Deep analyses of pawn endgames

[Dap Hartmann]

Recently, I have started looking into rather complicated pawn
endgames. One series of references that I use a lot, is Awerbach's
books on the subject. Some of the example he provides are very subtle,
and many chess programs will hhave great difficulty finding the right
solution. But that's a bit of a concern to me: is Awerbach right all
the time?

Let me give an example:

8/7k/6p1/5p2/6pP/3K2P1/4P3/8 w

According to Awerbach, White is winning with 1.e3!
(He gives the following line:
1.e3! Kh6 2.Kd4 Kh5 3.Kd5 Kh6! 4.Ke6 Kh5! 5.Ke7!)

Now then, is this right? Is there any program who finds that move and
the forced win?

There are many more such examples. I'm not saying that Awerbach is
wron, and that White doesn't have the win, but is 1.e3 really the only
winning move? What about 1.Kd4?

dap

[Valavan Manohararajah]

I don't know whether Kd4 is a winner, but Rajah (my program) running on a P133 seems to like 1. e3....

 

After 18 ply and 1.5 mins of thinking, PV is as follows:

 

+00.05  e3 Kh6 Kd4 Kh5 Kd5 Kh6 Ke6 Kh5 Ke5 g5 hxg5 Kxg5 Ke6 Kg6 Kd7 Kg7 Ke7 Kh7 Ke6

 

....Note that the score is a measly 0.05 - So it hasn't seen any significant event along that PV.

[brucemo]

Dap Hartmann wrote:

> 8/7k/6p1/5p2/6pP/3K2P1/4P3/8 w
>
> According to Awerbach, White is winning with 1.e3!
> (He gives the following line:
> 1.e3! Kh6 2.Kd4 Kh5 3.Kd5 Kh6! 4.Ke6 Kh5! 5.Ke7!)
>
> Now then, is this right? Is there any program who finds that move and
> the forced win?
>
> There are many more such examples. I'm not saying that Awerbach is
> wron, and that White doesn't have the win, but is 1.e3 really the only
> winning move? What about 1.Kd4?

I let my program work on this, and although it would play 1. e3 after two
seconds, it seems to have come to some sort of understanding of the position only
after about fifteen minutes, in ply 25, at which point it understands that black
has to give up some material.

This may be one of those positions where a program will win without really
understanding what it is doing, because it sees that all alternatives result in
either a draw or less perceived positional advantage.

bruce

a b c d e f g h
+---+---+---+---+---+---+---+---+
8 | |///| |///| |///| |///| 8
+---+---+---+---+---+---+---+---+
7 |///| |///| |///| |///| k | 7
+---+---+---+---+---+---+---+---+
6 | |///| |///| |///| p |///| 6
+---+---+---+---+---+---+---+---+
5 |///| |///| |///| p |///| | 5
+---+---+---+---+---+---+---+---+
4 | |///| |///| |///| p |/P/| 4
+---+---+---+---+---+---+---+---+
3 |///| |///| K |///| |/P/| | 3
+---+---+---+---+---+---+---+---+
2 | |///| |///| P |///| |///| 2
+---+---+---+---+---+---+---+---+
1 |///| |///| |///| |///| | 1
+---+---+---+---+---+---+---+---+
a b c d e f g h

PV 00:00:02.153 12 13 [right] e3 Kh6 Kd4 Kg7 Ke5 Kh6 Kf6 Kh7 h5 gxh5 Kxf5
Kh6
PV 00:00:02.824 13 174 [right] e3 Kh6 Kd4 Kg7 Ke5 Kh6 Kf6 Kh7 Kf7 Kh6 Kg8
g5 hxg5+ Kg6
PV 00:00:03.696 14 59 [right] e3 Kh6 Kd4 Kg7 Ke5 Kh6 Ke6 Kg7 Kd5 Kh7 e4
fxe4
PV 00:00:05.238 15 58 [right] e3 Kh6 Kd4 Kg7 Ke5 Kh6 Ke6 Kg7 Kd5 Kh7 e4
fxe4 Kxe4 Kh6 Ke3 g5
PV 00:00:07.141 16 58 [right] e3 Kh6 Kd4 Kg7 Ke5 Kh6 Kf6 Kh7 Kg5 Kg7 h5
gxh5 Kxf5 Kh6 e4 Kg7
PV 00:00:11.567 17 20 [right] e3 Kh6 Kd4 g5 hxg5+ Kxg5 Ke5 Kg6 Ke6 Kg5 Kf7
f4 exf4+ Kf5 Ke7 Ke4 Ke6 Kf3 f5 Kxg3
PV 00:00:19.188 18 53 [right] e3 Kh6 Kd4 g5 hxg5+ Kxg5 Ke5 Kg6 Ke6 Kg5 Kf7
f4 exf4+ Kf5 Ke7 Ke4 Ke6 Kf3 f5 Kxg3 f6
PV 00:00:28.051 19 53 [right] e3 Kh6 Kd4 Kg7 Ke5 Kh6 Kf6 Kh5 Ke6 Kh6 Kd5
Kg7 Kd4 Kh6 Ke5 Kg7 e4 fxe4 Kxe4 Kf7
PV 00:00:43.863 20 41 [right] e3 Kh6 Kd4 Kg7 Ke5 Kh6 Kd5 Kg7 Ke6 Kh7 Kf7
Kh6 Kg8 Kh5 Kh7 f4 exf4 g5 f5 gxh4
PV 00:01:16.030 21 42 [right] e3 Kh6 Kd4 Kg7 Ke5 Kh6 Kd5 Kg7 Ke6 Kh7 Kd7
Kh6 Kd6 Kh5 Kd5
PV 00:01:56.598 22 41 [right] e3 Kh6 Kd4 Kg7 Ke5 Kh6 Kd5 Kg7 Ke6 Kh7 Kd7
Kh6 Kd6 Kh5 Kd5 Kh6 Kc4 Kg7 Kd4 Kh6 e4 Kh5
PV 00:03:26.698 23 35 [right] e3 Kh6 Kd4 Kg7 Ke5 Kh6 Kd5 Kg7 Ke6 Kh7 Kd7
Kh6 Kd6 Kh5 Kd5 Kh6 Kc4 Kg7 Kd4 Kf7 e4 Kf6
exf5
PV 00:07:55.644 24 37 [right] e3 Kh6 Kd4 Kg7 Ke5 Kh6 Kd5 Kg7 Ke6 Kh7 Kd7
Kh6 Kd6 Kh5 Ke6 Kh6 Kf6 Kh5 Kg7 f4 exf4 g5
Kf7 gxh4
PV 00:14:48.929 25 235 [right] e3 Kh6 Kd4 Kg7 Ke5 Kh6 Ke6 Kh5 Ke7 Kh6 Kf8
Kh5 Kg8 Kh6 Kh8 Kh5 Kh7
PV 00:20:33.654 26 197 [right] e3 Kh6 Kd4 Kg7 Ke5 Kh6 Ke6 Kh5 Ke7 Kh6 Kf6
Kh5 Ke6 Kh6 Kd5 g5 hxg5+ Kxg5 Ke5 Kg6 Ke6
Kg5 Kf7 Kh5 Kf6 Kh6 Kxf5 Kh5
PV 00:30:59.264 27 241 [right] e3 Kh6 Kd4 Kg7 Ke5 Kh6 Ke6 Kh5 Ke7 Kh6 Kf8
Kh5 Kg8 Kh6 Kh8 g5 hxg5+ Kg6 Kg8 Kh5 Kf8 Kg6
Ke8 Kxg5 Ke7 Kg6 Ke6
PV 00:51:55.490 28 241 [right] e3 Kh6 Kd4 Kg7 Ke5 Kh6 Ke6 Kh5 Ke7 Kh6 Kf8
Kh7 Kf7 Kh6 Kf6 Kh5 Ke6 Kh6 Kd5 g5 hxg5+ Kg7
Ke5 Kg6 Ke6

[Howard Exner]

brucemo <bru...@nwlink.com> wrote in article
<330029...@nwlink.com>...

> Dap Hartmann wrote:
>
> > 8/7k/6p1/5p2/6pP/3K2P1/4P3/8 w
> >
> > According to Awerbach, White is winning with 1.e3!
> > (He gives the following line:
> > 1.e3! Kh6 2.Kd4 Kh5 3.Kd5 Kh6! 4.Ke6 Kh5! 5.Ke7!)
> >
> > Now then, is this right? Is there any program who finds that move
and
> > the forced win?
> >
> > There are many more such examples. I'm not saying that Awerbach
is
> > wron, and that White doesn't have the win, but is 1.e3 really the
only
> > winning move? What about 1.Kd4?

Black then draws with ...f4! so the point of e3! is to prevent f4.
How do the different programs do in finding f4! (once Kd4 is played)?

...SNIPPED...

[Dr A. N. Walker]

Dap Hartmann wrote:
>
> Recently, I have started looking into rather complicated pawn
> endgames. One series of references that I use a lot, is Awerbach's
> books on the subject.

I believe the pawn-ending book was largely the work of
Maizelis, Averbakh acting primarily as editor to the series.

> Let me give an example:

> 8/7k/6p1/5p2/6pP/3K2P1/4P3/8 w
> According to Awerbach, White is winning with 1.e3!
> (He gives the following line:
> 1.e3! Kh6 2.Kd4 Kh5 3.Kd5 Kh6! 4.Ke6 Kh5! 5.Ke7!)

Note that White wins after 1 e3 Kg7 2 Kd4 Kf6 3 Kd5 Kf7 4 Ke5
Ke7 5 e4 [h5? gxh 6 Kxf5 h4 7 Kxg4 hxg ==] fxe 6 Kxe4 Kf6 7 Kf4 Kg7
8 Kxg4 Kh6 9 Kf3 Kh5 [g5? 10 Kg4!, or ... Kg7 10 Kf4 Kf6 11 Kg4] 10
Kf4 Kh6 11 Kg4 Kh7 12 Kg5 Kg7 13 h5. If on the other hand Black stays
near h5, then the above manoeuvre gets the WK through to g8 [5 ... Kh6
6 Kf8 Kh7 7 Kf7 Kh6 8 Kg8], but then what? 8 ... Kh5 9 Kh7 f4! 10 exf
g5! 11 f5 gxh ==. Umm! [I haven't checked A&M, so I hope this is
all correct analysis!]

> Now then, is this right? Is there any program who finds that move and
> the forced win?

Well, I'm morally sure that my K&P program described in ACC5
could solve this ending, but the PDP11 that that program ran on fell
by the wayside many moons ago, and I haven't resurrected it. I'd be
interested to know what the big boys make of this ending -- the win
in the first line above is 29 ply deep just to get to the tablebase
K&P v K ending, and there may be delaying tactics, but the branching
factor in these endings is pretty small so it should be doable.

> There are many more such examples. I'm not saying that Awerbach is
> wron, and that White doesn't have the win, but is 1.e3 really the only
> winning move? What about 1.Kd4?

As far as I can judge, 1 Kd4 is equivalent; but you have to
play e3 reasonably soon, or you can't advance the WK [... f4!], and
perhaps you might as well play the forced moves first. There is one
extra trick if you delay e3, viz that in the sideline above, 5 h5 is
no longer a mistake, as the WK on g3 wins the K&P v K ending with a
pawn on e2, but only draws with the pawn on e3. Tricky little beasts
these endings! I think you should take any complicated ending that is
not confirmed by computer analysis [through to a clear win, not just
the win of a pawn or two] with several pinches of salt.

--
Andy Walker, Maths Dept., Nott'm Univ., UK.
a...@maths.nott.ac.uk