"The student should work this out"

In Chess Fundamentals by José Raúl Capablanca, the author frequently states that a given position, "should be worked out by the student", and other comparable phrases. This assertion vexes some readers and some coaches are loath to recommend the book. If the student does not understand something, how will they come to an understanding without assistance?

In some cases, especially with simple pawn endgames in chapter 1 of Chess Fundamentals, I believe that Capablanca provides the necessary resources in the explanations that he offers. Still, I have seen others struggle. They need more help. Capablanca recommends a teacher.

When Capablanca wrote Chess Fundamentals (he was checking the proofs in England in 1920 while negotiating conditions for the World Championship Match that took place in March and April 1921--see "WCC Havana 1921" in this site's index), there were fewer resources than we have today. I believe the standard endgame book then was Johann Berger, Theorie und Praxis der Endspiele (1890), a book in the German language that was probably not readily available or accessible to the majority of Capablanca's readers.

Today, however, we have an abundance of books, websites, YouTube, ready access to engines, and even tablebases. The danger to the student stems not from lack of help, but rather too much help. Easy access to answers cause many to fail to develop self-reliance. Capablanca's call to develop the habit of working things out may offer a more certain formula for strengthening a player's skills.

I often claim that I have zero natural ability at chess, but that I have learned a modest amount from books (see "My First Chess Book"). Many years ago when I started reading chess books, I found much that was confusing. The book I remember most clearly is Irving Chernev, The 1000 Best Short Games of Chess (1955). Often it was not evident to me why a game ended. Sometimes Chernev explained the reason, but even then I had questions. I sought answers to my questions by moving the pieces on a chess board, exploring variations. Certainly, with so little skill at the time, most of my fantasy variations were rubbish. Even so, the effort developed a habit of thinking for myself about chess.

The past few days I've found myself back in the classroom, seeking understanding. I started playing some bishop endgames against the computer on chess.com. Failure in my first effort got me hooked. My time struggling through five positions against the silicon monster engages me for hours every day. At the Learn/Endgames/Minor Pieces/Bishops tab on chess.com, there are five practice positions. To see the second one, you must checkmate the computer in the first. The first is simple and takes me from 12 to 24 seconds most times. 

The second one varies in difficulty, depending on how the engine plays.

White to move

Number Two

1.Bf5

I always play this move. It might be best.

1...h5 2.f3

Now the engine has played 2...a5, 2...Ke7, and 2...Kc6 most regularly. 2...Kc6 has proven most testing but I am reliably winning most of the time. Success grants me the opportunity to see number three.

White to move

Number Three

I found the pawn sacrifice quickly and now get to my seventh move in two seconds or less. Sometimes I reach this point with considerably less than two minutes total time elapsed for checkmating the computer in the first two and playing these seven moves.

1.c5 dxc5 2.Bc4 Bg4 3.Kxe5 Ke7 4.Kd5 Kxf7 5.Kxc5 Ke7 (the computer threw me a curve with 5...Kf6 at least once) 6.Kxb4 Kd6 7.Bd5

Black to move

The computer has played at least five different moves here.

a) 7...Bf3 proved challenging the first time I saw it. That line now often continues 8.Ka5 Be2 9.b4 Bg4 10.Kb6 Bh3 11.b5 Bg4 12.Ka7 and the computer must give up the bishop for my b-pawn.

Black to move

12...Kc5 has given me trouble when I am moving too fast, which the exercise encourages by tracking total time for the series and making me play simple checkmates all the way to the end. Sometimes I underpromote to practice bishop and knight or two bishop checkmates.

13.Bc6 Bc8

Here, 14.b6?? fails, but both 14.Kb8 and 14.e5 succeed.

I have seen most of the computer's responses several times, but this morning's effort presented me with a position I did not recall seeing before. 

b) 7...Bd7 8.Ka5 Kc7 9.Kb4 Kb6

White to move

10.Kc4!

There is more than one way to get rid of Black's bishop.

10...Be8 11.Kd4 Kb5 12.e5 Kb4 13.Ke4 Kc5

White to move

14.Bg8 Bc6+ 15.Kf5 Kb4 16.Kf6 Kc3 17.Bc4 Bd7

This move is Stockfish surrendering it seems.

White to move

18.e6 Bc6 19.Kf7 

Black must give up the bishop for the e-pawn. A few moves later, I underpromoted the b-pawn to a bishop. When I was nine or ten moves from mate, I made a hasty move that stalemated the engine. Now, I must start over at number one. I've played number five half a dozen times and have some ideas how to proceed. My current problems are two: 1) the engine lures me into a pawn ending that is lost foe me, and 2) I fail two, three, and four too often.

Have you tried these exercises? How did you do?

To Know a Position

Two pawns against one when the stronger side has one that is both passed and protected is generally a win. There are exceptions when the pawns are too close to the edge of the board with one of the pawns (stronger or weaker side) on its starting square. Having a pawn on a rook file also limits the stronger side's chances. The position of the kings often proves critical.

This position, ending no. 107 in Pandolfini's Endgame Course (1988), also arises while playing through examples 8 and 9 in José R. Capablanca, Chess Fundamentals (1921). Josef Kling and Bernhard Horwitz, Chess Studies, or the Endings of Games (1851) presents a study that reaches this position after the first two moves.

White to move

Sacrificing the forward pawn allows White to win Black's pawn after a few moves using opposition and outflanking maneuvers, resulting in a standard position that Bruce Pandolfini covers earlier in the book (endgames 60-62).

The diagram position is important enough in Lev Alburt's view that it appears in Chess Training Pocket Book: 300 Most Important Positions and Ideas (1997). Alburt writes that to become a strong tournament player one needs to know only 12 key pawn endings, promising that the right 12 are in the book (9). A similar position appears in Rashid Ziyatdinov, GM-RAM: Essential Grandmaster Knowledge (2000), but did not make the cut for Thomas Engqvist, 300 Most Important Chess Positions (2018).

Lest there be any doubt about the practical value of understanding how White should play, consider the ending from Polgar,I.--Ciocaltea,V., Baja 1971, which is presented in C.G. Van Perlo, Van Perlo's Endgame Tactics, new, improved and expanded edition (2014).

White to move

54.Kg3

54.Kg5 fails to make progress, Van Perlo notes.

54...Kf7 55.Kf3 Ke7 56.Ke3 Kd7 57.Ke4 Ke6

White to move

Flip the side to move, remove White's f-pawn and place a Black pawn on f6, and the position is identical to one that appeared at the Spokane Chess Club in April 2005 between two of the group's strongest players. Black pushed the unopposed pawn and the game was dead drawn, yet the game continued for many moves more because the weaker side has very little time left on the clock.

58.g5!

"Depriving the black king of some vital squares in the tempo battle" (Van Perlo 25).

58...Kd6 59.f5 Ke7 60.f6+

Now White has a passed pawn.

60...Kf7 61.Ke5 Kf8

We have reached the position at the top of this post.

62.f7

Black resigned.

We can move the initial position right or left, up or down. In most cases, the stronger side has an easy win.  Sacrifice of the forward pawn is the easiest method when the blocked pawn is on the fifth rank, but this fails when the pawn is further back.

Two key positions are analyzed in Johann Berger, Theorie und Praxis der Endspiele (1890), referencing the earlier work of George Walker, A New Treatise on Chess (1841).

No. 483

Das Spiel ist leicht zu gewinnen

It is an easy win, regardless of who has the move, Berger explains.

No. 484

Weiss gewinnt nur mit dem Zuge.

White wins only with the move.

Mark Dvoretsky, Dvoretsky's Endgame Manual, 5th ed. (2020) offers one full page of analysis with one winning and two drawing positions, plus a well-known 1921 study by Nikolai Grigoriev earlier in the chapter. Grigoriev's study, "underscore[s] that a system of corresponding squares certainly does not have to always be 'straight line', as with the opposition. Each case demands concrete analysis" (23). Alex Fishbein, King and Pawn Endings (1993) offers two positions, both of which are Grigoriev compositions. Reuben Fine, Basic Chess Endings (1941) has seven diagrams over a little more than three pages. Karsten Müller and Frank Lamprecht, Fundamental Chess Endings (2001) offer two positions from games, one winning and one drawing. Comparable positions do not appear in Jeremy Silman, Silman's Complete Endgame Course (2007), unfortunately.

Paul Keres, Practical Chess Endings (1974) offers the most thorough discussion with 11 diagrams over six pages. He begins with Berger's no. 483 (see above).

After nine moves in Keres' analysis, the following position is reached.

White to move

"White would spoil everything with 10.b6?" Keres notes (34).

10.Kd5! Kc7 11.Ke6 Kb6 12.Kd6

This outflanking idea is another standard technique.

12...Kb7 13.Kc5

Keres then turns to the most important technique for endgame book authors: shifting the position. Shift everything up on rank and White can no longer win because of the same stalemate threat noted after 10.b6? Shift one square down, and White still wins. Two squares down and it matters who has the move. White must have the move to win.

Moving the position one file to the right and one rank up, White wins, even when Black has the move.

Black to move

1...Kd6 2.Ke4 Ke6 3.Kf4 Kd6 4.Kf5 Kc7 5.Ke6 Kc8

White to move

6.c7!

The pawn must be sacrificed, as we should know from Capablanca and Pandolfini.

Continuing the shift to the right and this time down a rank, Keres sets the kings in a manner optimal for Black. After a few moves, the following position is reached.

White to move

To secure the win, White must use threats of moving to either side of the mass of pawns to perform the opposition and outflanking maneuvers.

6.Kc1!

Working out the rest is good training. Keres book is helpful, too. It was when I reached this position in my reading yesterday morning that I started playing against Stockfish from this position and then many other variations with the same arrangement of pawns across the range of possibilities.

Shift the starting position one rank down and this resource no longer exists for White.

Knowing a position well is knowing an arrangement of pieces that may be, in fact, many hundreds of possible positions. Some of these have arisen in my games in the past and can be expected to do so again. 

More Notes on Berger

Johann Berger, Theorie und Praxis der Endspiele (1890) systematically examines practical chess endings in a manner that ushered in the modern theory of the endgame. The book's availability has been enhanced by Google Books.

During my reading yesterday, some underpromotion exercises captured my interest. Berger credits Carl Ferdinand von Jaenisch as the composer. I played them out against Stockfish on my iPad and found the second one required some calculation to get the knight to its proper posting.

White to move

1.Rxg5+ Rxg5 2.fxg5 h2 3.g6 Kh3 4.g7 h4

White to move

White must underpromote to a bishop or knight to avoid stalemate. In this instance, a bishop is the better choice, but a knight can win.

Berger's second exercise from Jaenisch differs in the placement of two pawns.

White to move

1.Rxg5+ Rxg5 2.fxg5 h2 3.g6 Kh3 4.g7 h4

Now, while a bishop does not stalemate, it also cannot win. White must play 5.g8N.

5...Kg4

White to move

Berger's solution continues with 6.Nf6+. I played 6.Ne7, and the tablebases favor 6.Kxh2.

Preceding these studies, Berger offers a brief explanation of the square of the pawn. Following these, is a section on the opposition with several illustrative positions, culminating in this important one from Giambattista Lolli, published in 1763.

White/Black to move

White to move wins; Black to move draws. For some reason, I found the draw hard to believe, but I've practiced the position against students many times since learning it more than ten years ago. Winning with White to move is one one of my requirements for the Bishop Award in my Scholastic Chess Awards.

Notes on Berger

David Hooper states that Johann Berger, Theorie und Praxis der Endspiele (1890) is "the first comprehensive book in modern times devoted wholly to the practical endgame" (Golombek's Encyclopedia of Chess [1977], 101). In 2009, Google digitized a copy from Harvard Library, making it readily accessible to those interested in the history of the theory of the endgame. Although Hooper states Berger's text, "would not today be regarded as adequate for practical use", I am finding much that is instructive and interesting as I have been reading through it this morning.

Berger makes a point in the first pages to distinguish endgame theory from studies. The endgame, he asserts, "comprises only the battle of a few chess pieces against correspondingly low defensive forces" (2). Compositions leading to checkmate, stalemate, or a draw must be distinguished from endgame theory because, "the chess pieces have a completely different meaning and are used differently than in actual endgames" (2). He presents some illustrations of studies that are not endgames, beginning with a composition by Bernhard Horwitz.

White to move

Horwitz 1884 

White checkmates in six moves. Berger points out that the play of the pieces resembles the middlegame, and also that White's rook is superfluous. In the endgame, "the best possible use of the power of each individual piece should be expressed" (3), Berger opines. He offers:

White to move

1.Kc4 c1Q

Or 1...Ka1 2.Qd2 (to avoid an underpromotion threat)

2.Kb3 and checkmate in a few moves.

Berger's eighth example highlights two ways that a theoretical draw of rook vs. bishop is reached from the following position.

White to move

1.f7 Bd5 2.f8Q Rg8

Or 

1.Rc1+ Kh2 2.f7 Bd5 3.f8Q Rg8

Following this clarification of endgame theory as distinct from studies, Berger shows elementary checkmates--queen, rook, two rooks, two bishops, and then no less than five positions from which checkmate by bishop and knight can be executed.

Then he turns to the knight. Two knights, as we know, can only stalemate. What about three knights? Berger presents a composition of his that was published in Osterreichische Lesehalle (1889).

White to move

When I played this position against the computer, it opted for a line given by Berger as a variation. I was able to coordinate my pieces and win easily.

1.Rxe7 Qd4+

1...Qxe7 leads to 2.c8N+ winning the queen and leading to checkmate. Berger finds a mate 15 moves from the diagram.

Seeking Understanding

Five years ago, I posted "Two Endgame Compositions", giving only the solution to the second. This week I was asked to provide the solution to the first, an 1888 composition by Johann Berger that was first published in Columbia Chess Chronicle. The past two mornings, I have been studying the solution with an aim to understand every move. Although the maneuvers appear complex, they are based on some simple ideas.

White to move

J. Berger, 1888

1.Qb8

The only winning move, according to the tablebases. It forces the light-squared bishop to move because of the checkmate threat Qh2#.

1...Bc4

Threatens Be6+, followed by Bf2+ (or Bh2+).

Other moves lose more quickly.

1...Be2 2.Qf4 (see at move 4 below)
1...Bd3 2.Qf4
1...Bb5 2.Qxb5 Ba7 3.Qd5
1...Ba6 2.Qg8 Bb7 3.Qh7 Bc8+ (3...Bf2 4.Qxb7) 4.Kg3+

2.Qe5

Prevents the check while keeping the dark-squared bishop immobile.

2.Qd6 is one move slower. This move is presented as a "cook" in Harold van der Heijden's Endgame Study Database with a line leading to underpromotion of Black's pawn. It is an instructive alternative.

2...Ba6

Threatens Bc8+

2...Bd3 3.Qg5 threatens Qxg2#. 3...Be4 4.Qh4 Bf5+ (4...Bf2 5.Qxe4) 5.Kg3+
2...Be2 3.Qxe2
2...Bb5 3.Qxb5

3.Qc7

Prevents the check while keeping alive the Qh2 threat.

3.Qe1 is one move slower according to tablebases.

3...Bd3

3...Bb5 allows 4.Qg7

(4.Qc1 Is given ! in Genrikh Moiseyevich Kasparian, 888 Miniature Studies [2010]. Pins the dark-squared bishop so a check can be met by Kg3 and then Qh6+ 4...Bf1 5.Qf4 Ba6 6.Qg4; 4.Qb7)

4...Bc6 5.Qh6 Bd7+ (5...Bf2 6.Qxc6; 5...Be3 6.Qxc6) 6.Kg3+
3...Be2 is second best 4.Qg7 Bf3 5.Qa1 Be2 6.Kg3

4.Qf4

Threatening to move to g4 where checks along the c8-h3 diagonal are blocked and Qxg2 is threatened. This move forces the light-squared bishop onto the a8-h1 diagonal.

Black to move

4...Bb5 5.Qg4

Shields the king from check and threatens Qxg2#

5...Bc6

Defends g2

6.Qd1

Pins the dark-squared bishop and prepares Kg3

6...Be4

White to move

7.Kg3

Threatens Qh5+. The complex battle between White's queen and Black's light-squared bishop has concluded. Now, White threatens checks on the h-file, which Black can delay briefly.

7...Bg6

Guards h5

8.Qc1

Threatens Qh6+

8...Bh5

Prevents the check

9.Qa1

Forces the bishop off the h-file.

Black to move

The rest is easy.

9...Be2 10.Qh8+ Bh5 11.Qxh5+ Bh2+ 12.Qxh2#

Capablanca's Sources

As I am rereading J. R. Capablanca's classic Chess Fundamentals (1921), I marvel at how much content he packs into such a short book. With respect to pawn endgames, in particular, he presents a small number of examples that together constitute a substantial amount endgame knowledge.

When Nate Fewel showed me this position at the Spokane Chess Club in the mid-1990s, I had a copy of Chess Fundamentals, but had not spent much time studying it. I failed to solve this elementary position. When I was glancing through Capablanca's book a short time after Nate showed the position to me and saw it there, I began to to read the text with some diligence. Over the next few years, my endgame skills improved dramatically.

White to move

Capablanca did not compose the exercise. The breakthrough idea with pawns lined up as they are here dates back at least to Carlo Cozio, Il Giuoco degli Scacchi (1766). Endgame Study Database VI by Harold van der Heiden has this position credited to Cozio (see "Endgame Study Database").

White to move

Although I do not know the contents of Capablanca's library, it seems reasonable to believe that he would have had access to Johann Berger, Theorie und Praxis der Endspiele (1891), as it was the standard endgame work of the day. Position number 539 of Berger's book credits J. H. Sarratt, A Treatise on the Game of Chess (1808).

White to move

Sarratt has the White king on h1 and the Black king on g3, which is closer to what Nate showed me. In all cases, the moves are the same. White achieves the breakthrough by advancing the b-pawn, which Black captures. Then, depending on how Black captures, White sacrifices either the a-pawn or the c-pawn, so the other may promote.

Capablanca also notes that Black on the move draws by advancing the b-pawn.

Textbook Ending: Historical Considerations

This position arose twice in Fiebig -- Tartakower, Barmen 1905. It was reached after 58...Kc8 and again after 60...Kc8, at which point the game was agreed drawn.

White to move

Historical questions arise. What were the rules in 1905 regarding draw by repetition or by triple occurrence of position? What endgame books that should be known by aspiring masters of the time explain the technique of triangulation?

Fiebig missed an elementary win that is a textbook ending. Today, it is in many textbooks, but was it as well-known more than a century ago?

In "Pawn Ending" in Edward Winter, A Chess Omnibus (2003), 42-43, this position is reached after the first move from a diagram presented there. Winter references Das Endspiel im Schach (1917) as a source, noting that the score of the game Fahrni--Alapin has not been found. Winter notes the position from Fiebig--Tartakower, and that the game appears in the Barmen tournament book. Winter's article also appears at "Edward Winter Presents: Unsolved Chess Mysteries (14)" (2007).

Wilhelm Steinitz, The Modern Chess Instructor (1889) presents the rules that had been approved by the British Chess Association and many chess congresses. "When both players persist in repeating the same moves," is given as one circumstance that produces a drawn game. There is no reference to the number of repetitions necessary. I have previously written about the development of the Fifty Move Rule at "Max Judd's Draw Claim" (2016). Perhaps a narrative concerning the development of rules regarding repetition can be found somewhere. Winter states the game was "agreed drawn" (42).

J. Berger, Theorie und Praxis der Endspiele (1890) discusses opposition in a separate section within the larger portion devoted to kings and pawns (28-34), but I do not see any reference to triangulation--neither process nor terminology. As far as I am aware, Berger's was the standard endgame book of the time.

As I was playing through Fiebig -- Tartakower, I was certain that White should be winning after Tartakower blocked a check with his rook.

White to move

The game continued:

51.Kd4 b6

Hiarcs, running tablebases, likes 51...Kc6 52.b5+ Kc7 53.Rxd6 Kxd6 54.a4+-

52.Ke5 Rxd5+ 53.Kxd5 Kc7 54.a4 a6

54...Kd7 is more stubborn

White to move

According to Hiarcs, it is checkmate in nineteen moves.

55.a5

The second best move. White wins more quickly with 55.Ke5 Kd7 56.c5 Kc6 57.cxb6 Kxb6 58.Kd6

55...bxa5 56.bxa5 Kd7 57.c5 Kc7 58.c6 Kc8

The game has reached the position at the top of the post. After seeing how the game concluded, I opened my playing software and continued from the diagram against Stockfish 10. I checkmated the engine in sixteen moves.

59.Kc4

59.Kd6 was played by Fiebig.
59.Kd4 is given by Winter from Fahrni's book.

59...Kb8 60.Kd4 Kc8 61.Kd5

The diagram at the top of the post has been reached again, but the position has changed. Now, it is Black to move.

The rest was easy.

Two Endgame Compositions

These two compositions were brought to my attention through Genrikh Moiseyevich Kasparian, 888 Miniature Studies (2010), which I acquired last week. This book is an expansion of the author's 555 Miniature Studies (1975). This earlier book, as far as I know, was never translated into English. The present work was left in manuscript at the time of the author's death, but was brought into publication fifteen years later through the assistance of his son, Sergei Kasparian.

White to move

Johann Berger 1888

This study is number 17 in Kasparian. I read through the solution, which is under the diagram, and then proceeded to try making sense of it. When I thought I had reached a reasonable understanding of the ideas, I tried playing it against Stockfish. My first effort led to failure, so I returned to the solution. In my second try against Stockfish, I was able to win easily. I continued working with the problem, however, seeking to develop the ability to explain in plain English to beginning chess players how to understand the solution.

Having given the solution so much attention, I looked in Berger's book, Theorie und Praxis der Endspiele (1890) where I was surprised to find the problem was credited to an obscure publication, Columbia Chess Chronicle III, no. 13 (1888). After some searching, I found the problem on the cover of the issue named, where Berger is confirmed as the composer.

Readers of this blog are encouraged to offer their solutions in the comments below. I will refrain from presenting the solution, except in reply to comments.

White to move

Karl Behting 1894

Kasparian credits C. Behting, Rigaer Tageblatt 1894 (21). Tageblatt translates as "daily paper". I do not know whether that is the name of a specific news publication or a generic term for one or more of several newspapers in Riga. Its use in other publications that I have examined suggets that it is a specific paper.

Karl Behting (Kārlis Bētiņš) was a Latvian chess player and composer. The Latvian Gambit bears its name because he studied it with other Riga players and published an article in St. Petersburger Zeitung (1909). Many of his compositions were published in newspapers in Riga, then were republished in books and magazines that culled problems from other publications. I found a version of this problem in Baltische Schachblätter, Issues 6-8 (1898). Below this point, I am presenting the problem as found there and the solution. Of interest in the solution is a technical chess term that is new to me and worth adding to the lexicon of chess terms: Tempozug.

Tempozug means to waste a tempo; that is, to make a move that does not change the position. A Tempozug places the opponent in Zugzwang.


Solution to Second Problem

Behting's composition in Baltische Schachblätter.

Credit here is given to Johann Behting, Karl's older brother. A 1930 publication, Studien und Problem lists both Johann and Karl as authors, suggesting collaboration. Were there separate publications of this problem by both brothers? The position attributed to Johann begins one move earlier than the version of the same problem that Kasparian credits to Karl. Some insights into the compositions of these brothers is offered by John Beasley, "Some Studies by Johann and Carl Behting," British Endgame Study News 52 (September 2007), www.jsbeasley.co.uk/besn/s52.pdf.

Solution from Baltische Schachblätter.

Power of Pawns

Lesson of the Week

Rezső Charousek (1873-1900)* emerged on the tournament scene at Nuremburg in 1896, where he defeated World Champion Emanuel Lasker (1868-1941) in the final round. Lasker still won the tournament, while Charousek finished 12th. The manner in which the young Hungarian defeated Lasker led the World Champion to declare, "I shall have to play a championship match with this man some day." However, a few short years later Charousek was dead from tuberculosis.

Before his entry into master tournaments in 1896, Charousek distinguished himself in games against the top players in Hungary and a few others, including the man who wrote the book on the endgame. Johann Nepomuk Berger (1845-1933) was the author of the first comprehensive treatment of the endgame, Theorie und Praxis der Endspiele (1891). In this game against Charousek, however, the Hungarian demonstrates the power of three connected pawns.

Black to move

Charousek played 41...Be3!

41...g3 also wins.

The game finished 42.fxe3 g3 43.Rd7 f2+ 44.Kf1 h2 0-1

One of Black's pawns will promote and the queen will rule the board.

*Rezső Charousek is usually called Rudolf in English language sources.