A theoretical pawn endgame

Technical questions regarding Openings, Middlegames, Endings etc.
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Francis Fields
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A theoretical pawn endgame

Post by Francis Fields » Thu Feb 19, 2015 11:25 am

If you have the position of King and 3 pawns v King and 3 pawns (f, g & h) all on their starting square then white has a forced win with 1. f4 . Would anyone disagree?

Roger de Coverly
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Re: A theoretical pawn endgame

Post by Roger de Coverly » Thu Feb 19, 2015 12:12 pm

Francis Fields wrote:Would anyone disagree?
The position with f5,g5 and h5 against f7,g7 and h7 and the Kings elsewhere is a known win for the advanced pawns by playing g6. But not with pawns on f2,g2 and h2 against f7,g7 and h7.


Mike Gunn
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Re: A theoretical pawn endgame

Post by Mike Gunn » Thu Feb 19, 2015 1:23 pm

Isn't this covered by a contribution from Gary O'Grady on one of the Nick Pert Killer Endgames DVD's? (Some famous chesser analysed/ proved this in the 19th century. didn't he?) (I refer to the Francis Fields post, not Roger's.)

Jonathan Bryant
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Re: A theoretical pawn endgame

Post by Jonathan Bryant » Fri Feb 20, 2015 12:51 pm

Francis Fields wrote:If you have the position of King and 3 pawns v King and 3 pawns (f, g & h) all on their starting square then white has a forced win with 1. f4 . Would anyone disagree?
Yes.

If memory serves the Gary O’Grady position was White pawns on f2, g2, h2 and Black pawns on a7, b7, c7. That is - apparently - a win for whoever moves first. Again memory is hazy but I think it comes from Mason.

Roger de Coverly
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Re: A theoretical pawn endgame

Post by Roger de Coverly » Fri Feb 20, 2015 1:00 pm

Jonathan Bryant wrote:Yes.

If memory serves the Gary O’Grady position was White pawns on f2, g2, h2 and Black pawns on a7, b7, c7. That is - apparently - a win for whoever moves first. Again memory is hazy but I think it comes from Mason.


That seems very plausible. Presumably the initial squares of the Kings will sometimes matter.

harrylamb
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Re: A theoretical pawn endgame

Post by harrylamb » Sat Feb 21, 2015 1:03 pm

My chess engine indicates that even though it is White to move, Black is winning this position. (Kings on their original square. White pawns on f2 g2 h2 Black pawns on a7 b7 c7.)
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Jonathan Bryant
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Re: A theoretical pawn endgame

Post by Jonathan Bryant » Sat Feb 21, 2015 6:13 pm

harrylamb wrote:My chess engine indicates that even though it is White to move, Black is winning this position. (Kings on their original square. White pawns on f2 g2 h2 Black pawns on a7 b7 c7.)
Really? That’s a surprise. I could believe that White can’t win it but I’m struggling with the idea that Black has a forced win.

what engine and how long did you leave it?

One thing that I’ve discovered recently is that engines are often not to be trusted in king and pawn endings.


Anyhoo, more importantly I’ve had a chance to check the DVDs and I got the position slightly wrong. In the O’Grady/Mason game the kings start on the same side of the board as their pawns. So it’s w pawns f2, g2, h2 w king e1 and b pawns a7, b7, c7 b king on d8.

Actually he has black on the kingside and white on the queenside but obvs that doesn’t affect the evaluation. He says, it’ss win for whoever moves first.

Roger de Coverly
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Re: A theoretical pawn endgame

Post by Roger de Coverly » Sat Feb 21, 2015 6:43 pm

Jonathan Bryant wrote: Anyhoo, more importantly I’ve had a chance to check the DVDs and I got the position slightly wrong. In the O’Grady/Mason game the kings start on the same side of the board as their pawns. So it’s w pawns f2, g2, h2 w king e1 and b pawns a7, b7, c7 b king on d8.
Start with symmetry and you can believe the first to move will win the race. In the position with Kings on e1 and e8, Black has the distant opposition, so White could suffer by moving first.

James Coleman
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Re: A theoretical pawn endgame

Post by James Coleman » Sun Feb 22, 2015 12:14 am

You used to be able to practice this ending as an unrated "wild" variation on the ICC (presumably you still can). They had it as a2,b2,c2 Kd1 vs f7,g7,h7 Ke8 but it's the same thing. White is winning with correct play but it's certainly possible to misplay it.

harrylamb
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Re: A theoretical pawn endgame

Post by harrylamb » Sun Feb 22, 2015 1:03 pm

harrylamb wrote:My chess engine indicates that even though it is White to move, Black is winning this position. (Kings on their original square. White pawns on f2 g2 h2 Black pawns on a7 b7 c7.)
Jonathan Bryant wrote:Really? That’s a surprise. I could believe that White can’t win it but I’m struggling with the idea that Black has a forced win.

what engine and how long did you leave it?,
I used Rybka 4 x64 and a fairly powerful laptop. Actually Rybka initially suggested it was a draw, but when I played my "wining plan" it rapidly changed it mind, learned from what I was playing and started to evaluate the initial position as +7 for Black. My plan depends on the fact that White needs to get his king to b4 to blockade Black's pawns while Black can initially set up a blockade on f7. When both sides establish a full blockade White is in zugzwang and has to take off his blockade with a losing position. Here is the main line. I have omitted side lines as they all seem to transpose

1.Kd2 a5 2.Kc3 a4 3.Kb4 b5 4.h4 c5 5.Ka3 c4 6.Kb4 Kf7
7.g4 Kg6 8.h5 Kg5 9.f4 Kh6 10.f5 Kg5 11.Kc3 a3

And the Black pawns are queening
Jonathan Bryant wrote: Anyhoo, more importantly I’ve had a chance to check the DVDs and I got the position slightly wrong. In the O’Grady/Mason game the kings start on the same side of the board as their pawns. So it’s w pawns f2, g2, h2 w king e1 and b pawns a7, b7, c7 b king on d8... it’s win for whoever moves first.
I agree with that
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Ian Kingston
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Re: A theoretical pawn endgame

Post by Ian Kingston » Sun Feb 22, 2015 6:29 pm

I left my quad core Intel i7-4770 (3.4 GHz) desktop machine (not state of the art, but quite powerful) running Stockfish 6 and both Nalimov and Syzygy (6 piece) tablebases to analyse this today, and the results match Harry Lamb's. In the position with kings on e1 and d8, White wins with either ! Kd1 or 1 Kd2. By symmetry, then, the position with kings on e1 and e8 is a win for Black, even with White to move.

The tablebases may not be particularly relevant here, since by the time they are consulted by the engine, after a couple of pawns have been captured, the result may be obvious to human eyes anyway. On the other hand, when I first looked at the position on my ageing laptop using Stockfish 4 (which doesn't support Syzyzgy tablebases), the engine thought the position was a draw, so maybe the tablebases do matter.

Figuring out how to play the position over the board is another matter. Consider this position, which can be reached by following the computer's recommendation:



White (to move) wins by any of 1 h5, 1 Kc3, 1 Kc2 and 1 Kb2. But 1 f4, which looks very natural, loses. One of Black's winning moves after this is the equally natural 1...a5.

The ending is given (in mirror image - white pawns on a2, b2, c2 etc.) in the Encyclopaedia of Chess Endings, 2nd edition, Volume 1. It's position 396, attributed to Joseph Szén, Bell's Life, 1840. Szén gives the correct result. Endings 386-395 deal with some of the intermediate positions that can be reached. Studying those carefully is probably essential in order to understand how to play Szén's position.

E Michael White
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Re: A theoretical pawn endgame

Post by E Michael White » Mon Feb 23, 2015 10:03 am

harrylamb wrote:My chess engine indicates that even though it is White to move, Black is winning this position. (Kings on their original square. White pawns on f2 g2 h2 Black pawns on a7 b7 c7.)................

..................... My plan depends on the fact that White needs to get his king to b4 to blockade Black's pawns while Black can initially set up a blockade on f7. When both sides establish a full blockade White is in zugzwang and has to take off his blockade with a losing position. Here is the main line. I have omitted side lines as they all seem to transpose

1.Kd2 a5 2.Kc3 a4 3.Kb4 b5 4.h4 c5 5.Ka3 c4 6.Kb4 Kf7
7.g4 Kg6 8.h5 Kg5 9.f4 Kh6 10.f5 Kg5 11.Kc3 a3

And the Black pawns are queening
Harry, I think its a mistake to blockade with Kb4 so early as the chances to lose tempi are reduced. White might draw with this approach:-

Francis Fields
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Re: A theoretical pawn endgame

Post by Francis Fields » Mon Feb 23, 2015 12:46 pm

The point of stating the position I did in starting the post is missed in the position above. Black has an advantage as his pawns are further away from the kings.

Tim Harding
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Re: A theoretical pawn endgame

Post by Tim Harding » Fri Mar 06, 2015 3:26 pm

Jonathan Bryant wrote: One thing that I’ve discovered recently is that engines are often not to be trusted in king and pawn endings.
Anyhow, more importantly I’ve had a chance to check the DVDs and I got the position slightly wrong. In the O’Grady/Mason game the kings start on the same side of the board as their pawns. So it’s w pawns f2, g2, h2 w king e1 and b pawns a7, b7, c7 b king on d8.
Actually he has black on the kingside and white on the queenside but obvs that doesn’t affect the evaluation. He says, it’s win for whoever moves first.
It's a mistake to leave this sort of thing to engines; try to understand the principles behind the play.
Most endgame books don't discuss it because it's unlikely to arise in practice but see Fine's "Basic Chess Endings" no. 68 pages 50-51 which is the second version mentioned by Mr. Bryant, viz. WKd1; pawns a2, b2, c2 versus B Ke8, pawns f7, g7, h7,
Whoever moves wins, but if the starting king positions are varied the opposite could be the case.

I haven't seen the DVD referred to, and I don't know if the reference somebody made to Mason is correct, but anyway the origin of the position is older.

This position (Fine 68) was examined by the Hungarian master Szen in the 1830s who offered to the strongest chess players of Paris to play it out for money, alternating the colours.

This endgame was discussed at length by George Walker in the newspaper Bell's Life in London, 31 May and 7 June 1840 (available through the British Newspaper Archive).
Walker says that Szen and Saint-Amant played it out about 20 times alternating colours and Szen won almost every time.
Szen then came to London and Walker endeavoured to discover the secret as he explained in the second article.

Walker says that a similar position (can anybody find it?) was given by Greco as a draw, so Walker originally believed Szen's position should be drawn.

Circa 1973, I recall the Dutch master Hans Bohm offering to play this (or a very similar position) for money against all-comers. Like Szen he would almost always win because he understood the principles underlying the play.

Szen sometimes began 1 a4 (although he knew it wasn't the best move) because this prevented the opponents from learning the correct winning method, but Walker eventually worked out that 1 Ke2 was correct and Szen confirmed this was the case.
Tim Harding
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Author of 'Steinitz in London,' British Chess Literature to 1914', 'Joseph Henry Blackburne: A Chess Biography', and 'Eminent Victorian Chess Players'
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