Examples

Introduction

Oops has a large container full of chess positions, about 10 to the power of 120, which can be reached starting from the initial position with White to move (the so-called regular chess positions). They are hard to count. The age of the universe is not enough if you count one position every second. Because that yields – depending on the age of the universe of about 12 to 15 billion years – only 12 x 1000 000 000 x 365 x 24 x 60 x 60 or approximately 10 to the power of 17 positions. A small number compared to 10 to the power of 120. Some positions, such as the following

A non-regular Position if it is White to move.

do not belong in Oops container. They must be placed in another container, for non-regular positions, but that does not change anything fundamental.

A (=/+]-Position

For a definition of the (unbalanced) brackets s. Dictionary.

The following position (Exercise 2-98 by D. Gurgenidze) comes from the book „Recognising Your Opponents Resources – Developing Preventive Thinking“ by M. Dvoretzky.

Diagram 1: (=/+]-position

In this position, White is to move. Oops magnifying Zermelo-glass (5-pieces end game tablebase!) indicates a draw, i. e. =. However, Black threatens to win: +. So we have a (= / +]-position, because Black has moved. Could Black reach this position by reversing the right to move, than we would have a [= / +)-position: Such a position is called – do not be frightened – a nullzug-position with advantage for Black. However, switching the right to move works only by support of White. Unfortunately, as supposed in the cited book, there is no way for Black to accomplish that. Winning manoeuvres exist, if at all, only in positions already won (i. e. as a result of an enemy error!).

 With 1.Ra3+, the only move of a total of 22 options that keeps a draw, Black has no choice but to put his king on b1 or b2. Dvoretzky mistakenly gives this move a question mark, although this move, like Kb2, is a drawing-move. After the further moves 1… Kb2 2.Rg3 e3 3. Kd5 Kc2 4.Ke4 Kd2 5.Rh3 it comes to the following position (the coloured squares can be ignored at first, and on squares with a cross the king of the side not to move must not be placed – here the white king):

Diagram 2: [-/=)-position

If White would have played 2.Rg3 in the main variant, instead of 2.Rh3? (rightly marked with a question mark because it is a losing-move), then after 2… e3 (or c2) 4.Ke4 Kd2 the same position as the previous one is reached, but with White to move:

Diagram 3: (-/=]-position or one sided zugzwang-position with White to move

In this position, Black has (after White’s incorrect second move 2.Rh3) on every move of White a winning-move. Dvoretzky now notes: “ … the winning manoeuvre became possible only because the white rook had to leave the h-file.“ This is not correct, and it sounds as if Black just had to find the right manoeuvre to win: The mistake lies in the fact that the move 2.Rh3 is an error. The error width is only one half-move (and not a story!).

Also Dvoretzky’s comment that the following diagram shows a mutual (reciprocal) zugzwang-position is wrong. It shows a one sided zugzwang position with White to move, and only in the previous position (Diagram 3) with white to move.

Diagram 4: (/=)-position

Now to the coloured fields. If the white king in diagram 2 is on one of the green squares, then black to move is winning. If the king stands on the only yellow square e4, then he can keep a draw. 

In diagram 3 White can only draw, if his king is placed on one of the six yellow squares close to the black pawn. On all other squares the white king is lost. 

Diagram 4 summarises the results of diagrams 2 and 3 using the colour code explained here. The white king on e4 is in an exceptional position: White to move is losing. Black to move draws. So it is a (-/ =)-position. In the case that it is White to move, it is a one sided zugzwang-position (s. Diagram 3). 

Marginal notes about the margin of a chessboard 

The influence of the border of a chessboard on the objective value of a position can be shown by the coloured squares in diagrams 2 to 4. At the same time, the diagrams illustrate the problematic of evaluation a position by splitting it in positional and material factors.

Diagram 5

If the entire complex of pieces in the following diagrams 5 to 7 is moved with the white king as a guiding piece (not only, as in the diagrams 2 to 4, the white king), the value of the new position changes like the coloured fields Show. With a white king on e4 White can keep the game drawn independently from the right to move. All other locations of the complex of pieces are won with black to move. Obviously, statements like, the value of a pawn increases with proximity to the promotion square, are not always valid!

 The next diagram shows the value of a position in dependence of the location of the complex of pieces with White to move. If the white king as the leading piece of the complex is placed on a red square, White is losing. If, on the other hand, the king is placed on one of the yellow squares, White can hold a draw.

Diagram 6

Diagram 7 finally summarises the statements of the diagrams 5 and 6 in one diagram using the colour code from the menu item Dictionary.

Diagram 7

A 7-pieces end game with 6 different pieces

Oops would like to illustrate the problem of storytelling by a 7-pieces end game with 6 different pieces: 2 kings, 1 queen, 1 rook, 1 bishop, 1 knight and 1 pawn. It is a (= / +)-position: White to move can keep a draw, Black to move is Winning.

Diagram 8: A (= / )-position

If the whole complex of pieces is moved with the white king as the guiding piece, Oops finds a nice story (or rule): The closer the white pawn is from his promotion square on the 8th row (Oops favourite row for pawns), the better for White. However, Oops would not put it that way because there are too many exceptions. The rule would lose its generality (or the story its meaning). That’s why Oops is sceptical about rules.

Diagram 9: Type of position as a function of the position of the complex of pieces (leading piece: White´s king)
Diagram 10: Value of the position with White to move depending on the position of the complex of pieces (leading piece: White´s king)
Diagram 11: Value of the position with Black to move depending on the position of the complex of pieces (leading piece: White´s king)

It gets even crazier when Black has to answer the question where to put his king, so that he is not in a lost position, if he has to move (see also the game Nimzowitsch – Capablanca, NY 1927 , before the 36th move of Nimzowitsch). Of the two squares c6 and f3, c6 is probably the most understandable square. If the black king is put on this square, black is winning independent of the right to move. If the black king is put on f3, it is not that easy to explain why Black is winning. At least for Oops.

Diagram 12: Value of the position depending on the position of the black king

If things are already so complex in positions with only 7 pieces, what is to be expected of positions with more than 7 pieces?

The following diagrams 13 and 14 show the value of the position in dependence of the location of the black king from White´s and from Black´s point of view. In diagram 13, the black king must not be placed on any of the squares b8, b6, a1, or g5 when passing the right to move to White. Everything clear? Finally, in diagram 14, the black king must not be placed on one of the squares a5, b8, c8, e8, e7, f6, g7, h8 or h2 when passing the right to move to White. This is not immediately obvious, right?

Diagram 13: Value of position with White to move depending on the position of the black king
Diagram 14: Value of position with Black to move depending on the position of the black king

Oops recommends taking a look at the notation of a 7-pieces end game at master level. Not infrequently, the value of the position changes several times until the one with the happier hand wins. Of course, annotators know the “true“ reasons, principles and plans based on a lot of variants. For 7 or more than 7-pieces. Oops does not believe it.

 In the fog or jungle of variants 

Oops, the sceptic, says, what’s up with the magnifying Zermelo-glass? In most of the practical significant cases it does not resolve positions in winning, drawing or losing moves for each side. And that’s a good thing. For we want to have our chess game virtually insoluble at whatever level of play. But without contradictions – or fairy tales – in commenting, just as a chess game would look like under a Zermelo-corrected magnifying Steinitz-glass.

 For the purpose of demonstrations Oops refers to his favourite book by R. Reti, “Masters of the Chessboard“. It’s well advanced in years, but the way chess is taught and games are commented in this book is still exemplary.

 As an introduction Oops chooses Richard Reti’s credo: “There is much more chess truth in the ideas than in the variants.” Oops basic attitude is: That may be, but if the current chess theory is so full of wonderful principles, why is it only in the rarest cases possible to identify the ultimate mistake in a game? – A single mistake tilts a game. A sequence of moves (plans, stories) can not explain it. On the contrary variants (principles, plans, etc.) obscure finding the half-move long errors.

Nimzowitsch – Capablanca [B12], New York, 1927

1.e4 c6 2.d4 d5 3.e5 Bf5 4.Bd3

Diagram 15

At this point in the game, Reti takes stock of the positional characteristics in favour of Black: Space (here White has more of it), piece activity (after swapping bishops f5 and d3 White is left with his bad bishop, Black with his good one) and field weaknesses (after swapping bishops and the typical pawn break f2-f4-f5 White remains with weak squares in his own camp). Reti therefore sees black more in advantage. But since there are no small advantages, only a relative advantage can be meant here. But that does not change the absolute value of the position (even if this value is not known).

4…Bxd3 5.Qxd3 e6 6.Nc3 Qb6 7.Nge2 c5 8.dxc5 Bxc5 9.0–0 Ne7

Diagram 16

The move 9 … Ne7 allows White to swap his knight on c3 for the strong Black Bishop on c5. After this exchange white retains space advantages as well as attacking possibilities on the king side, while black occupies the central white squares and holds pieces on the queen side.

10.Na4 Qc6 11.Nxc5 Qxc5 12.Be3 Qc7 13.f4 Nf5 14.c3 Nc6 15.Rad1

Diagram 17

15…g6 

Here, Reti points out, that even 15 … h5 would have captured the (relative) position advantage achieved so far, and makes Capablanca’s style responsible for the move he played: “… that he clearly recognises small nuances as real advantages and their exploitation is a safe and perhaps not too troublesome matter of expedients.” However, since something that does not exist (small advantages) can not add up to a victory, this statement is an empty phrase. Reti continues: “But sometimes playing in this manner Capablanca had lost even games that he could have won, or flattened won games to a draw.” But you can only win a game by an error of the opponent (not by the addition of small advantages, or by a brilliant ingenious move). Also Capablanca can not lead a game from the beginning to victory. After an error by the opponent, he could have actively converted the game into a draw position by a “small” error (a “big” error would have put him in a losing position). 

16.g4 Nxe3 17.Qxe3 h5 18.g5

Diagram 18

If Reti no longer speaks of a white space advantage, but of a weak and holey pawn structure with strong, white squares for Black, then something essential must have happened, right? Reti calls this a transformation of one advantage into another. 

Oops is told that during a chess game there are transformations from positional advantages into material advantages and vice versa. But one has to think about that such a separation is artificial. A crutch in the jungle of variants with their always concrete moves. Only at the end of a game, in case of a mate, it is clear that somewhere in the variants, during some transformation, one or more flaws must exist, but where exactly? Oops marks the possible moves in the variants with the sign “?!”, and uses – long live contradiction – a chess engine based on a magnifying Steinitz-glass. It may seem strange in the eyes of masters, but they have to get used to the fact that correct moves (according to the magnifying Zermelo-glass) often come across as strange and incomprehensible moves, appearing flawless under the magnifying Steinitz-glass. 

18…0–0 19.Nd4?! Qb6 20.Rf2 Rfc8 21.a3 Rc7 22.Rd3 Na5?! [22…Nxd4!?] 23.Re2 Re8 24.Kg2 Nc6

Diagram 19

Reti: “Capablanca now discovers the correct plan …!” He uses the “weak” white squares c4 and e4 as a hub for his heavy pieces, to finally penetrate the second and first row in the white camp with his queen and rooks. That’s all very well. But there is still no indication of a critical flaw from White that turns this plan into a mating attack. 

25.Red2 Rec8 26.Re2 Ne7 27.Red2 Rc4 28.Qh3 Kg7 29.Rf2 a5

Diagram 20

30.Re2?! Why send the queen offside? On e3, the queen might have taken the white plan to absurdity. [30.Qe3!?=] 

30…Nf5 31.Nxf5+ gxf5 32.Qf3?! Kg6 33.Red2?! After Red2 the game might still be in balance. 33…Re4 34.Rd4 Rc4 35.Qf2 Qb5

Diagram 21

The critical Position, probably a (= / +)-position. Black threatens to win. Using Rcxd4 or Rexd4. However, White has at least one drawing move that neutralises Black’s threat. Oops asks to compare this position with the one after White’s next move. Both positions differ only in the position of the white king and the right to move. Two differences which are known to be crucial.

 36.Kg3?

Diagram 22

Possibly an error changing a (= / +)-position into a (- / +)-position which is won by Black independent of the right to move! Oops now refers to the diagram 13, where the value of the position in dependence of the location of the black king and the right to move in a 7-pieces end game position is shown by coloured squares – Oops asks: On which square, for example those squares close to b7, is the black king safely placed with White to move? Perhaps a master of chess is able to see with a single look the squares which are safe for the black king in diagrams 13 and 22. Oops, does not recognise them!

 36…Rcxd4 37.cxd4 Qc4 38.Kg2 b5

Reti: “White´s queen and rook are tied to protect the the second row and the pawns on d4 and f4 so that they can not move. We will see how Capablanca exploits this to decide the game by zugzwang.” Alas: Nobody can force Nimzowitsch into zugzwang, not even Capablanca. Nimzowitsch must have done this by himself. Through an error. This probably happened by Nimzowitsch on his 36th move. That’s not certain, but Reti’s reasoning is wrong! The positions which he calls zugzwang-positions are not of the type ( / ), ( / =) or (= / ), but of type ( / +). This has as little to do with zugzwang, as the regular right to move can not be called zugzwang. At best, Reti might have meant “outgoing of good moves“, which is only the case in lost positions with only losing moves. But if Nimzowitsch transfers his right to move to Capablanca, Nimzowitsch is still losing.

 39.Kg1 b4 40.axb4 axb4 41.Kg2 Qc1

Diagram 23

A ( / +) – position, no zugzwang-position, but a winning-position for Capablanca independent of the right to move.

 42.Kg3–+ Qh1 43.Rd3 Re1 44.Rf3 Rd1

Diagram 24

Reti: “A tempo move, as White is again in zugzwang.” Oops: The position is still a ( / +) – position, so no zugzwang-position, but a winning-position independent of the right to move. And what is a tempo? Passing the move order to put the opponent into zugzwang? Oops, bear in mind that no one can be brought into zugzwang! 

45.b3 Rc1 46.Re3 Rf1 0–1