Three Pawns Problem

A History

I read about the three pawns problem in The Oxford Companion to Chess, 2nd. ed. (1996) by David Hooper and Kenneth Whyld. They assert that it had been known for two centuries or longer before solved by József Szén in 1836. Hooper and Whyld present a portion of Szén's analysis, which I was able to read in its entirety at least a decade ago. But, they also noted it had been examined by Pietro Carrera in 1617 and was likely known earlier (420).

Peter J. Monté, The Classical Era of Modern Chess (McFarland 2014), a book I acquired last week (see "Monumental Scholarship"), fills in some details. A small untitled manuscript discovered in 1939 by chess historian Adriano Chicco contains what might be the oldest extant version of the problem. This MS was authored by Count Annibale Romei of Ferrara. Romei's date of birth is unknown, but his death in October 1590 seems clear. Chicco dates the MS within the years 1565-1568, making it "the oldest known work on modern chess written extensively by an Italian author" (Monté, 188).

Romei's MS contains this "Subtlety" (Monté, 193).

White to move

After 1.a6 king moves 2.b8Q Kxb8 3.c6, we reach a position that should be well-known today (see "Floating Square").

The next manifestation of the problem mentioned by Monté is Carrera's (Monté, 313).

Black to move

Successfully stopping Black's three connected passed pawns leads to stalemate, which under some rules in Carrera's day is a win, or a half-win, depending on where the game is being played.

Monté also notes that José Antonio Garzón believes that Francesch Vicent presented a version of the three pawns problem to the Ferrarese nobility about 1502. The argument appears in José Antonio Garzón, El regreso de Francesch Vicent. La Historia del Nacimiento y la Expansión del Ajedrez Moderno (Valenciana, 2005); English translation by Manuel Pérez Carballo, The return of Francesch Vicent : the History of the Birth and Expansion of Modern Chess (Valenciana, 2005). The website Valencia Origen del Ajedrez 1475 has generously made the critical chapter of the author's key argument available for reading in English online. In that chapter Garzón systematically presents every known manuscript preceding Vicent's to argue that modern chess did not develop over hundreds of years, as many historians have assumed, but emerged quickly in Valencia about 1475, and from there spread very rapidly across Spain and the Italian peninsula. Monté seems convinced, or nearly so.

Following Carrera, the three pawns problem next makes its appearance in the position that I posted two weeks ago ("A Greco Composition"). I found this position in Antonius von der Linde, Geschichte und Litteratur des Schachspiels (1874). Monté fills in some details. It appears in three Greco MSS: Grenoble MS (1624), the Paris MS (1625), and the Orléans MS--undated, but likely 1624-1625 based on its strong similarity to the other two--my observation (Monté, 352).

White to move

White can create a position that is losing with 1.Kd1, but there is no reason to play such a move except to taunt your opponent. If Black is on move, the position takes on much of the characteristics of Szén's, where the player on move has a forced win. I gave Black the move and played Greco's against Stockfish on my iPad a week or so ago. As Hooper and Whyld eloquently express. "understanding of the analysis is not without practical value" (420).

I presented Szén's position in 2009 ("Pawn Wars"), but as some readers will not be able to view the images in that post (I was using an external image hosting service), I repeat it here.

White/Black to move (and win)

In my view, all of these positions are worthy of study and practice.

A Greco Composition

This position is presented as mate in 17 moves by Antonius von der Linde in Geschichte und Litteratur des Schachspiels (1874), where he credits Gioachino Greco as the composer. Komodo 13 fails to confirm the forced checkmate, but there is no doubt that White wins with correct play. Shift the White king one square to the left and you have the position about which József Szén wrote with the solution in the 1830s (the player on the move wins in Szén's position).

White to move

Endgame Training

Eight to ten years ago, I played out one hundred pawn endings against the computer. I am now working through the same set of problems a second time. These one hundred problems are the first of three sets made available as PDF files by Michele Deiana at DejaScacchi. The selection contains composed endgame positions with instructive value for practical play. Many of these problems appear in standard endgame books, such as Mark Dvoretsky, Dvoretsky's Endgame Manual and Yuri Averbakh, Comprehensive Chess Endings.

Problem 14 in Deiana's collection is a study attributed to Jean-Louis Preti (1856). It is the same as a position that I posted last May, but with colors reversed (see "Three Pawns Problem"). It builds upon technique practiced while solving problem 11, attributed to Josef Kling, presumably from Chess Studies; or Endings of Games by J. Kling and Bernard Horwitz (1851).

White to move

1.Kc2 c4 2.Kc1

Black to move

This position is critical. White will step directly in front of whichever pawn Black moves forward. Soon, all three pawns fall.

2...b3 3.Kb2 d3 4.Kc3

Black to move

This position is the heart of a king versus three pawns. White's king stops all the pawns. However, if the pawns were one square closer to promotion, then one could be promoted to deflect the king from defense of the other's promotion square.

Playing these positions against the computer means playing until checkmate. I checkmated Stockfish 7 on move 24.

Three Pawns Problem

The problem of a king opposed to three united passed pawns was examined as early as 1617 by Pietro Carrera, but was first solved by József Szén in 1836.* Knowing the solution is the key to solving this endgame position.

White to move

A few years ago, I had the opportunity to look at an article that Szén wrote on the subject. I could not read the text as it was in Hungarian, but the analysis was a form of algebraic notation and there were diagrams. I also have spent many hours playing these positions against the computer (see "Pawn Wars" [October 2009]).

This morning, I played the diagram against Stockfish after someone posted the position on Facebook.

Stockfish 6 64 -- Stripes,James
Spokane, 23.05.2015

1.h4 Kf8

Black begins with a waiting game.

2.g3 Kg8 3.h5

Now, Black must move to the seventh rank.

3...Kg7 4.f4 Kh7 5.f5

Black to move

This position is critical for Black

5...Kg8

Only move. Black is able to occupy any of the three critical squares on the seventh rank, depending upon which pawn White moves.

6.g4

6.h6 Kh7 7.f6 Kxh6

6...Kg7 7.g5 Kg8

Only move.

White to move

 8.f6 Kf7 9.h6 Kg6

White to move

This position was one of the keys Szen discussed in the article that he wrote about the three pawns problem. It should be clear that White is in zugzwang.

10.f7

10.h7 Kxh7

10...Kxf7 11.h7 Kg7 12.g6 Kh8

White to move

Playing against Stockfish often means playing until checkmate.

13.Ka2

13.g7+ Kxg7 14.h8Q+ Kxh8 15.Ka2 c2

13...c2 14.Kxa3 c1Q+ 15.Kb4 Qb1+ 16.Kc3 Qxg6 17.Kd4 Kxh7 18.Kd5 Qc2 19.Kd4 Kg6 20.Kd5 Qc3 21.Kd6 Qc4 22.Ke5 Qd3 23.Ke6 Qd4 24.Ke7 Qd5 25.Ke8 Kf6 26.Kf8 Qa8# 0–1

*David Hooper and Kenneth Whyld, The Oxford Companion to Chess (1996), 420.

Opening Considerations

Szen -- Anderssen 1851

The 59 illustrative games in GM-RAM: Essential Grandmaster Knowledge (2000) are presented as the source for the 120 essential middlegame positions that an aspiring player should strive to know. However, Rashid Ziyatdinov also suggests in his book that the aspiring player should memorize these games.

This process of learning these games by rote drives the student into study of the openings employed in each game. To memorize the game and not gain some understanding of all phases from the first move to the last would seem senseless. Moreover, some of the middlegame positions occur fairly early in the game.*

GM-RAM Position 143

Position 143 is a case in point. It arises after White's ninth move in the fourth match game between József Szén and Adolf Anderssen in the 1851 London Tournament.

In understanding this position, opening principles come to the fore.

In terms of one classic formulation of the opening phase, the diagram position nears the end of the opening. White has castled, has all of his minor pieces posted to central squares, and his queen has stepped forward to connect the rooks. Black lags behind in terms of this classic definition. One minor piece remains immobile and the rooks are not connected.

It may be surprising, then, that from this position with Black, Anderssen chose to start an attack: 9...f5! After the ensuing 10.exf5 Rxf5, the absence of White's e-pawn made 11...d5 a serious threat. White suddenly faced some serious problems. It is hard to find an improvement to Szen's unfortunate retreat of his knight to its starting square as preparation to redevelop it on d2.

Black seized the initiative. Ten moves later, Anderssen missed a forced checkmate in ten moves.** Nonetheless, he launched a decisive assault of tremendous instructive value and won the game. Something went horribly wrong for White in the first nine moves. Where did Szén err?

Szén,József -- Anderssen,Adolf [B30]
International Tournament, London 1851 (2.4)

1.e4 c5 2.Nf3 Nc6 3.Nc3 e6

This position is found in the Encyclopedia of Chess Openings under B40, so the B30 classification by ChessBase might be inaccurate. Four possible moves for White are then given in ECO: 4.Be2, 4.g3, 4.d4, and 4.Bb5. Szén played none of these.

4.Bc4?!

This move should probably be considered dubious even though control of d5 is a strategic aim. The most popular moves 4.d4 and 4.Bb5 aim at control of d4. 4.Bc4 is more popular than 4.Be2 in the ChessBase database, but it scores worse. White's scoring percentage is poor enough to recommend against 4.Be2, but it is far worse after Bc4. The number of games reaching the position after 4.Bc4 is more than twice the number of times that 4,Bc4 was played. The difference suggests that move order variations account for this bishop's presence on c4 most of the time.

The only game in Chess Informant that reached this position had the move order 1.e4 c5 2.Nf3 Nc6 3.Bc4 e6 4.Nc3, CI 93/(122).

4...a6 5.a4

5.d4 is worth considering. 5...b5 6.Be2 when White's fourth move cost a tempo, but little else.

5...Nge7

The comparison of Staunton's play as Black against Anderssen to Anderssen's play as Black deserves analysis. Anderssen's placement of this knight resembles Staunton's. But, Anderssen's queen does not go wandering on pawn grubbing expeditions.

6.Qe2

6.d4 should be considered. If there is anything wrong with Black's slow deployment, White needs to act with vigor to demonstrate the point.

6...Ng6

Why not harass White with 6...Nd4! 7.Nxd4 cxd4 8.Nb1 Nc6?

7.d3 Be7 8.Be3 O-O 9.O-O

We have reached the diagram position.

My first impulse as Black might be to solve the problem of the light-squared bishop with 9...b6 and 10...Bb7. Anderssen, however, chose to strike.

9...f5!

Did Szén have a better way to meet this thrust? Did Black have an advantage that compelled him to attack? How can we best characterize the errors in White's opening play? Lethargy? Misplaced pieces?

The c4 square often proves an active square for the bishop in symmetrical king's pawn openings. The bishop also goes there frequently in open Sicilians. However, White chose a closed Sicilian, delaying the d4 thrust. It seems, perhaps, that in such positions, the bishop is better placed elsewhere.

Nonetheless, I often see such bishop placement in my own games--at least in online blitz. I usually thrust forward my d- or b-pawn and drive the bishop back to a2 or b3. Later in the game, this bishop bites back.

Anderssen's f-pawn thrust offers another way of looking at similar positions.



*Ziyatdinov's recommended references offer another indication that opening study walks hand in hand with comprehending essential middlegame positions. For example, he lists Paul Keres, and Alexander Kotov, The Art of the Middle Game. The English edition of this book contains an additional chapter by Harry Golombek, who also translated the book into English. Surely, Ziyatdinov would expect me to read Golombek's section as well. Golombek stresses that the middlegame plan, "must arise naturally and logically out of the opening" (17).

**I posted the other middlegame position from this game last month (see "Mate in Ten").

Mate in Ten

In the International Chess Tournament, London 1851, Adolf Anderssen prevailed over all of his opponents. Through play of casual games, he and József Szén determined that one of the two of them would win the event. The two met in the second round, which Anderssen won 4-2. This position occurred in the fourth game of their match. Anderssen won the game with a strong attack on Szén's king. However, his play was far from perfect.

Anderssen missed a forced checkmate in ten moves.

Black to move

It should not come as a surprise that this position is one of two from this game that appears in the "Essential Middlegame Knowledge" section of Rashid Ziyatdinov, GM-RAM: Essential Grandmaster Chess Knowledge (2000).

The Camp Workbook

This morning concluded my seventh summer chess camp for elementary age chess players. The first camp was in June 2008 and drew only youth from Deer Park School District, where the camp was part of a very active summer enrichment program. With permission of the summer coordinators, I began recruiting students from outside the district in 2009. The second year, the three hour block was split: 1:45 for the advanced camp and 1:15 for the beginning camp. This time seemed too short for strong youth players, but about right for beginners.

In 2012, I moved the camp to a private school where I was now coaching.* At the new school, I restored the three hour block and extended the camp from four days to five. Although I do not run a beginners camp, a few beginning players join each year. I make accommodations for them with some separate activities. Sometimes I produce a separate workbook for the beginners.

A distinctive element of my camp is the camp workbook. I do not know how common this element is among others who run camps for young players. I am certain that I am not unique. Even so, my changing themes year after year put me outside the norm.

My workbooks generally include annotated games, other related games presented without comments, tactics problems and a short glossary of tactical motifs, essential pawn positions. Some workbooks have more endgame positions, some less. Some elements of the workbooks are carried over from previous years.

My first two camps used the same workbook, except for the date on the cover. In 2010, my camp theme was "Attacking with Anderssen." The 56 page workbook contained several Anderssen games that I annotated for young players (see the link for an example). Also, the tactics problems stemmed from Anderssen's games. I reworked some of these annotations for this year's camp.

In all my camps, awards at the end of the week are based on accumulated camp points. Youth earn camp points for good behavior, solving chess problems, recording their games in the camp tournament, answering questions during presentations, and so on. The winner of the camp tournament does not always accumulate the most points, although that win is also worth some points.

In 2011, I produced my shortest camp workbook (41 pages), but edited it carefully. The focus was Vasily Smyslov's search for truth. I also found tactics puzzles from Smyslov's play. A section from that workbook on rook endings was imported into this summer's workbook, too, but was not included in the camp curriculum. The workbooks always contain more materials than we have time for in camp. Ambitious students go home with study material that will carry them through the summer.

The 2012 camp and workbook profiled a different chess player each day: Jozsef Szen, Paul Morphy, Mikhail Tal, Alexander Chernin, and Yasser Seirawan. This year's workbook recycled some of my materials on Morphy, which are built on the solid work of Valeri Beim, Paul Morphy: A Modern Perspective (2005).

In 2013, I omitted the endings from the workbook, although pawn wars remained part of the week's activities. This ambitious workbook of 59 pages was almost all new material. It had a long section on Gioachino Greco that was built on my work converting all the games and fragments from William Lewis, Gioachino and the Game of Chess (1819) into ChessBase format. Unfortunately, I failed to back-up this database and my hard drive crashed a month after camp. The material included in the workbook is all that remains. There was a shorter section on François-André Danican Philidor, which was also based on work with an old English text.

Most of the materials in this year's workbook were revisions of materials from previous years. However, I added a wholly new section: teacher vs. student. For many years, I have notated games played with young chess players during their chess club practice. I annotated two of these games for the workbook to highlight common errors made by young novice players. A camp theme was learning from errors.

Mistakes are part of chess. It is often said that the winner of a game was not the player who made no mistakes. Rather, the winner made the second to the last mistake. 

Good chess players learn from their own errors. After the game, they analyze with their opponent and often with a stronger player or coach. They seek to understand where they might have improved their play. Even wins are subjected to critical analysis. 

Better chess players learn from mistakes made by other players. The best chess players invest a lot of time studying other players’ games. They look for patterns that will be useful in their own games. They practice finding the critical errors and seeking better moves. They look for new ideas.
Stripes, "Dragon Chess Camp 2014: Basic Training for Chess Success" (7).

After presentation of one of these games, students worked together to identify the errors in a batch of other student vs. teacher games. Among their tasks was to try to discern which player was the teacher.

I also added checkmate in one problems to the start of the tactics problems at the back of the workbook. These proved helpful to the beginning students while also building confidence for the stronger players. At 87 pages. it was my longest workbook so far.



*I continue to coach the teams in Deer Park, as well. I started coaching chess in Deer Park as a parent volunteer, becoming a paid coach when we moved out of the district.

Pawn Wars

In Breaking Through: How the Polgar Sisters Changed the Game of Chess (2005), Susan Polgar mentions a game she played with her father when she was starting to learn chess.

After introducing the chess board and the pieces, for some time we only played "pawn wars". That means games where only the pawns participate without the rest of the army. The goal of the game was whoever queens a pawn first wins. Then later we added the kings and playing all the way to checkmate.
Polgar, 6-7

I had found that young children enjoy what we had been calling the pawn game a few years before this book came out. After reading that passage a few years ago, I've increased my investment in pawn wars as a teaching tool. It is a central element in my private lessons with young students. In classrooms full of seven year old children, I start with pawns.

The game can be modified easily. Last spring, a kindergarten student that had been playing chess one month with his grandfather showed some promise, and his father made arrangements for me to offer some instruction. We played pawn wars with the kings. He started with eight pawns to my six--my rook pawns were missing. It took him perhaps two or three games to learn that he could lure my king to one side of the board by creating a passed pawn there, then create one on the other side that was outside my reach. After several victories, we played eight against seven.

One need not use all the pawns.

The classic Szén Position is a challenge even to strong players that still need work on the endgame. The player to move has a theoretical win, but precision is necessary to keep the win in hand.



According to David Hooper and Kenneth Whyld, The Oxford Companion to Chess (1996), the three pawn problem--a king against three connected passed pawns--had been studied for over two hundred years without success until Jószef Szén solved it in 1836.

Another variation of pawn wars that I've been using the past few weeks appears to be a theoretical draw. Remove the kings, and the player on move should win.