Answers.Body: <p>Stockfish gives -8 on Lichess, <a href="https://lichess.org/analysis/6k1/6pp/4p3/3pP3/2pP1PP1/1p6/1K5P/8_b_-_-_0_1" rel="noreferrer">analysis</a>.</p>
  <p>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:</p>
  <pre><code>    [FEN &quot;6k1/6pp/4p3/3pP3/2pP1PP1/1p6/1K5P/8 b - - 0 1&quot;]
  
      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#
  </code></pre>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-09-08T16:44:19.773Z
Answers.LastActivityDate: 2021-09-08T16:44:19.773Z
Answers.UserDisplayName: Minot
Answers.Body: <p>If we look at the position we see a number of things:</p>
  <ol>
  <li>Black's connected passed pawns mean that the white king must remain at all times in the rectangle a1-a3-d3-d1.</li>
  <li>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.</li>
  <li>White has a healthy kingside majority which can a generate a passed pawn.</li>
  <li>White's immediate threat is f5 which would immediately create a supported passed e5 pawn.</li>
  <li>Therefore unless black can permanently stop that threat then the black king must always stay within the rectangle h8-h5-b5-b8.</li>
  <li>If black plays Kb4 then the result will depend on whether one player can queen first and then stop the opponent from queening.</li>
  </ol>
  <p>That said let's look at some sample lines starting with what happens if black allows an immediate f5 by white:</p>
  <pre><code>[FEN &quot;6k1/6pp/4p3/3pP3/2pP1PP1/1p6/1K5P/8 b - - 0 1&quot;]
  
  1...Kf7 2. f5 Ke7 3. fxe6 Kxe6 {and both side have their king's tethered to the opponent's passed pawn(s).
  </code></pre>
  <p>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.</p>
  <p>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.</p>
  <pre><code>[FEN &quot;6k1/6pp/4p3/3pP3/2pP1PP1/1p6/1K5P/8 b - - 0 1&quot;]
  
  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
  </code></pre>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-09-08T20:50:11.130Z
Answers.Text: 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.
Answers.UserDisplayName: Hauke Reddmann
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-09-10T03:15:53.493Z
Answers.Text: Brian it might be helpful to weaker players like me to note that f5 for white also sufficiently prevents black's king from getting in on the kingside (with proper play) when you first mention the f5 key... as I spent too long trying out variations before satisfying myself on that, then seeing you mention it later on :-)
Answers.UserDisplayName: JeopardyTempest
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-09-08T16:47:01.400Z
Answers.LastActivityDate: 2021-09-09T10:15:45.373Z
Answers.LastEditDate: 2021-09-09T10:15:45.373Z
Answers.UserDisplayName: Brian Towers
Body: <p>Black to move. My computer gives the evaluation -2.5 but I can't find the winning sequence for black.</p>
  <pre><code>[FEN &quot;6k1/6pp/4p3/3pP3/2pP1PP1/1p6/1K5P/8 b - - 0 1&quot;]
  </code></pre>
  <p>(Black goes up the board)</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-09-09T08:40:10.653Z
Comments.Text: This is reminiscent of an endgame trap Yuri Averbakh avoided in 1953 Zurich izt, vs Szabo IIRM...
Comments.UserDisplayName: Evargalo
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-09-09T09:48:29.777Z
Comments.Text: Can you clarify the orientation of the board, please? As presented, I would suggest "a1Q", which is not hard to find :)
Comments.UserDisplayName: Carsten S
Tags: <endgame><pawn-endgame>
Title: Can black win this pawn ending?
ThreadText: # Can black win this pawn ending?
  
  (Asked by: username_0 on 2021-09-08)
  
  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)
  
  **Tags:** endgame, pawn-endgame
  
  > **Comments:**
  > **username_1**: This is reminiscent of an endgame trap Yuri Averbakh avoided in 1953 Zurich izt, vs Szabo IIRM...  
  > **username_2**: Can you clarify the orientation of the board, please? As presented, I would suggest "a1Q", which is not hard to find :)  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_4 on 2021-09-08. Score: 15 | Accepted answer
  
  If we look at the position we see a number of things:
  
  Black's connected passed pawns mean that the white king must remain at all times in the rectangle a1-a3-d3-d1.
  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.
  White has a healthy kingside majority which can a generate a passed pawn.
  White's immediate threat is f5 which would immediately create a supported passed e5 pawn.
  Therefore unless black can permanently stop that threat then the black king must always stay within the rectangle h8-h5-b5-b8.
  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
  
  > **Comments:**
  > **username_5**: 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.  
  > **username_6**: Brian it might be helpful to weaker players like me to note that f5 for white also sufficiently prevents black's king from getting in on the kingside (with proper play) when you first mention the f5 key... as I spent too long trying out variations before satisfying myself on that, then seeing you mention it later on :-)  
  
  ---
  
  ### Answer by username_3 on 2021-09-08. Score: 6
  
  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#
  
  
  ---
  
  