Corresponding Squares

My quest to learn 300 chess positions in 60 days is proving time consuming. Most of the time that I could spare today was expended laboring to understand number 37. The first day was a review of some pawn endings that I know: positions 151-155 in Thomas Engqvist, 300 Most Important Chess Positions (2018). My quest is an effort to read all of this book in less than two months. On the second day, I reviewed some Paul Morphy positions that I know well. An obscure line in the Slav Defense captured my interest yesterday. Today, I went back into endgames with numbers 156-160 in Engqvist. Number 157 is a much analyzed study by Emanuel Lasker (some books employ the version published by Gustavus Reichhelm after Lasker and he discussed Lasker’s composition).

First, I set up Lasker’s position on my iPad and spent some time analyzing it. Then, I played against the engine, backing up and trying again when I failed. I have worked with this position in the past and knew the basic ideas, but have not developed well my ability to calculate the whole series of corresponding squares. Looking for help drove me into other books on the shelf. I confirmed that Jeremy Silman, Silman’s Complete Endgame Course (2007) lacks the position. I know that corresponding squares are mentioned early in Mark Dvoretsky, Dvoretsky’s Endgame Manual (2003) and the concept is trumpeted in Paul Keres, Practical Chess Endings (1974). I opted to check John Speelman, Endgame Preparation (1981) and was pleased with the instruction.

Speelman offers a digested version of what he found in Yuri Averbakh and Ilya Maizelis, Pawn Endings (1974), which I consulted later in the day. My process was to read some in Speelman, and then construct a position derived from Lasker/Reichhelm. First, I sought to find positions with Black to move that were winning for White. With all the pawns fixed as in Lasker’s study, I placed the Black king on a8. Where must I place the White king for the position to be winning if Black is on the move?

Black to move

Then, I repeated the process with Black’s king on b8. After several such efforts, I went back to Reichhelm’s version of the original study and played against the computer. Then, additional modifications and more play against the engine.

This version was one of the easier ones.

White to move

After many hours of play against the engine and study of several books, I have the sense that I am beginning to scratch the surface of this difficult position.

Fails

It seems that I pick up The Manual of Chess Combinations, vol. 2 by Sergey Ivashchenko once every other week to work a page of exercises. A few days ago, half a page occupied part of my morning. I solved three successfully. This morning, the fourth one on the page did not present difficulty, but the last two did. I also managed to err in the sixth exercise on each of the the next two pages.

Exercise 144 struck me as a study in corresponding squares on first glance, but I gave too little attention to the simplicity of Black's ability to gain and maintain the opposition. Had I considered the possibility of a sacrificial breakthrough, I might have more quickly perceived the floating square idea. I spent some time teaching the floating square to a couple of students last week and should have seen it.

White to move

1.Kf2 (or any other king move) fails. 1...gxh4 2.gxh4 Kg6 3.Ke3 Kf5 4.Kf3 Ke5 and Black can shuffle the king back and forth.

Instead, 1.g4! wins 1...hxg4 2.h5 (also 2.d6). 

Before that one, I thought I had correctly solved number 143, but had also overlooked something simple.

White to move

I tried 1.Kg5, overlooking that I had nothing after 1...e6 2.Kf6 Ke8 3.Kg7 Ke7 and somehow I had hallucinated there being possible an outflanking maneuver. After 1.Kg7 Ke8 2.e6! fxe6 3.Kg8 Kd8 4.Kf8 Kd7 5.Kf7 Kd6 6.Ke8, White has successfully outflanked the Black king.

Number 150 was familiar and I instantly knew the correct answer, but could not perceive the reason the rook had to move to d2 instead of d1, so I tried Rd1 against Stockfush. Again, simple opposition gives Black a draw.

White to move

1.Rd2! wins 1...d4 2.Rd1! Kd5 3.Kd7 Ke4 4.Kc6 d3 5.Kc5 Ke3 6.Kc4 d2 7.Kc3 and the rook captures the pawn on the next move. After 1.Rd1 d4 2.Kd7 Kd5, White can try 3.Rd2 Kc4 4.Ke6 Kc3 5.Rd1 d3 6.Ke5 Kc2 and the rook must be given up for the pawn.

My error in number 156 stemmed from failing to recognize the possibility of Black achieving a Philidor position.

White to move

Black got a Philidor-type position after 1.Kc4 Rg8 2.Kc5 Rg1 3.dxe6 Rc1+.

White wins easily either with 1.dxe6 fxe6 2.Ra7 Rf8 3.Ra8+ Kd7 4.Rxf8 or with 1.Ra7 straight away.

Thomas Engqvist's Study Plan

"Less is more", writes Thomas Engqvist in 300 Most Important Chess Positions: Study Five a Week to be a Better Chess Player (2018). His 300 positions are more positionally oriented than the 300 in Lev Alburt, Chess Training Pocket Book: 300 Most Important Positions and Ideas, 2nd. ed. (2000) and also include a larger number of endgame positions. I wrote about the first position in this book the week after I acquired it in 2019 (see "A New Book and a Morphy Game"), but have not been following his recommendation to study five per week. Nor have I followed any other disciplined training regimen. Even so, Engqvist's book has been a frequent reference and valued.

Study by J. Hasek

Although Engqvist asserts, "the less you know the less you'll forget. ... it will be easier to remember 300 positional ideas rather than, let's say, 1000" (7), his 300 series now constitutes a trilogy and contains 900 positions. The motivation to select five per week for serious study has been growing for me.

The fourth endgame position in 300 Most Important Chess Exercises (2022) caught my interest last Friday and again this morning because I set it up incorrectly Saturday morning while trying to show the critical idea to some youth players at a chess tournament.

At first glance, White's task appears hopeless (see photo). Going straight for the a-pawn leads to stalemate. Going after the f-pawn leads to a trebuchet (a position lost for White). The draw is better than a loss, but I had the sense that White should win this with a technique I was missing. After some trial and error playing against Stockfish on the iPad, I found the win, posted on social media the position that arose after two moves, and mentally questioned a response that identified the solution as one of taking the opposition.

The exercise is a study composed by Josef Hasek and published in Deutsche Schachzeitung (1928). Engqvist identifies the themes as "triangulation and corresponding squares" (222). I think it also bears similarity to the famous Reti study in which White draws by attempting simultaneously to accomplish two impossible tasks (see "Endgame Calculation"). Such is the power of the double attack.

Stripes, J -- Stockfish
14.04.2023

1.Kc6 Ke5 2.Kc7 Kd5

White to move

3.Kd7!

Yes, this move seizes the opposition and prepares an outflanking maneuver. But triangulation is a more precise term for White's idea.

3...Ke5

If Black tries 3...Kc5, the diagonal opposition is best because it threatens the f-pawn. 4.Ke7! From the initial position, White cannot imagine going after the f-pawn, but now this threat is what makes it possible to gain the a-pawn without getting trapped on the a-file.

4.Kc6

Because of triangulation, the position that has been reached is the same as after the first move, except that it is Black's move.

4...Kxf5

White to move

5.Kb7

Other moves draw. Black's king is now too far away to trap White's king on the a-file and White's pawn promotes long before Black's can make any progress.

1-0

300 Most Important Chess Exercises is divided into four sections of 75 exercises each. The first two sections are opening and middlegames with tactics emphasized in the second set. The last two sections are endgames, again with tactics emphasized in the final set.

I could see myself developing some consistency with Engqvist's study plan of five positions per week if these five come from all three books, instead of always following only one of them. Coming up soon in Exercises is the following position, the sixth endgame exercise. 

White to move

I have seen this position in other books and have trained with this it on chess.com. I know the idea--corresponding squares. Nonetheless, this is an exercise that I find difficult. The cases of correspondence which must be worked out encompass more than half of the board.