White to move. Can White win this?
Chess Daily News from Susan Polgar
King and Pawn endgame
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White to move. Can White win this?
Seems that white can win easily.
I thought that 1. Kb4 is winning. But my analysis showed me that it is impossible for white to win.
1. ka6 leads to a draw and so is 1. kc5.
1. kb4 and black has few options: 1.. a6, 1.. kc6 and 1..Kb7.
1. Kb4 a6 2. Kc5 takes the oppozition and wins
1. kb4 Kc6 2. c5
Now black has 3 reasonable options: 2..Kb7, 2.. Kc7, and 2..a6
After 1. Kb4 Kc6 2. c5 kb7 3. Kb5 a6! and draw
Conclusion: White cannot win. Draw.
Interesting. I hope that someone will be able to show me that it is possible to win here.
Leonid
queentoc2@yahoo.com
This comment has been removed by the author.
Move the position over one file to the right, and White can win. But because those two pawns are all the way over on the edge of the board, White can be trapped in the corner and stalemated. Rook pawns are always a special case…
The only win is to keep the c pawn back, then take the white king all the round and over the top of the black king.
1.Kc5! (all other moves draw)
1 … Kd7
Note that white’s opposition is not enough: the usual win by “outflanking ” with 1.Kb6 is taken away by black’s a7 pawn. So white must “outflank the other side”:
2.Kd5 Kc7
3.Ke6 Kc6
4.a6!
This tempo-wasting move gives white the opposition. Now we should consider all three of black’s attempts at defending.
(a) 4…Kb6 5.Kd6 Kxa6 6.c5 and runs to c8.
(b) 4…Kc5 5.Kc7 Kxc4 6.Kc6 and goes and grabs a7.
(c) 4…Kc7
5.Ke7 (take opposition)
5….Kc6
6.Kd8 (round the top)
6….Kb6
7.Kd7 Kc5 (taking a6 lets c-pawn run)
8.Kc7 Kxc4
9.Kb7 and wins a7 (without getting blocked by black King).
This is an *amazingly* subtle puzzle! One of the best I’ve ever seen. Where on earth did you find it?!
Great Puzzle Susan. Dynamite. I really liked this one. Took a lot of time and work. Great themes. Tricky moves.
I will give one clue.
Kc5 wins!
Good Luck guys dont give up. This is the one to learn something.
Oops someone spilled some of the beans. haha.
But my answer was a little different.
6. Kd6
7. Kc8 Kc6
8. Kb8 Kb6
9. c5+ wins
But I do not like to list the answer so early in a puzzle life. But basically the entire puzzle was laid out so I added this nice finesse to complete the puzzle and bust a little ego. haha.
Hopefully next time people will keep their ego in check.
dead draw
It’s a win for white, but it is not obvious:
1. keep the c-pawn back;
2. feint toward the queenside;
3. let black take the c-pawn while you scoot back toward the a-file;
4. burn a reserve tempo with the a-pawn;
5. shoulder the black king out by zigzagging to capture on a7 and avoid being locked onto the a-file;
6. promote.
This is a great “simple” endgame puzzles.
To anonymous 1:42:00 AM:
6.Kd6 is illegal after 5…Kc6. Hence “round the top” with 6.Kd8.
As for “ego in check”, maybe a short one-line comment like “Seems that white can win easily” is somewhat egotistical, but most of the comments here seem to be detailed analysis, people laying out their thoughts for discussion/criticism. Nice and detailed.
Remember that people who wish to solve the puzzle can do so BEFORE they look at these comments!
Let me clarify. To me obviously.
6. Kd6
7. Kc8 Kc6
8. Kb8 Kb6
9. c5+ wins
begins with a black move here.
6. Kd6
7. Kc8 Kc6
8. Kb8 Kb6
9. c5+ wins
this comes in place of
6. Kd8 Kb6
Kb6 is not the strongest reply.
Kd6 is stronger since this requires 9. c5+ to win.
OH , I see what happens the computer removes the blank spaces. Here again.
6. ….Kd6
7. Kc8 Kc6
8. Kb8 Kb6
9. c5+ wins
now the blank spaces are filled. I thought I had the Kd6 in the black column the first time. and sure had it a second ago. so the computer squeezes out the spaces.
To Anonymous @ 1:17.
1.Kc5! (all other moves do draw)
1 … Kd7
2.Kd5 Kc7
3.Ke6 Kc6?
4.a6!
but…
3. Ke6 a6!
White has three (reasonable) choices:
Choice #1:
4. Ke7? Kc6
5. Kd8 Kc5
6. Kc7 Kxc4
7. Kb6 Kd5
8. Kxa6 Kc6
black has the opposition and draws.
Choice #2:
4. c5?? Kc6 and wins both c and a pawns… white must run for b2 to draw…
Choice #3:
4. Kd5 Kd7
5. Kc5 runs into Kc7 so instead…
5. c5 Kc7
if 6. c6 not Kc7? but..
6….Kc8!
7. Kc5 Kc7 (and position will repeat)
7. Kd6 Kd8
if 8. Kc5 Kc7 (and position will repeat)
so 8. c7 Kc8 draw
if 5. c5 Kc7 and instead of 6. c6
6. K moves, then Kc6 and either the (6.c6) position will occur leading to draw, or black K will take c-pawn.
While black has to be extremely careful, I believe black draws.
I’m not sure that 1 Kc5 wins.
What about 1… a6! Black keeps the opposition and white cannot make any progress.
Imagine this
1. Kc5 a6!
2. Kd5 Kd7
3. c6+ Kc7!
4. Kc5 Kc8
5. Kd6 Kd8
6. c7+ Kc8
Then on 7. Kc6, stalemate
or
7. Kc5 Kxc7 and white can make no progress.
I think draw. This is all without aid of computer or board.
I’d love to be proven wrong!
Brad Hoehne
My above post also applies to:
anonymous @ 1:25, 1:42
Dan Dalthorp
anonymous @ 8:37, 8:54
and anyone else that thinks white can win.
I see only a draw. Am I missing a better 4th move for white after 3….a6!
I think the a6! tempo wasting move is always avaible to black to save before white. In several lines, if black fails to move a6! at the critical moment, then white can win with a6! or (in one neat line, by forcing a6 so as to prevent a stalemate of the black king, then white K to b6 and black king has an available move to d7).
I believe best play for black draws in any line, no matter where the white king “feints”.
I believe Brad is right, no need to wait for 3….a6!, 1….a6! is simpler.
1. Kc5 a6!
2. Kd5 Kd7
of course, 3.c6+ is impossible, so
3. c5 Kc7
4. c6 Kc8
and then if
5. Kc5 Kc7
and white can make no progress
or, as Brad says:
5. Kd6 Kd8
6. c7+ Kc8
with stalemate to follow…
I have used a board to confirm my analysis, but no computer.
Hat tip to Brad, I like you solution better than mine.
Kerry
Thanks for the compliment, Kerry. And thanks for pointing out that I had I left two moves out of my analysis. I don’t think it changes the final verdict though.
Once again, I’d be thrilled if someone could demonstrate a win for white here.
Brad Hoehne
Of course White is winning! (The lines after 3… Kc6 have been described in detail by some anonymus bloggers) After 3…a6 he can apply a method, known as triangulation:
1.Kc5! Kd7
2.Kd5 Kc7
3.Ke6 a6
4.Kd5 Kd7
5.c5 Kc7
6.c6 Kc8
7.Kc4! start of triangulation!
7… Kd8
8.Kd4! Kc8
9.Kd5 Kc7
10.Kc5 end of triangulation!
10…Kc8 11.Kb6
Kb8 12.Kxa6+-
BTW 1… a6 is just the same thing: after 1…a6 2.Kd5 Kd7 3.c5 Kc7 4.c6 Kc8 5.Kc4! start of triangulation 5… Kb8 6.Kd4 Kc8 7.Kd5 Kc7 (7…Kd8 8.Kd6 Kc8 9.c7+-) 8.Kc5 end of triangulation white wins.
🙂 greetings
In Kerry’s ‘drawing line’ “if 6. c6 not Kc7? but..
6….Kc8!
7. Kc5 Kc7 (and position will repeat)”
white wins by triangulating:
6..kc8 7 Kd4! kd8 8 Kc4! Kc8 9 kd5 and wins
1 Kc5 wins in all lines
Now that I’ve sat down at a board I understand how white wins. The “triangulation” theme is what I was missing. It, as I used to say, “puts the ‘b’ in subtle.”
Brad Hoehne
I realized my failure to follow through the analysis after 5. Kc5 Kc7 late Friday, but had no internet access to correct it until today. As Vohaul and others noted, that position is won for white due to the triangulation technique.
Thanks to Vohaul and anonymous for pointing out the path to victory.
Hi, I’m just a beginner, but
when vohaul mentioned
6. c6 Kc8
7. Kc4! Kd8
Why would black play Kd8 when he
could play Kc7?
All this talk of
#. … a6
as good for black seems strange to
me because it would seem that the
b6 square needs to be defended
against the white king.
My thought is that if the white
king gets in there, he has two
queening threats.
A scenario I imagine with … a6
in it:
1. Kc5 a6
2. Kd5 Kd7
3. Ke5 Kc6
4. Kd4 Kd6
5. c5+ Kc6
6. Kc4 Kc7
7. Kd5 Kd7
8. c6+ Kc7
9. Kc5 Kc8
10.Kb6 Kb8
11.Kxa6 Kc7
12.Kb5 Kb8
13.a6 Ka7
14.c7 Ka8
15.c8Q+ Ka7
16.Qb7#
or:
11.Kxa6 Ka8
12.Kb6 Kb8
13.a6 Ka8
14.Kc7
and the c pawn will queen.
Thoughts?
Anton
Anton,
Defending the b6 square is precisely why Vohaul has:
5.c5 Kc7
6.c6 Kc8
7.Kc4! Kd8
If instead:
5. c5 Kc7
6. c6 Kc8
7. Kc4! Kc7
then:
8. Kc5 and the b6 square you rightly mention is unprotected.
8. Kc5 Kc8 (or Kb8,Kd8; black king necessarily goes to the 8th rank) and white continues:
9. Kb6 and follows Vohaul’s and your line beginning with 10. Kxa6 (or, if 9….Kc8, then 10. c7 Kd7 11. Kb7 queens and wins).
Thus, for example:
5. c5 Kc7
6. c6 Kc8
7. Kc4! Kc7
8. Kc5 Kc8
9. Kb6 Kb8
10. Kxa6 Kc7
11. Kb5 Kc8
12. Kb6 Kb8
13. c7+ Kc8
14. a6 Kd7
15. Kb7 queening the c-pawn followed by mate or a second queen depending on taste.
The point being, after moving a6, the only attempt to keep the white king out of a6 is to never move Kc7 unless the white king first moves to Kc5. Due to triangulation, black cannot achieve both the Kc5-Kc7 maneuver and the also necessary Kd6-Kd8 maneuver (which itself also requires a Kd5-Kc8, leaving Kc7 in case of white-Kc5).
Black’s best shot is still a6, at least from a length of lines point of view. If white can determine the necessary Kc4! (or Kd4!), then the end is inevitable, though slightly delayed.
Anton,
In your line, black’s best is to require white to find the triangulation method as well.
Thus, not:
8. c6+ Kc7
9. Kc5 Kc8
10.Kb6 Kb8
But:
8. c6+ Kc8
9. Kc4!
Because:
9. Kd6 Kd8
10. Kc5 Kc7
11. Kd5 Kc8 and white is back at the position after move 8.
Or:
9. Kd6 Kd8
10. Kd5 Kc8 and white starts over.
So Vohaul’s Kc4! (or Kd4!) is necessary if black remembers to always hold Kc7 in reserve for white’s Kc5.
If that clears up anything.
Kerry,
Thanks–I think I had failed to
advance black’s a-pawn when looking
at it. But that brings me back to
why should black ever advance the
a-pawn?
vohaul has:
1. Kc5 Kd7
2. Kd5 Kc7
3. Ke6 a6
Why not:
3. Kc6 Kc6
(I realize that if the black king
goes after a pawn, he will lose–
so he shouldn’t go after one.)
And continuing maybe:
4. a6 Kc6
…
With this is there still some way
for white to win? The idea being
somehow make black only have two
squares to use so he can’t
triangulate?
Anton