[Event "Advanced Endgames You Must Know!: The W maneuver"]
[Site "https://lichess.org/study/UO2zqigQ/qJ91WwQh"]
[Date "????.??.??"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "*"]
[Annotator "https://lichess.org/@/NoseKnowsAll"]
[ECO "?"]
[FEN "8/8/8/2N5/8/2K5/2B5/k7 w - - 0 1"]
[Opening "?"]
[SetUp "1"]
[UTCDate "2021.08.01"]
[UTCTime "17:27:52"]
[Variant "Standard"]

{ Because white can only force checkmate on the black king in the corner that is the same color as the bishop, black should be trying to stay centralized or run to a corner of the opposite color. Here, we see that black is trapped on the a file, and so all we have to do is walk the black king up the board until its doom on a8. This is done with the so-called W maneuver: } 1. Nb3+ $1 { Looking at these arrows, you can now see why this is called the W maneuver: in performing this king walk, the knight will only travel to these squares in this order, forming a W. If you're ever thinking of making a knight move, be sure it will only be the next one in this shape.
First we kick the king out of the wrong-colored corner. [%cal Gb3d4,Gd4b5,Gb5d6,Gd6b7] } 1... Ka2 2. Bh7 { Always use the bishop for any waiting moves. We want to play Bb1 next to block the king from the a2 square next, but Bb1 last move would give up a full bishop... } 2... Ka3 3. Bb1 { Now the king can no longer reach the a2 square either. Black is forced further up the board. [%csl Ba2,Bb2,Bb3,Bb4] } 3... Ka4 4. Nd4 $1 { The key maneuver to memorize. As soon as black tries to escape up the board, we continue the W maneuver with the knight, preventing the black king off the a file. [%cal Gb3d4] } 4... Ka3 { If the black king does his best to avoid the a8 corner, we can continue the W maneuver successfully. } ( 4... Ka5 $1 { We'll see how this move works out in the next chapter. } ) 5. Nb5+ { The knight, bishop, and king combine to form a wall against the black king. With the knight on a light square, it controls all of the important dark squares, and the king and bishop work together to close off the cage on the light squares. [%csl Ba3,Ba2,Bb2,Bb3,Bb4][%cal Gd4b5] } 5... Ka4 6. Kc4 Ka5 7. Kc5 Ka4 8. Bc2+ { A wall has been formed, and black is forced further up the a file towards a8. [%csl Ba3,Bb3,Bb4,Bb5] } 8... Ka5 9. Bb3 { This is the same position reached on move 3, but shifted up by 2 squares. We keep repeating this configuration, until we reach the position from the previous chapter. } 9... Ka6 10. Nd6 { The key maneuver to memorize. As soon as black tries to escape up the board, we continue the W maneuver with the knight, preventing the black king off the a file. [%cal Gb5d6] } 10... Ka5 11. Nb7+ { The W maneuver is complete, and now we look to trap the black king on the two remaining squares (here, that's a7 and a8). [%cal Gd6b7] } 11... Ka6 12. Kc6 { [%csl Ba5,Bb5,Bb6,Bb7] } 12... Ka7 13. Kc7 Ka6 14. Bc4+ { [%csl Ba5,Bb5,Bb6,Bb7] } 14... Ka7 15. Bb5 Ka8 { We have repeated the same configuration as before, and now we've reached the position from the previous chapter. Do you remember how to force checkmate? If not, take the time right now to calculate to mate. I'm sure you can do it! } 16. Nd6 Ka7 17. Nc8+ Ka8 18. Bc6# { Once you've mastered this maneuver, you can directly apply this same technique to the crucial task of forcing the enemy king to one side of the board. Recalling the key positions where black is in zugzwang, the fact that your king must be as active as possible, and that both of your pieces should stay on the same color to maximally control the board is all you need - no memorization required! } *