Can black win this pawn ending?

Black to move. My computer gives the evaluation -2.5 but I can't find the winning sequence for black.

``````[FEN "6k1/6pp/4p3/3pP3/2pP1PP1/1p6/1K5P/8 b - - 0 1"]
``````

(Black goes up the board)

• This is reminiscent of an endgame trap Yuri Averbakh avoided in 1953 Zurich izt, vs Szabo IIRM... Sep 9, 2021 at 8:40
• Can you clarify the orientation of the board, please? As presented, I would suggest "a1Q", which is not hard to find :) Sep 9, 2021 at 9:48

3 Answers

If we look at the position we see a number of things:

1. Black's connected passed pawns mean that the white king must remain at all times in the rectangle a1-a3-d3-d1.
2. The fact that the white king can stop the pawns from queening on their own by just cycling between b2 and a3 means that the pawns will never queen without the help of the black king. In particular the black king needs to get to b4 without losing otherwise the game is going to be a draw.
3. White has a healthy kingside majority which can a generate a passed pawn.
4. White's immediate threat is f5 which would immediately create a supported passed e5 pawn.
5. Therefore unless black can permanently stop that threat then the black king must always stay within the rectangle h8-h5-b5-b8.
6. If black plays Kb4 then the result will depend on whether one player can queen first and then stop the opponent from queening.

That said let's look at some sample lines starting with what happens if black allows an immediate f5 by white:

``````[FEN "6k1/6pp/4p3/3pP3/2pP1PP1/1p6/1K5P/8 b - - 0 1"]

1...Kf7 2. f5 Ke7 3. fxe6 Kxe6 {and both side have their king's tethered to the opponent's passed pawn(s).
``````

So, to have any chance of winning black's first move is forced: g6 to stop the immediate f5. Black then also needs to restrain white's kingside majority enough so that black has enough time to get the king to b4 and be able to force one of the pawns through before white can queen a pawn.

After g6 the other key move for black is h5. The idea is fix the white pawns into a slower structure (white pawn on g5) or a losing structure where the black king can enter on f5 because the g pawn has been lured away by taking the h5 pawn.

``````[FEN "6k1/6pp/4p3/3pP3/2pP1PP1/1p6/1K5P/8 b - - 0 1"]

1...g6 2. Ka3 Kf7 3. Kb2 h5 4. g5 (4. h3 hxg4 5. hxg4 g5 {key move breaking up and taking the pawns or creating a new black passer} 6. f5 (6. fxg5 Kg6 7. Ka3 Kxg5 8. Kb2 Kxg4) exf5 7. gxf5 g4 {and the new passer runs home}) Ke7 5. Ka3 Kd7 6. Kb2 Kc6 7. Ka3 Kb5 8. Kb2 Kb4 9. f5 c3+ 10. Kb1 Ka3 11. fxg6 b2 12. Kc2 (12. g7 Kb3 13. g8=Q c2#) Ka2 13. g7 b1=Q+ 14. Kxc3 Qb8
``````
• Why on Earth would White reply to ...h5 with g5 instead of h3? Sep 8, 2021 at 19:32
• Something wrong with your eyesight, @David? The variation with 4. h3 is clearly there. It loses more quickly which is why I gave it as a variation rather than the main line. Sep 8, 2021 at 20:39
• On small comment: The black pawns can also generate mates (as seen in the g8Q variation), thus it is not immediately obvious whether allowing f5 throws away the Black win, especially as Black can triangulate. But it does indeed, as one can check with Syzygy. Sep 8, 2021 at 20:50
• @Breakingnotsobad Thanks! I've fixed it. Sep 9, 2021 at 10:16
• @App-Devon en passant is only possible when a pawn moves two spaces in one move, so doesn't apply as an option. Sep 10, 2021 at 3:11

Stockfish gives -8 on Lichess, analysis.

And the reason is very simple actually. b and c pawns are protected passed pawns which means the white king cannot leave there. If it leaves, you will promote. So their king is stuck there and you are pretty much free with your king to collect all pawns. There are multiple winning lines but I will leave here a little bit complicated one:

``````    [FEN "6k1/6pp/4p3/3pP3/2pP1PP1/1p6/1K5P/8 b - - 0 1"]

1... g6 2. h4 h5 3. g5 Kf7 4. Kc3 Ke7 5. Kb2 Kd7 6. Kc3 Kc6 7. Kb2 Kb6 8. Kc3 Kb5 9. Kb2 Kb4 10. f5 c3+ 11. Kb1 Ka3 12. fxg6 b2 13. g7 Kb3 14. g8=Q c2#
``````
• Isn't h4 a horrible move here though? Shouldn't the pawn stay on h3 to have an easier time pushing f5 later on? Sep 8, 2021 at 19:32
• @David How would h3 help f5? Sep 8, 2021 at 19:48
• Not playing g5 is what helps f5 Sep 8, 2021 at 21:22
• @David a White h3-g4-f4 structure will be attacked by hg4 hg4 g5!, either creating a black passed pawn on the kingside (after f5 ef5 gf5 g4 etc.) or isolating White's pawn on the g-file, where the bK will pick them (after fg5 Kg7-g6 etc.). Sep 9, 2021 at 8:46

I don't know, the first thing I looked at was an immediate ... h5. It looks like on any reply you're creating a passed pawn while your king holds off the white pawns. If he plays h3 you take and play g5 like in one of the other sub-variations.

• 1...h5?! 2.f5 will be a draw after both 2...hg4 3.fe6 or 2...ef5 3.gf5 g5 4.fg6 ep, but there still seems to a complicated win after 2...ef5 3.gf5 h4! followed by Kh7-h6-g5, and if e6 then ...Kf6 and ...g6, or if no e6 then ...Kxf5 and ...g5-g4. Unnecessary complications, though. Sep 9, 2021 at 8:49
• @Evargalo on your 2... ef5, don't believe black king can get to h6 (without first forcing an f-g pawn trade) because white's f5 pawn means black can't get back to cover the e pawn from h6. If so, it's fully a draw from Jeremy's move Sep 10, 2021 at 3:34
• @JeopardyTempest is right, I forgot that g7 is not available for the bK to come back. So 1...h5? is actually a huge mistake throwing away the win. Sep 10, 2021 at 12:28