical attacking piece (rook or queen) that can check an entire file or rank at once. The last two squares have to be eliminated in sequence, one at a time, on two consecutive moves, by the two white pieces. If Black is ever left with exactly one safe square for the king on their move, it's stalemate. Hence the last move before checkmate has to be a check. The bishop gives the final mating check. The knight must check on the penultimate move to avoid stalemate.
From the position at the end of the last diagram, the knight moves to d6 and then c8, to check the king on a7. So that has to be Nc8+ to avoid stalemate. After Nd6, the white bishop makes a waiting move to ensure that the next move is a check.
Checkmate at last!
There are other techniques discussed on Wikipedia and elsewhere. But this methodology is not hard to learn and apply. And it's infallible if played correctly. There is no defense. It is forced checkmate in about 20 any way you slice it.
I learned the W maneuver from a correspondence game, incidentally. That gave me the opportunity. It would not have been possible to learn a new technique between moves in a live game. Nevermind the rules; there isn't time. And I was highly motivated by the desire not to draw a long game I should have won more easily.
Of course, many coaches, authors and masters will tell you that you're not likely ever to face this challenge in your chess career, or maybe once. So perhaps I'll never have the chance again, but of course nothing would please me more than to be able to break this out in an OTB tournament. Maybe this post will be useful to you if you should have the opportunity.