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.

  • Unfortunately, often engine-generated puzzles suck! – Ywapom Dec 5 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 6 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 6 at 17:04

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.

  • 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 6 at 17:09

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.

  • 1
    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 5 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 5 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 5 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 5 at 14:12
  • After Qd6+, can black play Re6 and try to run with the king towards g4? – user1583209 Dec 5 at 15:44

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.

  • 2
    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 5 at 11:34
  • Such is impossible. – QuIcKmAtHs Dec 5 at 13:55

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