Bdtyktl

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.

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.

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.

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.