19

Update: ​ ​ ​ ​ I emailed Tim Krabbé, and he agrees that ​ 41. b4 bxa4 ​ draws.
He has posted a PS about this just under his old analysis.



With respect to "Skawinski - Tomczak, European ch rapid, Warsaw 2011",
Tim Krabbé says that "White could have won with 41.b4!".
After ​ 41. b4 bxa4 , ​ they would have reached the position

[Title "The Position I'm Actually Interested In"]
[fen "8/8/2p5/p2k1ppp/pP1P5/3K1PPP/8/8 w - - 0 42"]


with white to move. ​ Stockfish believes that from the above position,
everything other than bxa5 loses outright for white, and that after bxa5, a3 probably
holds for black due to the counter-breakthrough on the kingside. ​ ​ ​ Tim Krabbé does
address that counter-breakthrough, but only for ​ 41. ... axb4 , ​ rather than ​ 41. ... bxa4 .

Here's what I currently believe to be optimal play from the above diagram:

[Title "What I Currently Believe is Optimal Play From That Position"]
[fen "8/8/2p5/p2k1ppp/pP1P5/3K1PPP/8/8 w - - 0 42"]

1.bxa5 a3 2.Kc2 a2 3.Kb2 a1=Q+ 4.Kxa1 g4 5.hxg4 f4 6.gxf4 h4 7.a6 h3 8.a7 h2 9.a8=Q


Proof that white does not have a forced win after that line:


The main line continues 9. ... h1=Q+ 10.Kb2 Qg2+ 11.Kb3 Qxf3+ 12.Kb4 Qxf4 13.Qd8+ Ke4. ​ Playing Ka2 instead of Kb2 doesn't change anything.
If white's king goes back to rank 1 instead of to rank 3 or back to rank 2 instead of to
rank 4, then black checks horizontally from the f-file until white's king goes to rank 4.
Otherwise, black doesn't care how white's king goes from a1 to rank 4.

Let "6ptbd" be short for "6-piece tablebase draw-or-win-for-black".

If white's king goes to a4 instead of b4 then:
Black plays Qd1+. ​ If white plays Ka3 then black plays Qa1+.
If white doesn't play that or doesn't follow it up with Kb3 then Qxd4 followed by Qxf4
yields a 6ptbd, so for the next sentence, assume 12.Ka4 Qa1+ 13.Kb3 Qxa8.
If Kc3 then Qa1+ followed by Qxd4 yields a 6ptbd, else Kxd4 yields a 6ptbd.

Stephen comments that after Qxf4, the position is a finalgen table base draw. ​ Since I already
had a majority of the relevant analysis together before I read that, I'll give analysis which, without relying on finalgen (but still relying on 5&6-piece tablebases being correct about certain positions
not being forced wins for white), shows that white doesn't have a forced win after Qxf4.
After Qxf4, Qd8+ is the only move which doesn't let black immediately
capture on d4 for a 6ptbw. ​ ​ ​ After Ke4, the only moves for white which
don't let black immediately capture for a 6ptbd are ​ Kc3,Qd7,g5 .

After Ke4, if Kc3 then black gets at least a draw as follows:
Black starts with Qc1+, and then black's queen moves as far up as doesn't let white capture
it immediately while still checking from below unless white's king goes to c5 or rank 6.
If Kc5 then Qa3+. ​ Since b5 and and d3 and d5 are covered by black's pawn and king,
the only way out of those checks is going to rank 6, and the only ways for
white's king to get there are a5 and c5, which mean black's queen will be on a3.
In that case, Kxc6 is a 6ptbd, and if Kb6 then Qb4+ followed by Qxd4 is a tablebase draw.

After Ke4, if Qd7 then black gets at least a draw as follows:
Black starts with Qd2+. ​ If Kc4 or Kc5 then black mostly follows the procedure described in the previous paragraph, but if Qb4+ Ka6 then Qa4+ followed by Qxd4 rather than an immediate Qxd4, and if Qb4+ Kxc6 then it's already a 6ptbd which Qxd4 would lose.
Otherwise, Qxd4 gives a 6ptbd.

After Ke4, if g5 then black gets at least a draw as follows:
Until black can check from below in a way that's not Qb1 checking Kb4, black moves so that [white_king's_square,black_queen's_square] is an element of {[a1,d1],[b1,d1],[a2,d2],[b2,d2],[a3,c1],[b3,d1],[b4,d2]}. Once black can check from below in a way that's not Qb1 checking Kb4, black then does so as close to white's king as doesn't let white capture it immediately, and continues that until white's king reaches rank 6. ​ If Kd6 then Qxd4+ is a 6ptbd. ​ The only other way out of the part of this paragraph that came before this sentence is Kb6. ​ Once white has played that, until white captures c6 or blocks a check or the rest of this sentence calls for Qxg5, black moves so that [white_king's_square,black_queen's_square] is an element of
{[a6,a4],[a7,a4],[a8,a4],[b6,b4],[b7,b5],[b8,b5],[c7,a5],[c8,f5],[d6,d5],[d7,d5],[e7,g5],[e8,g8]}.
White capturing c6 is a 6ptbd, and if white blocks a check then queen-takes-pawn is a 6ptbd.
The sentence two ago only calls for Qxg5 after Ke7, and in that case it's a 6ptbd.

Therefore, none of Kc3,Qd7,g5 keep a forced win for white. ​ QED


Thus, any forced win for white must deviate from that line before h1=Q+.

  • I analyzed the position with an engine and I came to the same conclusion. The line you give is more or less forced. I think you're right, the position is a draw. – Maxwell86 Sep 12 '15 at 8:29
  • I let FinalGen generate a tablebase for the final position in your second diagram (3Q4/8/2p5/8/1K1PkqP1/8/8/8 w - - 0 1) - it's a draw. (The pawn endgame in the first diagram is too complex for FinalGen.) – Stephen Sep 12 '15 at 9:21
  • So, after a8=Q, there can't be a forced win for white. ​ – user2668 Sep 12 '15 at 9:31
  • @Tony Ennis: The tablebase I generated shows that the position is already a draw after 12...Qxf4, so 13.Qd8+ is not at fault. – Stephen Sep 12 '15 at 18:39
  • @TonyEnnis: ​ I didn't explore that because 13.Qa5+ Kxd4 gives a 6-piece tablebase draw. ​ ​ ​ ​ – user2668 Sep 12 '15 at 19:58
1

I've looked at this question a lot since I first saw it. I spent the last day of 2016 looking at its variations. I wasn't able to find a variation with white winning.

SETUP:

  • GUI: Athena-3.5.1 build 2861
  • ENGINE: stockfish_16123114_x64_modern (daily build - none more recent)
  • ENGINE: komodo-10.1-64bit
  • ENGINE: andscacs-0.89
  • ENGINE: Fire_5_x64-popcnt

I always assigned white the strongest chess engine to give it advantage to win, and I used more resources (more memory and CPUs) to allowed for deeper analysis.

MAIN LINE:

The so-called 'main line' simply deteriorates into move repetition; so a draw.

This position ultimately appears unwinnable for white because black's act of advancing a pawn with 1 .. a4 draws white's King away from the centre with 2. Kc2 .. ultimately placing the King on a1 with 6. Kxa1 ... Black exploits this positioning in a very clever way with another foot race white falsely appears to win.

Looking forward to having whites King capture the promoted a column black pawn, Black chooses to moves 2. .. g4 to sacrifice material and to open the h column. This material sacrifice 2. .. g4 ultimately allows the pawn on h file to race to promotion and gains black tempo by putting whites a1 King in check. The sacrifice doesn't look it provides advantage yet because black has to wait for whites King to be put in check. However black's material sacrifice on 2. .. g4 indeed gains tempo because of the positioning of white's King.

Recall, white's king has been drawn to a1. The foot race between white's a5 pawn and black's soon-to-be h4 pawn seems to advantage white (who promotes first) except that black Pawn's promotion putting white's a1 King in check is where black realizes the tempo. As long as black continues to check, white position is unwinnable. White's promoted Queen never gets a chance.



[Event "Ricky Demer's Position: Main Line"]
[Site "GHOST"]
[Date "2016.12.31"]
[Round "2"]
[White "Stockfish 16123114 x64 POPCNT"]
[Black "Stockfish 16123114 x64 POPCNT"]
[Result "*"]
[BlackElo "3397"]
[Time "13:29:29"]
[WhiteElo "3397"]
[TimeControl "300"]
[SetUp "1"]
[FEN "8/8/2p5/p2k1ppp/pP1P4/3K1PPP/8/8 w - - 0 1"]
[Termination "normal"]
[PlyCount "71"]
[WhiteType "human"]
[BlackType "human"]
[FEN "8/8/2p5/p2k1ppp/pP1P4/3K1PPP/8/8 w - - 0 1"]

1. bxa5 a3 2. Kc2 g4 3. hxg4 f4 4. gxf4 a2 5. Kb2 a1=Q+ 6. Kxa1 h4 7. a6 h3 8. a7 h2 9. a8=Q h1=Q+ 10. Ka2 Qg2+ 11. Ka1 Qh1+ 12. Ka2 Qg2+ 13. Ka1 Qf1+ 14. Ka2 Qe2+ 15. Ka1 Qe1+ 16. Ka2 Qf2+ 17. Ka1 Qf1+ 18. Ka2 Qf2+ 19. Ka1 Qxd4+ 20. Kb1 Qd1+ 21. Ka2 Qc2+ 22. Ka1 Qd1+ 23. Ka2 Qd2+ 24. Ka1 Qc1+  25. Ka2  Qc2+ 26. Ka1 Qc3+ 27. Kb1 {(Ka1-b1 Qc3-e1+ Kb1-c2 Qe1-f2+ Kc2-b1 Qf2-e1+) 0.00/42 4} Qe1+  28. Ka2  Qf2+  29. Ka1 Qe1+ 30. Ka2 Qf2+ 31. Ka1 Qg1+ 32. Ka2 Qg2+ 33. Ka1 Qf1+ 34. Ka2 Qe2+ 35. Ka1 Qe1+ 36. Ka2 (36. Ka2 {(Ka1-a2)
0.00/47 3-fold repetition}) *


FALSE HOPE:

The variation you suggest has white's King taking the pawn on a2 with 6. Kxa2 rather than allow it to promote and take it on a1.

The apparent advantage to white is illusory. Because black appears to win the second race to pawn promotion 8. .. h1=Q, and because white's King is still on a2 white King's moves are nuanced, ultimately allowing black to take all white's Pawns (as white is taking black's pawns) leading to a stalemate (again) due to insufficient material.

The variation supposedly advantaging white, in fact allows black to take all of white's other pieces. Here are some examples using Stockfish against Stockfish.



[Event "Ricky Demer's Position: White hope?"]
[Site "GHOST"]
[Date "2016.12.31"]
[Round "1"]
[White "Stockfish 16123114 x64 POPCNT"]
[Black "Stockfish 16123114 x64 POPCNT"]
[Result "*"]
[BlackElo "3210"]
[Time "13:05:02"]
[WhiteElo "3210"]
[TimeControl "40/2400:40/2400:40/2400"]
[SetUp "1"]
[Termination "insufficient material"]
[PlyCount "53"]
[WhiteType "program"]
[BlackType "program"]
[FEN "8/8/2p5/p2k1ppp/pP1P4/3K1PPP/8/8 w - - 0 1"]

1. bxa5 {(b4xa5 a4-a3 Kd3-c3 g5-g4 f3xg4 a3-a2 Kc3-b2 a2-a1B+ Kb2xa1 h5-h4
g3xh4 f5-f4 Ka1-a2 f4-f3 a5-a6 f3-f2 a6-a7 f2-f1Q a7-a8Q Qf1-f2+ Ka2-b3
Qf2-e3+ Kb3-c2 Qe3-e2+ Kc2-c3 Qe2-e3+ Kc3-b4 Qe3xd4+ Kb4-b3 Qd4-d3+ Kb3-b2
Qd3-d2+ Kb2-b1 Qd2-d3+ Kb1-c1 Qd3-e3+ Kc1-b2 Qe3-e2+ Kb2-b1 Qe2-f1+ Kb1-b2
Qf1-e2+) 0.00/30 11} a3 {(a4-a3 Kd3-c3 g5-g4 f3xg4 h5-h4 g3xh4 a3-a2 Kc3-b2
a2-a1Q+ Kb2xa1 f5-f4 a5-a6 f4-f3 a6-a7 f3-f2 a7-a8Q f2-f1Q+ Ka1-a2 Qf1-f2+
Ka2-b3 Qf2-e3+ Kb3-c2 Qe3-e2+ Kc2-c3 Qe2-e3+ Kc3-b4 Qe3xd4+ Kb4-b3 Qd4-d3+
Kb3-b2 Qd3-d2+ Kb2-b1 Qd2-d3+ Kb1-c1 Qd3-e3+ Kc1-b2 Qe3-e2+ Kb2-b1 Qe2-f1+
Kb1-b2 Qf1-e2+) 0.00/32 6} 2. Kc2 {(Kd3-c2 g5-g4 h3xg4 a3-a2 Kc2-b2 f5-f4
g3xf4 h5-h4 a5-a6 h4-h3 a6-a7 a2-a1R Kb2xa1 h3-h2 Ka1-a2 h2-h1Q a7-a8Q
Qh1-g2+ Ka2-a3 Qg2xf3+ Ka3-b4 Qf3xf4 Qa8-d8+ Kd5-e4 g4-g5 Qf4-d2+ Kb4-c5
Qd2-c3+ Kc5-b6 Qc3-b4+ Kb6xc6 Qb4-c4+ Kc6-b7 Qc4-b5+ Qd8-b6 Qb5xg5 Qb6-b1+
Ke4xd4 Qb1-b4+ Kd4-e3 Qb4-c3+ Ke3-e2) 0.00/29 9} g4 {(g5-g4 f3xg4 h5-h4
g3xh4 f5-f4 a5-a6 a3-a2 Kc2-b2 f4-f3 a6-a7 a2-a1R Kb2xa1 f3-f2 a7-a8Q
f2-f1Q+ Ka1-b2 Qf1-e2+ Kb2-c1 Qe2-f1+ Kc1-d2 Qf1-f2+ Kd2-d3 Qf2-f3+ Kd3-c2
Qf3-e2+ Kc2-b3 Qe2-c4+ Kb3-b2 Qc4-e2+) 0.00/31 5} 3. hxg4 {(h3xg4 a3-a2
Kc2-b2 f5-f4 g3xf4 h5-h4 a5-a6 h4-h3 a6-a7 a2-a1Q+ Kb2xa1 h3-h2 a7-a8Q
h2-h1Q+ Ka1-b2 Qh1-g2+ Kb2-b3 Qg2xf3+ Kb3-b4 Qf3xf4 Qa8-d8+ Kd5-e4 Kb4-c5
Qf4xg4 Kc5xc6 Qg4-e6+ Kc6-c5 Qe6-f5+ d4-d5 Qf5-f2+ Kc5-c6 Qf2-c2+ Kc6-d7
Ke4xd5 Qd8-a5+ Kd5-e4 Qa5-b5 Ke4-f3 Qb5-d5+ Kf3-f4 Qd5-f7+ Kf4-e3 Qf7-e7+
Ke3-f4) 0.00/27 10} a2 {(a3-a2 Kc2-b2 f5-f4 g3xf4 h5-h4 a5-a6 h4-h3 a6-a7
a2-a1Q+ Kb2xa1 h3-h2 a7-a8Q h2-h1Q+ Ka1-b2 Qh1-g2+ Kb2-b3 Qg2xf3+ Kb3-b4
Qf3xf4 Qa8-d8+ Kd5-e4 Kb4-c5 Qf4xg4 Kc5xc6 Qg4-e6+ Kc6-c5 Qe6-f5+ d4-d5
Qf5-f2+ Kc5-c6 Qf2-c2+ Kc6-d6 Qc2-h2+ Kd6-c5 Qh2-c2+ Kc5-b6 Qc2-b3+ Kb6-c5
Qb3-c3+ Kc5-d6 Qc3-e5+ Kd6-c6 Qe5-c3+ Kc6-d7 Qc3-h3+ Kd7-c7 Qh3-c3+ Kc7-d7)
0.00/31 6} 4. Kb2 {(Kc2-b2 f5-f4 g3xf4 h5-h4 a5-a6 h4-h3 a6-a7 a2-a1Q+
Kb2xa1 h3-h2 a7-a8Q h2-h1Q+ Ka1-b2 Qh1-g2+ Kb2-b3 Qg2xf3+ Kb3-b4 Qf3xf4
Qa8-d8+ Kd5-e4 Kb4-c5 Qf4xg4 Kc5xc6 Qg4-e6+ Kc6-c5 Qe6-f5+ d4-d5 Qf5-f2+
Kc5-c6 Qf2-c2+ Kc6-b6 Qc2-b3+ Kb6-c5 Qb3-c3+ Kc5-d6 Qc3-e5+ Kd6-c6 Qe5-c3+
Kc6-d7 Qc3-h3+ Kd7-c7 Qh3-c3+ Kc7-d7) 0.00/33 9} f4 {(f5-f4 g3xf4 h5-h4
a5-a6 h4-h3 a6-a7 a2-a1Q+ Kb2xa1 h3-h2 a7-a8Q h2-h1Q+ Ka1-b2 Qh1-g2+ Kb2-b3
Qg2xf3+ Kb3-b4 Qf3xf4 Qa8-d8+ Kd5-e4 Kb4-c5 Qf4xg4 Kc5xc6 Qg4-e6+ Kc6-c5
Qe6-f5+ d4-d5 Qf5-f2+ Kc5-c6 Qf2-c2+ Kc6-b6 Qc2-b3+ Kb6-c5 Qb3-c3+ Kc5-b5
Qc3-d3+ Kb5-c6 Qd3-c4+ Kc6-b7 Qc4-b5+ Kb7-a7 Qb5-c5+ Ka7-b7 Qc5-b5+)
0.00/33 4} 5. gxf4 {(g3xf4 h5-h4 a5-a6 h4-h3 a6-a7 a2-a1Q+ Kb2xa1 h3-h2
a7-a8Q h2-h1Q+ Ka1-b2 Qh1-g2+ Kb2-b3 Qg2xf3+ Kb3-b4 Qf3xf4 Qa8-d8+ Kd5-e4
Kb4-c5 Qf4xg4 Kc5xc6 Qg4-e6+ Kc6-c5 Qe6-f5+ d4-d5 Qf5-f2+ Kc5-c6 Qf2-c2+
Kc6-b6 Qc2-b3+ Kb6-c5 Qb3-c3+ Kc5-b5 Qc3-d3+ Kb5-b4 Qd3-d4+ Kb4-a3 Qd4-c5+
Ka3-a4 Qc5-d4+ Ka4-a3) 0.00/34 10} h4 {(h5-h4 Kb2xa2 h4-h3 a5-a6 h3-h2
a6-a7 h2-h1Q a7-a8Q Qh1-g2+ Ka2-b3 Qg2xf3+ Kb3-b4 Qf3xf4 Qa8-d8+ Kd5-e4
Kb4-c5 Qf4xg4 Kc5xc6 Qg4-e6+ Kc6-c5 Qe6-f5+ d4-d5 Qf5-f2+ Kc5-c6 Qf2-c2+
Kc6-b6 Qc2-b3+ Kb6-c5 Qb3-c3+ Kc5-b5 Qc3-d3+ Kb5-c6 Qd3-c4+ Kc6-b6 Qc4-b4+
Kb6-c6 Qb4-c4+) 0.00/31 5} 6. Kxa2 {(Kb2xa2 h4-h3 a5-a6 h3-h2 a6-a7 h2-h1Q
a7-a8Q Qh1-g2+ Ka2-b3 Qg2xf3+ Kb3-b4 Qf3xf4 Qa8-d8+ Kd5-e4 Kb4-c5 Qf4xg4
Kc5xc6 Qg4-e6+ Kc6-c5 Qe6-f5+ d4-d5 Qf5-f2+ Kc5-c6 Qf2-c2+ Kc6-b6 Qc2-b3+
Kb6-c5 Qb3-c3+ Kc5-b5 Qc3-d3+ Kb5-b4 Qd3-d4+ Kb4-a3 Qd4-c5+ Ka3-a4 Qc5-d4+
Ka4-a3) 0.00/31 6} h3 {(h4-h3 a5-a6 h3-h2 a6-a7 h2-h1Q a7-a8Q Qh1-g2+
Ka2-b3 Qg2xf3+ Kb3-b4 Qf3xf4 Qa8-d8+ Kd5-e4 Kb4-c5 Qf4xg4 Kc5xc6 Qg4-e6+
Kc6-c5 Qe6-f5+ d4-d5 Qf5-f2+ Kc5-c6 Qf2-c2+ Kc6-b6 Qc2-b3+ Kb6-c5 Qb3-c3+
Kc5-b5 Qc3-d3+ Kb5-b4 Qd3-d4+ Kb4-a3 Qd4-c3+ Ka3-a4 Qc3-d4+ Ka4-a3) 0.00/32
6} 7. a6 {(a5-a6 h3-h2 a6-a7 h2-h1Q a7-a8Q Qh1-g2+ Ka2-b3 Qg2xf3+ Kb3-b4
Qf3xf4 Qa8-d8+ Kd5-e4 Kb4-c5 Qf4xg4 Kc5xc6 Qg4-e6+ Kc6-c5 Qe6-f5+ d4-d5
Qf5-f2+ Kc5-c6 Qf2-c2+ Kc6-b6 Qc2-b3+ Kb6-c5 Qb3-c3+ Kc5-d6 Qc3-e5+ Kd6-c6
Qe5-c3+ Kc6-d7 Ke4xd5 Kd7-e8+ Kd5-e4 Qd8-h4+ Ke4-d5 Qh4-d8+) 0.00/33 10} h2
{(h3-h2 a6-a7 h2-h1Q a7-a8Q Qh1-g2+ Ka2-b3 Qg2xf3+ Kb3-b4 Qf3xf4 Qa8-d8+
Kd5-e4 Kb4-c5 Qf4xg4 Kc5xc6 Qg4-e6+ Kc6-c5 Qe6-f5+ Kc5-c4 Qf5-e6+ d4-d5
Qe6-a6+ Kc4-c5 Qa6-a3+ Kc5-c6 Qa3-a4+ Kc6-d6 Qa4-a3+ Kd6-e6 Qa3-h3+ Ke6-d6
Qh3-h2+ Kd6-c5 Qh2-c2+ Kc5-b6 Qc2-b3+ Kb6-c5 Qb3-c3+ Kc5-b5 Qc3-d3+ Kb5-b4
Qd3-d4+ Kb4-b5 Qd4-b2+ Kb5-c6 Qb2-c3+ Kc6-b5) 0.00/34 7} 8. a7 {(a6-a7
h2-h1Q a7-a8Q Qh1-g2+ Ka2-b3 Qg2xf3+ Kb3-b4 Qf3xf4 Qa8-d8+ Kd5-e4 Kb4-c5
Qf4xg4 Kc5xc6 Qg4-e6+ Kc6-c5 Qe6-f5+ Kc5-c4 Qf5-e6+ d4-d5 Qe6-a6+ Kc4-c5
Qa6-a3+ Kc5-c6 Qa3-a4+ Kc6-d6 Qa4-a3+ Kd6-e6 Qa3-h3+ Ke6-d6 Qh3-h2+ Kd6-c5
Qh2-c2+ Kc5-b6 Qc2-b3+ Kb6-c5 Qb3-c3+ Kc5-b5 Qc3-b2+ Kb5-c6 Qb2-c3+ Kc6-b5)
0.00/35 20} h1=Q {(h2-h1Q a7-a8Q Qh1-g2+ Ka2-b3 Qg2xf3+ Kb3-b4 Qf3xf4
Qa8-d8+ Kd5-e4 Kb4-c5 Qf4xg4 Kc5xc6 Qg4-e6+ Kc6-c5 Qe6-f5+ Kc5-c4 Qf5-e6+
d4-d5 Qe6-a6+ Kc4-c5 Qa6-a3+ Kc5-c6 Qa3-a4+ Kc6-d6 Qa4-a3+ Kd6-e6 Qa3-h3+
Ke6-d6 Qh3-h2+ Kd6-c5 Qh2-c2+ Kc5-b6 Qc2-b3+ Kb6-c5 Qb3-c3+ Kc5-b5 Qc3-b2+
Kb5-c6 Qb2-c3+ Kc6-b5) 0.00/35 4} 9. a8=Q {(a7-a8Q Qh1-g2+ Ka2-b3 Qg2xf3+
Kb3-b4 Qf3xf4 Qa8-d8+ Kd5-e4 Kb4-c5 Qf4xg4 Kc5xc6 Qg4-e6+ Kc6-c5 Qe6-f5+
Kc5-c4 Qf5-e6+ d4-d5 Qe6-a6+ Kc4-c5 Qa6-a3+ Kc5-c6 Qa3-a4+ Kc6-d6 Qa4-a3+
Kd6-e6 Qa3-h3+ Ke6-d6 Qh3-h2+ Kd6-c5 Qh2-c2+ Kc5-b6 Qc2-b3+ Kb6-c5 Qb3-c3+
Kc5-b5 Qc3-b2+ Kb5-c6 Qb2-c3+ Kc6-b5) 0.00/35 3} Qg2+ {(Qh1-g2+ Ka2-a1
Qg2-g1+ Ka1-b2 Qg1-f2+ Kb2-b3 Qf2xf3+ Kb3-b4 Qf3xf4 Qa8-d8+ Kd5-e4 Kb4-c5
Qf4xg4 Kc5xc6 Qg4-e6+ Kc6-c5 Qe6-f5+ Kc5-c4 Qf5-e6+ d4-d5 Qe6-a6+ Kc4-c5
Qa6-a3+ Kc5-c6 Qa3-a4+ Kc6-d6 Qa4-a3+ Kd6-e6 Qa3-h3+ Ke6-d6 Qh3-h2+ Kd6-c5
Qh2-c2+ Kc5-b6 Qc2-b3+ Kb6-c5 Qb3-c3+ Kc5-b5 Qc3-b2+ Kb5-c6 Qb2-c3+ Kc6-b5)
0.00/35 12} 10. Ka1 {(Ka2-a1 Qg2-f1+ Ka1-b2 Qf1-f2+ Kb2-b3 Qf2xf3+ Kb3-b4
Qf3xf4 Qa8-d8+ Kd5-e4 Kb4-c5 Qf4xg4 Kc5xc6 Qg4-e6+ Kc6-c5 Qe6-f5+ Kc5-c4
Qf5-e6+ d4-d5 Qe6-a6+ Kc4-c5 Qa6-a3+ Kc5-c6 Qa3-a4+ Kc6-d6 Qa4-a3+ Kd6-e6
Qa3-h3+ Ke6-d6 Qh3-h2+ Kd6-c5 Qh2-c2+ Kc5-b6 Qc2-b3+ Kb6-c5 Qb3-c3+ Kc5-b5
Qc3-b2+ Kb5-c6 Qb2-c3+ Kc6-b5) 0.00/36 8} Qf1+ {(Qg2-f1+ Ka1-a2 Qf1-e2+
Ka2-a1 Qe2-d1+ Ka1-b2 Qd1-d2+ Kb2-a1 Qd2-d1+) 0.00/37 19} 11. Ka2 {(Ka1-a2
Qf1-e2+ Ka2-a1 Qe2-d1+ Ka1-b2 Qd1-d2+ Kb2-a1 Qd2-d1+) 0.00/38 8} Qg2+
{(Qf1-g2+) 0.00/42 26} 12. Kb3 {(Ka2-b3 Qg2xf3+ Kb3-b4 Qf3xf4 Qa8-d8+
Kd5-e4 Kb4-c5 Qf4xg4 Kc5xc6 Qg4-e6+ Kc6-c5 Qe6-f5+ Kc5-c4 Qf5-e6+ d4-d5
Qe6-a6+ Kc4-c5 Qa6-a3+ Kc5-c6 Qa3-a4+ Kc6-d6 Qa4-a3+ Kd6-e6 Qa3-h3+ Ke6-d6
Qh3-h2+ Kd6-c5 Qh2-c2+ Kc5-b6 Qc2-b3+ Kb6-c5 Qb3-c3+ Kc5-b5 Qc3-b2+ Kb5-c6
Qb2-c3+ Kc6-b5) 0.00/35 26 Black forfeits on time} Qxf3+ {(Qg2xf3+ Kb3-b4
Qf3xf4 Qa8-d8+ Kd5-e4 g4-g5 Qf4-d2+ Kb4-c5 Qd2-c3+ Kc5-b6 Qc3-b4+ Kb6-a7
Qb4-a4+ Ka7-b8 Qa4-b5+ Kb8-c8 Qb5-f5+ Kc8-b7 Qf5-b5+ Kb7-c7 Qb5-a5+ Kc7-c8
Qa5-f5+) 0.00/35 123} 13. Ka2 {(Kb3-a2 Qf3xf4 Qa8-a5+ Kd5-e4 Qa5-c5 Qf4-d2+
Ka2-b3 Qd2-d3+ Kb3-a2 Qd3xd4 Qc5xc6+ Qd4-d5+ Qc6xd5+ Ke4xd5 g4-g5 Kd5-e5
Ka2-b3 Ke5-f5 g5-g6 Kf5-f6 g6-g7 Kf6xg7 Kb3-c4 Kg7-f6 Kc4-d4 Kf6-g5 Kd4-e4
Kg5-g4 Ke4-d3 Kg4-h3 Kd3-d4 Kh3-g2 Kd4-c3 Kg2-f1 Kc3-b2 Kf1-e2 Kb2-c2
Ke2-e3 Kc2-c3 Ke3-f4 Kc3-c2 Kf4-g5 Kc2-d3 Kg5-g6 Kd3-c3 Kg6-g5) 0.00/39
234} Qxf4 {(Qf3xf4 Qa8-d8+ Kd5-c4 Qd8-b6 Qf4-d2+ Ka2-a3 Qd2-c1+ Ka3-a2
Qc1-c2+ Ka2-a3 Qc2-c3+ Ka3-a2 Qc3-d2+) 0.00/42 278} 14. Qa5+ {(Qa8-a5+
Kd5-e4 Qa5-c5 Qf4-d2+ Ka2-b3 Qd2-d3+ Kb3-a2 Qd3xd4 Qc5xc6+ Qd4-d5+ Qc6xd5+
Ke4xd5 g4-g5 Kd5-e5 g5-g6 Ke5-f6 Ka2-b3 Kf6-g7 Kb3-c4 Kg7-f8 Kc4-d5 Kf8-g7
Kd5-c5 Kg7-f6 Kc5-d5 Kf6-g7) 0.00/41 247} Kxd4 {(Kd5xd4 Qa5-b4+ Kd4-e5
Qb4-c5+ Ke5-f6 g4-g5+ Kf6-g6 Qc5xc6+ Kg6-f7 Ka2-b1 Qf4xg5 Qc6-c4+ Kf7-f6
Qc4-a6+ Kf6-g7 Qa6-b7+ Kg7-f6 Qb7-a6+) 0.00/43 354} 15. Kb2 {(Ka2-b2 Qf4-e3
Qa5-a4+ Kd4-d5 Kb2-c2 Kd5-d6 Qa4-b4+ Kd6-d5 g4-g5 Qe3-e2+ Kc2-c3 Qe2-d1
Qb4-f4 Qd1-e1+ Kc3-d3 Qe1-d1+ Kd3-c3) 0.00/36 67} Ke4 {(Kd4-e4 Qa5-a4+
Ke4-e3 Qa4xc6 Qf4-d4+ Kb2-b3 Qd4-d1+ Kb3-a3 Qd1-d3+ Ka3-a4 Qd3-d4+ Ka4-b5
Ke3-f4 Kb5-a5 Qd4-e5+ Ka5-b4 Qe5-e4+ Qc6xe4+ Kf4xe4 Kb4-b5 Ke4-f4 Kb5-c5
Kf4xg4 Kc5-d4 Kg4-g5 Kd4-c4 Kg5-h4 Kc4-c3 Kh4-g5 Kc3-c4) 0.00/35 52} 16.
Qc3 {(Qa5-c3 Ke4-d5 Qc3-a5+ Kd5-e6 g4-g5 Qf4-d4+ Kb2-b3 c6-c5 Qa5-c3 Qd4-e4
Qc3xc5 Qe4-e5 Qc5-b6+ Ke6-f7 Qb6-f2+ Kf7-g6 Qf2-f3 Qe5-e6+ Kb3-b4 Kg6xg5
Kb4-c3 Kg5-g6 Qf3-g3+ Kg6-f7 Qg3-f4+ Kf7-g6 Kc3-d2 Qe6-d5+ Kd2-c3 Qd5-c5+
Kc3-b2 Qc5-d5 Qf4-g3+ Kg6-f7 Qg3-f4+ Kf7-g6) 0.00/36 43} Kd5 {(Ke4-d5
Qc3-d3+ Qf4-d4+ Kb2-c2 Qd4xd3+ Kc2xd3 Kd5-e5 g4-g5 Ke5-f5 g5-g6 Kf5xg6
Kd3-d4 Kg6-f5 Kd4-c5 Kf5-e4 Kc5-c4 c6-c5 Kc4-c3 Ke4-d5 Kc3-d3 c5-c4+ Kd3-c3
Kd5-c5 Kc3-c2 Kc5-d4 Kc2-d2 c4-c3+ Kd2-c2 Kd4-e5 Kc2-d1 Ke5-f6 Kd1-c2
Kf6-g6 Kc2-d1 c3-c2+ Kd1-c1 Kg6-f6 Kc1xc2 Kf6-g7 Kc2-c3 Kg7-g6 Kc3-c4
Kg6-g5 Kc4-c3 Kg5-h4 Kc3-d4 Kh4-g5 Kd4-c3) 0.00/46 64} 17. Qd3+ {(Qc3-d3+
Qf4-d4+ Kb2-c2 Qd4xd3+ Kc2xd3 Kd5-e5 g4-g5 Ke5-f5 g5-g6 Kf5xg6 Kd3-d4
Kg6-f5 Kd4-c5 Kf5-e4 Kc5-c4 c6-c5 Kc4-c3 Ke4-d5 Kc3-d3 c5-c4+ Kd3-c3 Kd5-c5
Kc3-c2 Kc5-d4 Kc2-d2 c4-c3+ Kd2-c1 Kd4-d3 Kc1-d1 c3-c2+ Kd1-c1 Kd3-e3
Kc1xc2 Ke3-e4 Kc2-c3 Ke4-e3 Kc3-c2) 0.00/48 56} Qd4+ {(Qf4-d4+ Kb2-c2
Qd4xd3+ Kc2xd3 Kd5-e5 g4-g5 Ke5-f5 g5-g6 Kf5xg6 Kd3-d4 Kg6-f5 Kd4-c5 Kf5-e4
Kc5-c4 c6-c5 Kc4-c3 Ke4-d5 Kc3-d3 c5-c4+ Kd3-c2 Kd5-d4 Kc2-d2 c4-c3+ Kd2-c2
Kd4-e4 Kc2xc3 Ke4-e3 Kc3-c2 Ke3-f4 Kc2-d2 Kf4-f3 Kd2-d3 Kf3-f2 Kd3-d2
Kf2-f3) 0.00/51 72} 18. Kc2 {(Kb2-c2 Qd4xd3+ Kc2xd3 Kd5-e5 g4-g5 Ke5-f5
g5-g6 Kf5xg6 Kd3-d4 Kg6-f5 Kd4-c5 Kf5-e4 Kc5-c4 c6-c5 Kc4-c3 Ke4-d5 Kc3-d3
c5-c4+ Kd3-c2 Kd5-d4 Kc2-d2 c4-c3+ Kd2-c2 Kd4-e4 Kc2xc3 Ke4-e3 Kc3-c2
Ke3-e4 Kc2-c3) 0.00/55 55} Qxd3+ {(Qd4xd3+ Kc2xd3 Kd5-e5 g4-g5 Ke5-f5 g5-g6
Kf5xg6 Kd3-d4 Kg6-f5 Kd4-c5 Kf5-e4 Kc5-c4 c6-c5 Kc4-c3 Ke4-d5 Kc3-d3 c5-c4+
Kd3-c3 Kd5-c5 Kc3-b2 Kc5-d4 Kb2-c2 c4-c3 Kc2-c1 Kd4-d3 Kc1-d1 c3-c2+ Kd1-c1
Kd3-e3 Kc1xc2 Ke3-e2 Kc2-c1 Ke2-f2 Kc1-d2 Kf2-g3 Kd2-c3 Kg3-h2 Kc3-d2
Kh2-g3) 0.00/57 47} 19. Kxd3 {(Kc2xd3 Kd5-e5 g4-g5 Ke5-f5 g5-g6 Kf5xg6
Kd3-d4 Kg6-f5 Kd4-c5 Kf5-e4 Kc5-c4 c6-c5 Kc4-c3 Ke4-d5 Kc3-d3 c5-c4+ Kd3-c3
Kd5-c5 Kc3-b2 Kc5-d4 Kb2-c2 c4-c3 Kc2-c1 Kd4-d3 Kc1-d1 c3-c2+ Kd1-c1
Kd3-c3) 0.00/56 54} Ke5 {(Kd5-e5 g4-g5 Ke5-f5 g5-g6 Kf5xg6 Kd3-d4 Kg6-f5
Kd4-c5 Kf5-e4 Kc5-c4 c6-c5 Kc4-c3 Ke4-d5 Kc3-d3 c5-c4+ Kd3-c3 Kd5-c5 Kc3-b2
Kc5-d4 Kb2-c2 c4-c3 Kc2-c1 Kd4-d3 Kc1-d1 c3-c2+ Kd1-c1 Kd3-c3) 0.00/56 52}
20. g5 {(g4-g5 Ke5-f5 g5-g6 Kf5xg6 Kd3-d4 Kg6-f5 Kd4-c5 Kf5-e4 Kc5-c4 c6-c5
Kc4-c3 Ke4-d5 Kc3-d3 c5-c4+ Kd3-c3 Kd5-c5 Kc3-b2 Kc5-d4 Kb2-c2 c4-c3 Kc2-c1
Kd4-d3 Kc1-d1 c3-c2+ Kd1-c1 Kd3-c3) 0.00/55 56} Kf5 {(Ke5-f5 g5-g6 Kf5xg6
Kd3-d4 Kg6-f5 Kd4-c5 Kf5-e4 Kc5-c4 c6-c5 Kc4-c3 Ke4-d5 Kc3-d3 c5-c4+ Kd3-c3
Kd5-c5 Kc3-b2 Kc5-d4 Kb2-c2 c4-c3 Kc2-c1 Kd4-d3 Kc1-d1 c3-c2+ Kd1-c1
Kd3-c3) 0.00/53 48} 21. g6 {(g5-g6 Kf5xg6 Kd3-d4 Kg6-f5 Kd4-c5 Kf5-e4
Kc5-c4 c6-c5 Kc4-c3 Ke4-d5 Kc3-d3 c5-c4+ Kd3-c3 Kd5-c5 Kc3-b2 Kc5-d4 Kb2-c2
c4-c3 Kc2-c1 Kd4-d3 Kc1-d1 c3-c2+ Kd1-c1 Kd3-c3) 0.00/54 70} Kxg6 {(Kf5xg6
Kd3-c2 Kg6-f6 Kc2-d3 Kf6-e5 Kd3-e3 c6-c5 Ke3-d3 Ke5-d5 Kd3-c3 Kd5-e4 Kc3-c4
Ke4-e3 Kc4xc5 Ke3-f2 Kc5-c4 Kf2-g1 Kc4-c3 Kg1-f2 Kc3-c4) 0.00/50 49} 22.
Kc2 {(Kd3-c2 c6-c5 Kc2-d3 Kg6-f5 Kd3-c4 Kf5-e4 Kc4-c3 Ke4-d5 Kc3-d3 c5-c4+
Kd3-c3 Kd5-c5 Kc3-b2 Kc5-d4 Kb2-c2 c4-c3 Kc2-c1 Kd4-d3 Kc1-d1 c3-c2+ Kd1-c1
Kd3-c3) 0.00/82 54} c5 {(c6-c5 Kc2-b1 Kg6-f5 Kb1-c2 Kf5-e4 Kc2-c3 Ke4-d5
Kc3-d3 c5-c4+ Kd3-c3 Kd5-c5 Kc3-b2 Kc5-d4 Kb2-c2 c4-c3 Kc2-c1 Kd4-d3 Kc1-d1
c3-c2+ Kd1-c1 Kd3-c3) 0.00/108 48} 23. Kb1 {(Kc2-b1 c5-c4 Kb1-c2 Kg6-f7
Kc2-c3 Kf7-e6 Kc3-b2 Ke6-e5 Kb2-c3 Ke5-d5 Kc3-b2 Kd5-d4 Kb2-c2 c4-c3 Kc2-c1
Kd4-d3 Kc1-d1 c3-c2+ Kd1-c1 Kd3-c3) 0.00/125 59} c4 {(c5-c4 Kb1-c2 Kg6-f7
Kc2-c3 Kf7-e6 Kc3-b2 Ke6-e5 Kb2-c3 Ke5-d5 Kc3-b2 Kd5-d4 Kb2-c2 c4-c3 Kc2-c1
Kd4-d3 Kc1-d1 c3-c2+ Kd1-c1 Kd3-c3) 0.00/127 7} 24. Kb2 {(Kb1-b2 Kg6-f7
Kb2-c3 Kf7-e6 Kc3-b2 Ke6-e5 Kb2-c3 Ke5-d5 Kc3-b2 Kd5-d4 Kb2-c2 c4-c3 Kc2-c1
Kd4-d3 Kc1-d1 c3-c2+ Kd1-c1 Kd3-c3) 0.00/127 26} Kh5 {(Kg6-h5 Kb2-c3 Kh5-g5
Kc3-c2 c4-c3 Kc2-b1 Kg5-g6 Kb1-c2 Kg6-g7 Kc2xc3 Kg7-g6 Kc3-b2 Kg6-g7
Kb2-c3) 0.00/127 3} 25. Ka1 {(Kb2-a1 c4-c3 Ka1-b1 Kh5-g6 Kb1-c2 Kg6-g7
Kc2xc3 Kg7-g6 Kc3-b2 Kg6-g7 Kb2-c3) 0.00/127 6} c3 {(c4-c3 Ka1-b1 Kh5-g6
Kb1-c2 Kg6-g7 Kc2xc3 Kg7-g6 Kc3-c4 Kg6-g5 Kc4-d3 Kg5-f6 Kd3-c4 Kf6-g5)
0.00/127} 26. Kb1 {(Ka1-b1 c3-c2+ Kb1xc2 Kh5-g6 Kc2-b3 Kg6-f6 Kb3-c4 Kf6-e6
Kc4-c5 Ke6-f6 Kc5-b6 Kf6-g7 Kb6-c5 Kg7-f6) 0.00/127} c2+ {(c3-c2+ Kb1xc2
Kh5-g6 Kc2-b3 Kg6-f6 Kb3-c4 Kf6-e6 Kc4-c5 Ke6-f6 Kc5-b6 Kf6-g7 Kb6-c5
Kg7-f6) 0.00/127} 27. Kxc2 {(Kb1xc2 Kh5-g6 Kc2-b3 Kg6-f6 Kb3-c4 Kf6-e6
Kc4-c5 Ke6-f6 Kc5-c4) 0.00/127 1 Insufficient material} *


QUESTION: Does white really have a win in this pawn ending, as claimed by Tim Krabbé?

ANSWER: With respect to Tim Krabbé, if the strongest chess engines in the world cannot find a winning line for White, it's reasonable to infer there isn't one.

  • Feel free to find it. – user34445 Feb 26 at 22:04
  • I'm not implying anything about your claim about this particular pawn ending. I commented only about your final statement that relies on "the strongest chess engines in the world", which is not a very good argument as can be seen from the examples in the linked post. That's all. =) – user21820 Feb 27 at 7:46
  • It's true that there may be blind-spots in 'a chess engine'. There are far bigger blindspots in human chess thinking. So while your comment may be factually correct, it is not helpful. – user34445 Feb 27 at 16:46

protected by Community Dec 7 '15 at 18:35

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