What is the key idea for winning with KQ against KBN? (How to break the barrier?)

Mastering winning with KQ versus KR is one of my biggest daydreams. Well, in a few particular cases I was able to checkmate (after reaching Philidor and then capturing the rook), but that was just a single specific line of black's response. (And I want to know a full algorithm.) It seems that the endgame is terribly difficult. I'll keep continue watching YouTube videos though.

I have another but similar question: what about KQ against KBN?

E.g. this interactive puzzle:

https://www.chessvideos.tv/endgame-training/queen-vs-bishop-knight-h-pawn-13.php

``````[Title "White to play and win"]
[fen "8/1kn4p/2b5/8/8/8/4KQ2/8 w - - 0 1"]
``````

I usually start with 1. Qh4 (bishop cannot defend it, because we'll take the bishop instead...). Then, on my second move, I take the pawn (2. Qxh7). After that, I have no good ideas. Either I am too silly or this is a pretty hard endgame. Bishop and knight together form a strong barrier.

What you've learnt, you'll forget; what you've understood, you'll remember. I am trying to understand rather than to memorize what I should do.

• In general these endings are usually winning (81.8% of all positions according to syzygy tables), however not all of them are winnable in presence of fifty move rule. For example position with white king on e1, white queen on e2, black king on e5, black knight on f5 and black bishop on e4 has with best play 79 moves to mate and 59 moves to first capture - so it's drawn by 50 move rule. Oct 18, 2023 at 7:14

First some guidelines:

1. Ideally black wants to build a fortress round the king with the bishop, knight and pawn. The pawn is too far away so it will have to be just the bishop and knight
2. The black pawn is a long way from queening so it is a low priority. No need to chase it just yet. If black tries too hard to defend it that will take a piece (probably the bishop) away from the defence of the king.
3. White wants to try and checkmate. For that the white king is going to have to be close to the black king. Currently they are a long way apart and the kings move slowly so first priority is probably to get the white king closer
4. Once the white king and queen are close to the black king it becomes much more difficult for the black pieces to retain coordination in protecting the black king. Try and force a zugzwang where one of the pieces has to move away from the king and fall to a queen fork.

Here's what I got trying this against the interactive puzzle:

``````[fen "8/1kn4p/2b5/8/8/8/4KQ2/8 w - - 0 1"]

1. Kd3 Nb5 2. Qb2 h5 3. Kc4 Be8 4. Kc5 Kc7 5. Qe5+ Kd8 6. Qg5+ Kc7 7. Qe7+ Bd7 {I want this position with black to move to force the knight to move so time for some triangulation} 8. Qf6 Be8 9. Qf8 Bd7 10. Qe7 Na3 11. Qe5+ Kd8 12. Qg5+ Ke8 13. Qe3+ Kf7 14. Qxa3 Kg6 15. Kd6 Bb5 16. Ke5 Bc4 17. Qf3 Ba2 18. Qf6 Kh7 19. Qg5 Bb1 20. Kf6 Bg6 21. Qxg6+ Kh8 22. Qg7#
``````
• Danger, Will Robinson! For this concrete example, Black is only three moves away from the only fortress, so you must play precise. 1.Qh4 Nd5 2.Qxh7+? Ka/b8 draw, because now you can't hinder Black to ultimately play Bb7. The computer thus plays 1.Qc5. ("Trash doesn't run", GM Lanka. Ph7 goes nowhere.) Oct 19, 2023 at 7:03