an easy way to mate with KBN against K

Hi all.  I have noticed that just about everybody who posts youtube videos on the bishop and knight mate recommends the Philidor W pattern.  I propose an easier method (seems easier to me anyways).  By the way, I am not a clever guy who invented this.  I learned it by practicing with an endgame tablebase.   Suppose you have reached the position white Kf6, Bf5, Nf7 and black Kg8 with white to move.

To drive the king from the corner we make a waiting move with the bishop, say 1. Be4,  Then 1. ...Kf8, 2. Bh7, Ke8. 3. Ne5.  Now if the black king returns to f8 play continues  3. ...Kf8. 4. Nd7ch, Ke8. 5. Ke6, Kd8. 6. Kd6, Ke8. 7. Bg6ch, Kd8. 8. Bf7, Kc8.  Now just repeat the pattern to drive the king to the a8 corner.  The game might finish 9. Nc5, Kd8. 10. Nb7ch, Kc8. 11. Kc6, Kb8. 12. Kb6, Kc8. 13. Be6ch,, Kb8. 14. Nc5, Ka8. 15. Bf5 (don't stalemate with Na6), KB8. 16. Na6ch, Ka8. 17. Be4 mate.

     The above is quite standard.  The more interesting question is what to do if the black king tries to run instead of returning to f8 on the third move.  So after 1.Be4, Kf8. 2. Bh7, Ke8. 3. Ne5, suppose Black tries to run away with 3. ... Kd8.  One must use the bishop and knight to contain the black king.  There are two equally efficient moves.  4. Ke6 and (easier in my opinion) 4. Be4.  According to a tablebase either move mates in 16.

Philidor method:  4. Ke6, Kc7. 5. Nd7, Kb7. 6. Bd3, Kc6. 7. Be2, Kc7. 8. Bb5, Kd8. 9. Nc5 and mates in 10 more moves.  There are of course other variations here.

     I find the following pattern much simpler and easier to execute in time pressure.

My preferred method:  4. Be4,  Now if 4. ...Kc7. 5. Nc4.  Observe that the black king is confined behind a wall of squares b6,c6,d6 that are controlled by bishop and knight.  So the white king can herd the black king to the corner.  Play would continue 5... Kd7. 6. Kf7, Kd8. 7. Bc6, Kc7. 8. Bb5, Kd8. 9. Ke6, Kc7. 10. Ke7, Kc8. 11. Kd6, Kd8. 12. Na5, Kc8. 13. Bd7ch, Kb8 (or 13. ...Kd8. 14. Nb7 or c6 mate). 14. Kc6, Ka7; 15. Bc8, Kb8. 16. Kd7 and now Black can choose between 16. ... Ka8. 17. Kc7, Ka7. 18.Nc6ch, Ka8. 19. Bb7 mate or 16. ... Ka7, 17. Kc7, Ka8. 18. Bb7ch, Ka7. 19. Nc6 mate.   If after 4. Be4 Black plays 4. ...Ke8 then 5. Bd5.  If now 5. ... Kf8 then 6. Nd7, Ke8,  7. Ke6 etc.  If 5. ... Kd8. 6. Ke6, Kc7. 7. Ke7, Kc8. 8. Bc6, Kc7. 9. Bb5, Kc8. 10. Kd6 leads to a previous variation.

      Does anyone care to agree that my preferred way is simpler?  To me the coordination of the bishop and knight is more natural and easier to execute without much thought (which is nice if you are in time pressure).  Of course it is dumb for a weak player like me to study this instead of something more useful like rook and pawn endings.  But if anyone cares to master the KBN mate you might find my suggestion easier than the usual book recommendation.