Strategy to win with a king and queen against a king and pawn about to promote?

Question

I've been doing puzzles on a site and like to continue practicing against the computer. In many of the puzzles I end up with a situation like this where I was able to promote my black pawn to a queen one move ahead of white and keep the king in check so the pawn doesn't promote:

[FEN "5K2/4P3/4q3/8/8/4k3/8/8 b - - 20 11"]

As Black, is it possible to force a checkmate in this situation? My thought is that I need to either A) fork the king and pawn in such a way that the king is forced to move away so I can take the pawn without being captured or B) force the king in front of the pawn, so that I have a free move to get the black king closer. I can't seem to find a way to reliably do it.

I was able to do it in this game but sometimes I end up just repeating moves until I get a draw by repetition. It seems like the position on move 5 is a key one, the king either has to move to e8 under the pawn which allows me to move the king, or g7 as in this game, which allows me to move to e6 on top of the pawn, forcing kf8 to protect the pawn, allowing qf6+ which forces the king under the pawn allowing me to move the king.

[Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "0-1"]
[SetUp "1"]
[FEN "8/3K4/4P3/8/8/8/5k2/4q3 w - - 0 1"]

1. e7 Qd2+ 2. Kc7 Qa5+ 3. Kd7 Qd5+ 4. Ke8 Ke3 5. Kf8 Qf5+ 6. Kg7 Qe6 7. Kf8 Qf6+
8. Ke8 Kd4 9. Kd7 Qf5+ 10. Kd8 Qg5 11. Ke8 Qg8+ 12. Kd7 Qf7 13. Kd8 Qd5+ 14. Kc7
Qe6 15. Kd8 Qd6+ 16. Ke8 Ke5 17. Kf7 Qf6+ 18. Ke8 Ke6 19. Kd8 Qxe7+ 20. Kc8 Kd6
21. Kb8 Kc6 22. Kc8 Qc7# 0-1

I'm looking for some kind of understandable general strategy. Is it to keep the queen checking on ranks 5 and 6 until one of these positions comes up?

Answer 1

I fully cover this endgame in my advanced endgame study on lichess if you're interested for full details. Start on chapter 9 and progress through chapter 15 if you only care about the queen vs pawn endgames.

Essentially, there are several key positions that you should memorize in order to make progress. One of them is how to keep checking the opponent king until they are forced to block their own pawn (allowing you for one move to bring your king closer to the action). Your technique in the example you show is not the absolute most effective, but definitely good enough to convert! The next key position is how to create stalemate traps if the pawn is on the a or h file. The final key position is how to create stalemate traps if the pawn is on the c or f file. Due to those stalemate traps, the game should be drawn if the pawn is on a bishop or rook file (unless your king is already active enough that you can create mating threats). The game should otherwise be winning for the player with the queen.

Answer 2

1) If the king or the queen has arrived to the promotion square it is won.

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2) If both king and pawn have reached 7th rank, so the queen can't move to the promotion square (same in 6th range if it is the weak side to move), the method is to force the king with queen checks to move to the promotion square. Then you can move your king in the pawn direction.

[FEN "8/3pk3/8/8/8/8/8/3Q3K w - - 0 1"]

1. Qe2+ Kf8 2. Qf3+ Ke7 3. Qe4+ Kf8 4. Qf5+ Ke7 5. Qe5+ Kf8 6. Qd6+ Ke8 7. Qe6+ Kd8 8. Kg2 Kc8 9. Qc6+ Kd8 10. Kf3 Ke8 11. Qe6+ Kd8 12. Ke4 Kc8 13. Qc6+ Kd8 14. Kd5 Ke8 15. Qe6+ Kd8 16. Kd6 Kc8 17. Qxd7+ 1-0 

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3) If the pawn in 7th rank is the rook pawn or the bishop pawn, it is draw:

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3a) In the rook pawn case, you just move king from h8 to g8 and from h8 to g8-g7 (or a1 to b1-b2, a8 to b8-b7, h1 to g1-g2) and the queen is checking g8 king in g file, so when the king moves to h8, the king can't approach as it would be stalemate.

[FEN "8/6kp/8/8/8/8/8/3Q3K w - - 0 1"]

1. Qg4+ Kh8 {White cannot aproach his king because it would be stalemate} 2. Qh5 Kg8 3. Qg6+ Kh8 {no matter what the queen do, there is no way} 1/2-1/2

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3b) If it is the bishop pawn, when the pawn is in f7, the king in g8 and the queen ckechs in g6, you can move to h8, because, if the queen captures, it is stalemate too.

[FEN "8/5pk1/8/8/8/8/8/3Q3K w - - 0 1"]

1. Qg4+ Kh8 2. Qh5+ Kg8 3. Qg6+ Kh8 4. Qh6+ Kg8 5. Qg6+ Kh8 6. Qxf7 1/2-1/2

Answer 3

When your opponent does not threaten to promote, use that move to bring your king closer. For instance, on move 11 White is not threatening anything, so you don't need to give another check. The rest was played more or less correctly: you need to force the enemy king in front of his pawn so you can use the next turn to move your own king

Answer 4

The side with the Queen should win in every case except that of bishop pawns (c or f file). (Or, as always, rook pawns.)

The basic theory is you either double-attack the King and pawn or pin the pawn to the King until the King is force to move in front of the pawn, to block its advance, at which point you bring your King one step closer to the action. Eventually the King is close enough to also attack the pawn, winning the pawn and eventually forcing mate.

The reason this fails with c- and f-pawns is stalemate. The King always stays to the short side of the board from the pawn, and when faced with a choice of having to block the pawn's advance or lose it chooses to lose it by stepping to the corner square, when capturing the pawn with the Queen is stalemate.