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A LiChess.org puzzle ends at this position with white to move. Apparently, black has a win here, but running through moves with LiChess's Stockfish, I can't seem to figure out how to end the checks.

[FEN "1K6/PPPq2PP/5P2/3p4/1p2Q3/7p/8/k2r4 w - - 0 1"]

Question: Can black end the checks and win?

Maybe there's a humanly understandable reason that the checks don't end. Or maybe the web version of Stockfish is not looking deep enough.

Rebecca J. Stones
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  • Unfortunately, often engine-generated puzzles suck! – Ywapom Dec 05 '18 at 17:57
  • Well i played about 30 moves with stockfish, and really couldnt get out of checks, despite the evaluation always being -2 or better for black. So it really does look like stockfish has a hard time accessing the position as a draw – Isac Dec 06 '18 at 11:46
  • @Isac: I had no trouble winning as black against Stockfish level 7 on lichess.org; against 8 I ended up in a rook and pawn endgame that ended up drawn, but which I think might have been winnable with better play. I think one of Stockfish 8's moves is sub-optimal, however. – supercat Dec 06 '18 at 17:04
  • I'm confident Black wins in this position, but the moves are mysterious and difficult/impossible to explain in human-understandable terms. To the observer, it looks like shuffling - until suddenly Black is dead lost. – Allure Sep 24 '22 at 20:38
  • @Allure I am not sure it must be difficult to explain. I didn't try too hard in my answer below to make all the lines conform to the Re8-e6-f6-f7-d7, then tuck the king behind and move the rook to c7 plan – alphacapture Sep 25 '22 at 00:58
  • @alphacapture are you able to win the position against a computer, even with 50-move rule disabled? – Allure Sep 25 '22 at 03:42
  • @Allure Using the strategy I mentioned, I can consistently get Lichess level 8 to make a non-checking move, without computer assistance (with takebacks, but without using these takebacks to make the computer do something different). As for winning the game without computer assistance, I would need to do a bit of studying just to win KQRvkq (though I think this is one of the reasonable ones to learn), so I can't do that at this time. – alphacapture Sep 25 '22 at 04:58

4 Answers4

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Looks like you are correct with your second assumption - the evaluation didn't (cannot) look deep enough.

It's a classic application of the horizon effect.

The white queen essentially has half of the chessboard at her disposal to give checks, while the black king has no shelter (the single rook is not enough (but moving it every now and then will reset the 3-fold-repetition countdown) and the black queen is cut off) but a lot of space to run around. The pawn on g5 will fall with check at some point and reset the 50-move countdown, too. The number of lines increases exponentially and since none of them actually changes anything significant about the position, Stockfish cannot efficiently prune any of them. Thus the search tree grows too large to process even for a modern engine on presumably good hardware.

PS: I've tried and removed the white pawns and the black pawn on g5 who look insignificant to the perpetual at first glance to reduce the number of chessmen to 7 - low enough to use Lichess' tablebase. And indeed, that position is won for black. However, this is meaningless as both sides will quickly play moves that are impossible in the puzzle position, e.g. the white queen will move to a1 and the black king will run towards e3.

Annatar
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  • The pawns are a key aspect of the position, since black can maneuver things so white would need to push one. Black's level of control goes down when White pushes a pawn, however, since until White has done that many king-rook forks won't be a threat. – supercat Dec 06 '18 at 17:09
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At first I thought that the black king could hide on h5, but then I realized that I had made a fatal mistake for white in my analysis. With this mistake corrected, it is clear that black's king cannot hide on h5 without allowing a capture on e8 with check.

   [FEN "4r2k/8/p7/3Q2p1/4p3/2P5/PP2qPPP/6K1 w - - 0 1"]

  1.Qd4+ Kh7 2.Qd7 Kh6 3.Qc6+! Kg7 4.Qd7+! Kf6 5.Qd6+ (4.Qc7?? Kg8!)(3.Qd6+?? Kh5 {White is out of checks, and under the threat of mate on e1. It is, however, not game over just yet.} 4.h3 (4.g3 Qg4! {shuts down white's play completely.}) Qe1+ 5.Kh2 Qxf2 6.Qd7!? {Trying to set up a little trap.} Rh8 (6...Qf8?? 7.Qh7+ Qh6 8.g4+! {and now white is winning.}) 7.Qg7 (7.Qg4 Kg6 8. Qxe4+ Qf5 9.Qe6+ Qf6 10.Qe4+ Kh6! {White is out of checks, and black is winning.})( 7.g4+ Kg6! 8.Qe6+ Qf6 9.Qxe4+ Kh6 {and black's king is safe. Game over.}) Qf8)

The final position seems like a draw to me, since black cannot really escape the queen checks by any other means than by getting the king to c2. But this seems impossible, since that requires black's king to cross the d-file at some point, which white will be able to prevent.

Edit: I realized that my initial line was incorrect, and that white shouldn't just check along the d-file.

Scounged
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    I throw in 3. Qc6+ instead of 3. Qd6+, and now 3...Kh5 fails because White can take the rook with check (also not engine checked). – Annatar Dec 05 '18 at 13:58
  • @Annatar Thanks for pointing it out. I realized this as well, but only after I had already posted my answer. My analysis (and subsequent evaluation of the position) is now updated. – Scounged Dec 05 '18 at 14:00
  • It was not a bad thought. And at the very least it's a much better attempt to swindle a win out of an unalert opponent than just running around aimlessly. – Annatar Dec 05 '18 at 14:06
  • @Annatar Agreed, but in the end I tried so hard to swindle white in my analysis that I ended up swindling myself :) – Scounged Dec 05 '18 at 14:12
  • After Qd6+, can black play Re6 and try to run with the king towards g4? – user1583209 Dec 05 '18 at 15:44
  • @user1583209 Running towards g4 will not escape from the checks since white can always play h3. So the king would still be stuck in the line of fire even after getting to g4. – Scounged Dec 05 '18 at 16:38
  • @Scounged But perhaps you could get the king along this route towards h5 without losing the rook to a check? Something like (assuming appropriate position of white queen) Kg4 h3+ Kh5 Qf7+ Rg6 Qh7 Rh6 Qf7+ Kh4 g3 Kxh3 ? – user1583209 Dec 05 '18 at 17:07
  • @user1583209 Maybe, but after Kg4 h3+ Kh5 Qf7+ Rg6 g4+ it seems like black either loses the rook or gets the king stuck in a perpetual checking trap. – Scounged Dec 05 '18 at 17:10
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Black may be able to get his king trapped on a8:

[FEN "4r2k/8/p7/3Q2p1/4p3/2P5/PP2qPPP/6K1 w - - 0 1"]

1. Qd4+ Kh7 2. Qd7+ Kh6 3. Qc6+ Kg7 4. Qd7+ Kf6 5. Qd6+ Re6 6. Qd8+ (6.
Qf8+ Kg6 7. Qg8+ Kf5 8. Qh7+ Ke5 9. Qg7+ Rf6 10. Qxg5+ Ke6 11. Qg8+ Rf7 
12. Qe8+ (12. Qg6+ Ke7 13. Qg5+ Kd6 14. Qd8+ Rd7 15. Qb6+ Ke7 16. Qc5+ 
Kf7 17. Qf5+ Ke8 18. Qe6+ (18. Qe5+ Re7 19. Qb8+ Kf7 20. Qf4+ Ke6 21. 
Qh6+ Kd7 22. Qh3+ Re6 23. Qh7+ Kd6) 18... Kd8 19. Qb6+ Rc7 20. Qf6+ Kc8 
21. Qf8+ Kb7 22. Qb4+ Ka8) 12... Kf6 13. Qh8+ (13. Qd8+ Kg7 14. Qg5+ Kh7 
15. Qh4+ Kg6 16. Qg3+ Kf5 17. Qh3+ Qg4 18. Qxg4+ Kxg4) 13... Rg7 14. 
Qh6+ Kf7 15. Qf4+ Kg8 16. Qb8+ Kh7) 6... Kg6 7. Qg8+ Kf5 8. Qf7+ (8. 
Qh7+ Ke5 9. Qg7+) 8... Rf6 9. Qd7+ (9. Qh7+ Ke6 10. Qg8+ Rf7) 9... Kg6 
10. Qe8+ Rf7 11. Qg8+ Kf6 12. Qd8+ Ke6 13. Qe8+ Kd6 14. Qd8+ Rd7 15. 
Qb8+ Ke7 16. Qe5+ Kf8 17. Qc5+ Kf7 18. Qf5+ Ke8 19. Qe6+ (19. Qe5+ Re7 
20. Qh8+ (20. Qb8+ Kf7 21. Qb3+ Kg7) 20... Kd7 21. Qd4+ Ke6 22. Qb6+ 
Kf7) 19... Kd8 20. Qb6+ Rc7 21. Qf6+ Kc8 22. Qf8+ (22. Qe6+ Kb8) 22... 
Kb7 23. Qb4+ Ka8

The general strategy may be something like: Get the king to the middle of the board so you can block checks by moving re8-e6-f6-f7-d7, then get the king to the back rank and go Rd7-c7, and run the king to a8 (keeping in mind that if ke8 rd7 Qd5 then re7 will run white out of checks soon; the pawn on g5 is not necessary for this).

Losing the pawn on g5 seems OK; not sure if we need to.

(In the above game, I made little attempt to make all the lines follow my strategy above, opting instead to show other positions where white can run out of checks. I know it is possible to deviate from the game above and instead follow the strategy more closely because I did it against Lichess level 8.)

alphacapture
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My feeling is that since black has mate in 1 threat, he can leave the rook undefended and march the K to go behind white's a/b/c pawns and end the checks. How exactly to get there I'm not sure, but I think white can't always keep d3 defended while giving checks non-stop.

Edit: After trying half hour against my phone, I now agree with the comments and other answers that such a plan is not possible.

jf328
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    The only path toward c2 is through c4-d3. But when the black king goes to c4, the wQ can stop it either with Qd4 or Qa6 (the later is even winning). It means the bK has to go to c4 when the wQ doesn't control either c4,d4,or a6. On such an open board it is only feasible if the wQ stands on b8,e8,e7 or f8 after bR has moved away. (from h7 it wouldn't be checking the bK on d5/c5/b5). Forcing the queen to allow the rook to move **and** to occupy such remote squares for checking the bK on the 5th rank would be quite a feat. – Evargalo Dec 05 '18 at 11:34
  • Such is impossible. – QuIcKmAtHs Dec 05 '18 at 13:55