user30501: I recently ran across notes I made from a book on endgames (I don't remember the book).  According to my notes, Black wins this position regardless of whose move it is.  I don't see it, and Stockfish doesn't see it.  What am I missing?
[FEN "8/p7/2k1p1pp/1p1pPp2/1P3P2/3K2P1/P6P/8 w - - 0 1"]


Thanks to everyone for the thoughtful answers.  I haven't had time to go through all of them yet.  However, I had Stockfish analyze every move (both black & white) for at least 30 moves.  And, it found a winning line.  I will now go through the comments to see how and why Stockfish differed from the answers given.  Note, White's two pawn pushes (a3 & h3) didn't show up until Stockfish was at least 56 ply deep.
[FEN "8/p7/2k1p1pp/1p1pPp2/1P3P2/3K2P1/P6P/8 b - - 0 1"]

1... Kb6 2. Kc3 a6 3. a3 Kc7 4. h3 Kd7 5. Kd4 Ke7 6. Ke3 Kf7 7. 
h4 Ke8 8. Kd3 Kd8 9. Kc3 Kc7 10. Kd2 Kd7 11. Ke3 d4+ 12. Kxd4 Kc6 
13. h5 gxh5 14. Kc3 Kd5 15. Kd3 h4 16. gxh4 h5 17. Ke3 Kc4 *


user4418: 
According to my notes, Black wins this position regardless of whose move it is.

Your notes are wrong. Black has no entry squares and never will have. For the most part white moves the king between d3 and d4 unless white makes a pawn break with a4 in which case white just protects the b pawn with a3. In general on both sides of the board white declines to capture pawns when offered but does recapture.
Meanwhile black's king can never move away from protecting the c5 square since if white is allowed to play Kc5 then it is black who is in danger of losing.

user9321: Black has D5-D4 to create an opening for entry onto white's position. Needs analysis to determine if black can then force the opposition and win.

user32285: I have not fully analyzed this position, but contrary to the other answers, I see a possible win for black. Here is a possible series of moves:
[FEN "8/p7/2k1p1pp/1p1pPp2/1P3P2/3K2P1/P6P/8 b - - 0 1"]

1... Kd7 2. Kd4 Ke7 3. Kc5 a6 4. Kd4 Kf7 5. h4 Ke7 6. Kc5 Kd7 7. Kd4 Kc6 8. Kd3 Kb6 9. Kd4 a5 10. a3 axb4 11. axb4 Kc7 12. Kd3 d4 13. Kxd4 Kc6 14. Kc3 Kd5 15. Kd3 h5

After black reaches f7 with the king, white is forced to play h4 because otherwise black would infiltrate the king's side. This hands the crucial tempo to black.
Edit: Carlo Wood found a nice refutation of this line (for details see his answer). In summary, the position is a draw, but only through a very complicated line involving a queen and pawn endgame.

user20841: This is a draw because white has enough tempo's to keep black out. For example after
[Variant "From Position"]
[FEN "8/p7/2k1p1pp/1p1pPp2/1P3P2/3K2P1/P6P/8 b - - 0 1"]

1... Kd7 2. Kd4 Ke7 3. Kc5 a6 4. Kd4 Kf7

White must play 5. h4
And if black tries to break with 5... g5 white must play 6. h5! and the king's side of the board is closed.
Also after
[Variant "From Position"]
[FEN "8/p7/2k1p1pp/1p1pPp2/1P3P2/3K2P1/P6P/8 b - - 0 1"]

1... g5 2. h3 gxf4 3. gxf4

white can keep the King's side closed. White could also have played 2. h4 by the way. But those are the only moves.
The queen side is already closed but very importantly, white has the tempo a2-a3 here. With the pawn already on a3 this would be winning for black simply by giving away the d pawn and putting the king on d5. White then plays Kd3 but black has a pawn tempo more and will enter the position.
For example,
[Variant "From Position"]
[FEN "8/p7/2k1p1pp/1p1pPp2/1P3P2/P2K2P1/7P/8 b - - 0 4"]

4... a6 5. Ke3 Kd7 6. Kd4 Ke7 7. h4 Kd7 8. Kd3 d4 9. Kxd4 Kc6 10. Kc3 Kd5 11. Kd3 h5 0-1

where I even started with 4... a6 because we have to walk to the Kings side to force white to close it there (play the h-pawn) and white can enforce a6 anyway by going to c5 with their king.
Note that in this case playing h3, in order to get an extra "tempo" doesn't work for white. For example,
[Variant "From Position"]
[FEN "8/p7/2k1p1pp/1p1pPp2/1P3P2/P2K2P1/7P/8 b - - 0 4"]

4... Kd7 5. Kd4 Ke7 6. Kc5 a6 7. Kd4 Kf7 8. h3 g5 9. Ke3 Kg6 10. Kd4 gxf4 11. gxf4 Kh5 12. Kc5 Kh4 13. Kd6 d4 14. Kxe6 d3 15. Kf7 d2 16. e6 d1=Q 17. e7 Qd7 18. Kf8 Kxh3 19. e8=Q Qxe8+ 20. Kxe8 Kg4 21. Kf7 h5

EDIT:
All credits go to EigenTime (see their answer) for the attempt of black to gain a tempo with a5! I wouldn't be surprised that this is how the endgame book thought black would win - it is only a draw because of a very narrow path that white has to keep it a draw that you can only find with an engine:
[Variant "From Position"]
[FEN "8/p7/2k1p1pp/1p1pPp2/1P3P2/3K2P1/P6P/8 b - - 2 21"]

1... Kd7 2. Kd4 Ke7 3. Kc5 a6 4. h4 Kd7 5. Kd4 Kc6 6. Kc3 Kb6 7. Kd2 a5 8. g4 fxg4 9. h5 gxh5 10. f5 g3 11. Ke1 d4 12. bxa5+ Kc7 13. f6 d3 14. f7 g2 15. Kf2 d2 16. f8=Q g1=Q+ 17. Kxg1 d1=Q+ 18. Kf2 Qd4+ 19. Kf1 Qa1+ 20. Kf2 Qxa2+ 21. Kg3 h4+ 22. Kh3 Qb3+ 23. Kxh4 Qc4+ 24. Kh5 Qe2+ 25. Kxh6 Qe3+ 26. Kg6 Qg3+ 27. Kh6 Qe3+ 28. Kg6 Qg3+ 29. Kh6 Qh2+ 30. Kg6 Qxe5 31. Qe7+ Kc6 32. a6 Qf5+ 33. Kh6 Qf4+ 34. Kg6 Qg4+ 35. Kh7 Qh5+ 36. Kg7 Qg4+ 37. Kh6 Qf4+ 38. Kh5 Qf5+ 39. Kh6 Qh3+ 40. Kg5 Qg2+ 41. Kh5 Kb6 42. a7 Qh1+ 43. Kg6 Qg2+ 44. Kf6 Qf3+ 45. Kg6 Qe4+ 46. Kh6 Qe3+ 47. Kg6 Qd3+ 48. Kg7 Qg3+ 49. Kh6 Qh2+ 50. Kg5 Qg2+ 51. Kf6 Qa8 52. Qxe6+ Kxa7 53. Qe3+ Ka6 54. Qa3+ Kb7 55. Qxa8+ Kxa8 56. Ke5 Ka7 57. Kd4 Ka6 58. Kc3 Ka5 59. Kb3

Note that almost all moves from 6 through 17 are forced for white!

user8300: How can you be certain that your notes are correct? This position is a bit complicated to work out at a glance, but as I see it there is only one possible winning plan for black here, consisting of the following:

play a well-timed ...d4, and after White plays Kxd4 Black will play ...Kc6 and force White's king back.

However, White has pawns that they can use to manipulate tempi, and in order to actually break through in the center with the plan I outlined above Black actually needs to force zugzwang TWICE! This is because even if White has to move their king from d4 after ...Kc6, White can still move their king to e3 and counter Black's ...Kd5 with Kd3.
And so, the question becomes rather simple: can Black engineer this position so that they have TWO more spare tempi than White instead of one? We note immediately that at most one spare tempo can come from the queenside pawns with ...a7-a6 (if White is careless and plays, say, a2-a3 prematurely), meaning that Black needs at least one spare tempo from the kingside as well.
If White is to move, then White will just pass the move over to Black with 1.Kc3, Ke3 or Kd4. This does not really affect the evaluation of the underlying position, since the only real winning plan is still a successful ...d4 push. Thus, we may consider ways for black to force the issue.
Black has, in total, four pawn moves and a bunch of king moves. The king moves clearly don't lead to any substantial progress, so let us consider the available pawn moves.
1...a6 and 1...h5 are immediately off the table, since they waste Black's precious opportunity to create an extra tempo, and thus we may consider the other pawn moves as the only possibly winning moves.
If Black plays 1...g5, then White can respond with 2.h4 with the threat of playing 3.h5! This would force Black into going for the draw, since otherwise White could easily create a passed pawn. Thus, we get that after 1...g5 2.h4 Black needs to play either 3...g4 or 3...gxf4. Out of these, 3...gxf4 is the only move that can actually work. But even this move fails, since after 3...gxf4 4.gxf4 we see that Black has only managed to create ONE spare tempo; after 4...d4 5.Kxd4 h5 6.a3! a6 7.Ke3, the position is indeed drawn. From this, I make the conclusion that the position is drawn after 1...g5.
Left to consider is 1...a5!? This move looks quite odd at first glance, but it's actually not completely harmless. If White plays 2.bxa5?, then black responds with 2...b4 followed by ...Kb5 and ...Kxa5. This would indeed be winning, so White needs to play 2.a3 here (2.Kc3 axb4+ 3.Kxb4 d4! wins for black). Thus, we may conclude that the line has to go 1...a5 2.a3, and here we run into some issues as Black. Now the pawn on b5 can never be protected by a pawn on a6, so Black has to be careful about allowing Kc5. Moreover, as long as Black's pawn on a5 remains undefended Black cannot play the ...d4 push and get the desired zugzwang with ...Kc6, since this would let White just take on a5 and win. Thus, we can conclude that Black NEEDS to play either ...axb4 or ...a4 before the ...d4 push. But this means that Black has zero spare tempi on the queenside. Because of this, I conclude that the position is drawn after 1...a5.
To summarize: your notes are definitely wrong, and the position is a draw no matter who makes the first move.
Edit: As indicated by other answers, there is one serious attempt involving a king march to provoke h4, followed by engineering an ...a5 push to gain the extra tempo needed in order to make the ...d4 break work. I did not consider this option when I posted my answer, and although my conclusions are still correct (the position is still a draw after some precise moves from White, see Carlo Wood's answer to get an idea of the lines that need to be considered), this answer is definitely incomplete. I guess it just goes to show how tricky pawn endgames really can be. Take care, and remember: don't make any hasty assumptions about pawn endgames!

30501: <p>I recently ran across notes I made from a book on endgames (I don't remember the book).  According to my notes, Black wins this position regardless of whose move it is.  I don't see it, and <a href="https://en.wikipedia.org/wiki/Stockfish_%28chess%29" rel="nofollow noreferrer">Stockfish</a> doesn't see it.  What am I missing?</p>
<pre><code>[FEN &quot;8/p7/2k1p1pp/1p1pPp2/1P3P2/3K2P1/P6P/8 w - - 0 1&quot;]
</code></pre>
<hr/>
<p><sub>Thanks to everyone for the thoughtful answers.  I haven't had time to go through all of them yet.  However, I had Stockfish analyze every move (both black &amp; white) for at least 30 moves.  And, it found a winning line.  I will now go through the comments to see how and why Stockfish differed from the answers given.  Note, White's two pawn pushes (a3 &amp; h3) didn't show up until Stockfish was at least 56 ply deep.</sub></p>
<pre><code>[FEN &quot;8/p7/2k1p1pp/1p1pPp2/1P3P2/3K2P1/P6P/8 b - - 0 1&quot;]

1... Kb6 2. Kc3 a6 3. a3 Kc7 4. h3 Kd7 5. Kd4 Ke7 6. Ke3 Kf7 7. 
h4 Ke8 8. Kd3 Kd8 9. Kc3 Kc7 10. Kd2 Kd7 11. Ke3 d4+ 12. Kxd4 Kc6 
13. h5 gxh5 14. Kc3 Kd5 15. Kd3 h4 16. gxh4 h5 17. Ke3 Kc4 *
</code></pre>
 4418: <blockquote>
<p>According to my notes, Black wins this position regardless of whose move it is.</p>
</blockquote>
<p>Your notes are wrong. Black has no entry squares and never will have. For the most part white moves the king between d3 and d4 unless white makes a pawn break with a4 in which case white just protects the b pawn with a3. In general on both sides of the board white declines to capture pawns when offered but does recapture.</p>
<p>Meanwhile black's king can never move away from protecting the c5 square since if white is allowed to play Kc5 then it is black who is in danger of losing.</p>
 9321: <p>Black has D5-D4 to create an opening for entry onto white's position. Needs analysis to determine if black can then force the opposition and win.</p>
 32285: <p>I have not fully analyzed this position, but contrary to the other answers, I see a possible win for black. Here is a possible series of moves:</p>
<pre><code>[FEN &quot;8/p7/2k1p1pp/1p1pPp2/1P3P2/3K2P1/P6P/8 b - - 0 1&quot;]

1... Kd7 2. Kd4 Ke7 3. Kc5 a6 4. Kd4 Kf7 5. h4 Ke7 6. Kc5 Kd7 7. Kd4 Kc6 8. Kd3 Kb6 9. Kd4 a5 10. a3 axb4 11. axb4 Kc7 12. Kd3 d4 13. Kxd4 Kc6 14. Kc3 Kd5 15. Kd3 h5
</code></pre>
<p>After black reaches f7 with the king, white is forced to play h4 because otherwise black would infiltrate the king's side. This hands the crucial tempo to black.</p>
<p>Edit: Carlo Wood found a nice refutation of this line (for details see his answer). In summary, the position is a draw, but only through a very complicated line involving a queen and pawn endgame.</p>
 20841: <p>This is a draw because white has enough tempo's to keep black out. For example after</p>
<pre><code>[Variant &quot;From Position&quot;]
[FEN &quot;8/p7/2k1p1pp/1p1pPp2/1P3P2/3K2P1/P6P/8 b - - 0 1&quot;]

1... Kd7 2. Kd4 Ke7 3. Kc5 a6 4. Kd4 Kf7
</code></pre>
<p>White <em>must</em> play 5. h4</p>
<p>And if black tries to break with 5... g5 white must play 6. h5! and the king's side of the board is closed.</p>
<p>Also after</p>
<pre><code>[Variant &quot;From Position&quot;]
[FEN &quot;8/p7/2k1p1pp/1p1pPp2/1P3P2/3K2P1/P6P/8 b - - 0 1&quot;]

1... g5 2. h3 gxf4 3. gxf4
</code></pre>
<p>white can keep the King's side closed. White could also have played 2. h4 by the way. But those are the only moves.</p>
<p>The queen side is already closed but very importantly, white has the tempo a2-a3 here. With the pawn already on a3 this would be winning for black simply by giving away the d pawn and putting the king on d5. White then plays Kd3 but black has a pawn tempo more and will enter the position.</p>
<p>For example,</p>
<pre><code>[Variant &quot;From Position&quot;]
[FEN &quot;8/p7/2k1p1pp/1p1pPp2/1P3P2/P2K2P1/7P/8 b - - 0 4&quot;]

4... a6 5. Ke3 Kd7 6. Kd4 Ke7 7. h4 Kd7 8. Kd3 d4 9. Kxd4 Kc6 10. Kc3 Kd5 11. Kd3 h5 0-1
</code></pre>
<p>where I even started with 4... a6 because we have to walk to the Kings side to force white to close it there (play the h-pawn) and white can enforce a6 anyway by going to c5 with their king.</p>
<p>Note that in this case playing h3, in order to get an extra &quot;tempo&quot; doesn't work for white. For example,</p>
<pre><code>[Variant &quot;From Position&quot;]
[FEN &quot;8/p7/2k1p1pp/1p1pPp2/1P3P2/P2K2P1/7P/8 b - - 0 4&quot;]

4... Kd7 5. Kd4 Ke7 6. Kc5 a6 7. Kd4 Kf7 8. h3 g5 9. Ke3 Kg6 10. Kd4 gxf4 11. gxf4 Kh5 12. Kc5 Kh4 13. Kd6 d4 14. Kxe6 d3 15. Kf7 d2 16. e6 d1=Q 17. e7 Qd7 18. Kf8 Kxh3 19. e8=Q Qxe8+ 20. Kxe8 Kg4 21. Kf7 h5
</code></pre>
<p>EDIT:</p>
<p>All credits go to EigenTime (see their answer) for the attempt of black to gain a tempo with a5! I wouldn't be surprised that this is how the endgame book thought black would win - it is only a draw because of a <em>very</em> narrow path that white has to keep it a draw that you can only find with an engine:</p>
<pre><code>[Variant &quot;From Position&quot;]
[FEN &quot;8/p7/2k1p1pp/1p1pPp2/1P3P2/3K2P1/P6P/8 b - - 2 21&quot;]

1... Kd7 2. Kd4 Ke7 3. Kc5 a6 4. h4 Kd7 5. Kd4 Kc6 6. Kc3 Kb6 7. Kd2 a5 8. g4 fxg4 9. h5 gxh5 10. f5 g3 11. Ke1 d4 12. bxa5+ Kc7 13. f6 d3 14. f7 g2 15. Kf2 d2 16. f8=Q g1=Q+ 17. Kxg1 d1=Q+ 18. Kf2 Qd4+ 19. Kf1 Qa1+ 20. Kf2 Qxa2+ 21. Kg3 h4+ 22. Kh3 Qb3+ 23. Kxh4 Qc4+ 24. Kh5 Qe2+ 25. Kxh6 Qe3+ 26. Kg6 Qg3+ 27. Kh6 Qe3+ 28. Kg6 Qg3+ 29. Kh6 Qh2+ 30. Kg6 Qxe5 31. Qe7+ Kc6 32. a6 Qf5+ 33. Kh6 Qf4+ 34. Kg6 Qg4+ 35. Kh7 Qh5+ 36. Kg7 Qg4+ 37. Kh6 Qf4+ 38. Kh5 Qf5+ 39. Kh6 Qh3+ 40. Kg5 Qg2+ 41. Kh5 Kb6 42. a7 Qh1+ 43. Kg6 Qg2+ 44. Kf6 Qf3+ 45. Kg6 Qe4+ 46. Kh6 Qe3+ 47. Kg6 Qd3+ 48. Kg7 Qg3+ 49. Kh6 Qh2+ 50. Kg5 Qg2+ 51. Kf6 Qa8 52. Qxe6+ Kxa7 53. Qe3+ Ka6 54. Qa3+ Kb7 55. Qxa8+ Kxa8 56. Ke5 Ka7 57. Kd4 Ka6 58. Kc3 Ka5 59. Kb3
</code></pre>
<p>Note that almost all moves from 6 through 17 are forced for white!</p>
 8300: <p>How can you be certain that your notes are correct? This position is a bit complicated to work out at a glance, but as I see it there is only one possible winning plan for black here, consisting of the following:</p>
<blockquote>
<p>play a well-timed ...d4, and after White plays Kxd4 Black will play ...Kc6 and force White's king back.</p>
</blockquote>
<p>However, White has pawns that they can use to manipulate tempi, and in order to actually break through in the center with the plan I outlined above Black actually needs to force zugzwang TWICE! This is because even if White has to move their king from d4 after ...Kc6, White can still move their king to e3 and counter Black's ...Kd5 with Kd3.</p>
<p>And so, the question becomes rather simple: can Black engineer this position so that they have TWO more spare tempi than White instead of one? We note immediately that at most one spare tempo can come from the queenside pawns with ...a7-a6 (if White is careless and plays, say, a2-a3 prematurely), meaning that Black needs at least one spare tempo from the kingside as well.</p>
<p>If White is to move, then White will just pass the move over to Black with 1.Kc3, Ke3 or Kd4. This does not really affect the evaluation of the underlying position, since the only real winning plan is still a successful ...d4 push. Thus, we may consider ways for black to force the issue.</p>
<p>Black has, in total, four pawn moves and a bunch of king moves. The king moves clearly don't lead to any substantial progress, so let us consider the available pawn moves.</p>
<p>1...a6 and 1...h5 are immediately off the table, since they waste Black's precious opportunity to create an extra tempo, and thus we may consider the other pawn moves as the only possibly winning moves.</p>
<p>If Black plays 1...g5, then White can respond with 2.h4 with the threat of playing 3.h5! This would force Black into going for the draw, since otherwise White could easily create a passed pawn. Thus, we get that after 1...g5 2.h4 Black needs to play either 3...g4 or 3...gxf4. Out of these, 3...gxf4 is the only move that can actually work. But even this move fails, since after 3...gxf4 4.gxf4 we see that Black has only managed to create ONE spare tempo; after 4...d4 5.Kxd4 h5 6.a3! a6 7.Ke3, the position is indeed drawn. From this, I make the conclusion that the position is drawn after 1...g5.</p>
<p>Left to consider is 1...a5!? This move looks quite odd at first glance, but it's actually not completely harmless. If White plays 2.bxa5?, then black responds with 2...b4 followed by ...Kb5 and ...Kxa5. This would indeed be winning, so White needs to play 2.a3 here (2.Kc3 axb4+ 3.Kxb4 d4! wins for black). Thus, we may conclude that the line has to go 1...a5 2.a3, and here we run into some issues as Black. Now the pawn on b5 can never be protected by a pawn on a6, so Black has to be careful about allowing Kc5. Moreover, as long as Black's pawn on a5 remains undefended Black cannot play the ...d4 push and get the desired zugzwang with ...Kc6, since this would let White just take on a5 and win. Thus, we can conclude that Black NEEDS to play either ...axb4 or ...a4 before the ...d4 push. But this means that Black has zero spare tempi on the queenside. Because of this, I conclude that the position is drawn after 1...a5.</p>
<p>To summarize: your notes are definitely wrong, and the position is a draw no matter who makes the first move.</p>
<p><strong>Edit:</strong> As indicated by other answers, there is one serious attempt involving a king march to provoke h4, followed by engineering an ...a5 push to gain the extra tempo needed in order to make the ...d4 break work. I did not consider this option when I posted my answer, and although my conclusions are still correct (the position is still a draw after some precise moves from White, see Carlo Wood's answer to get an idea of the lines that need to be considered), this answer is definitely incomplete. I guess it just goes to show how tricky pawn endgames really can be. Take care, and remember: don't make any hasty assumptions about pawn endgames!</p>
