﻿ Chess through a magnifying glass - Zermelo meets Steinitz

#### QUESTIONS

1. Who is Zermelo? A
2. What if the thesis that the starting position of chess is a drawn position, is not true? A
3. What is a mistake? A
4. What is zugzwang? A
5. What is chess? A
6. Chess and Statistics: A Contradiction? A
7. Are there simple, and at the same time effective and basic procedures - or strategies - in chess? A
8. What help is a magnifying Zermelo-glass in practice? A
9. What is the point of the coloured diagrams, causing confusion? A
10. Often you hear comments like "White (or Black) plays to win". Is that nonsense? A
11. Which statements form the core of the magnifying Zermelo-glass? A

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Who is Zermelo?

German mathematician, b. 1871 in Berlin, died 1953 in Freiburg, Breisgau. He proved the so-called Zermelo theorem, published in 1913 i. a. in „About an Application of Set Theory to the Theory of Chess“, Proceedings of the Fifth International Congress of Mathematicians, p. 501-504, 1913.

This theorem is essential for the arguments on this web site, although the theorem - like his creator Zermelo - probably nobody misses. It seems to be trivial that someone who is said to be winning must have a strategy to realise it. Sure, but Zermelos theorem had to set the course for this. In a game like chess, either White has a winning strategy, or Black has a winning strategy, or both have a strategy guaranteeing a draw. What these strategies look like in practical play is not stated. This is where the imagination of the masters comes in, but they intentionally ignore, knowingly or unknowingly, Zermelo's theorem.

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What if the thesis that the starting position of chess is a drawn position, is not true?

Then two alternatives to this hypothesis must be considered, "At the beginning of a chess game, White wins", and "White loses".

In the first case, all opening books, in which you can read (after a few moves): White is slightly better or similar statements, could be thrown in the garbage. At the start of the game White has at least one winning move. Zermelos´ theorem guarantees, that White always has a winning move after every move of Black. A potentially difficult task, because in winning positions there could also be drawing or losing moves. In principle, however, the task can always be solved in favour of Weiss. Black, on the other hand, does not need to think at all: he could throw dice in order to determine a move because he has only losing moves - with more or less short mating variants. However, he also can with a losing move in some positions - paradoxically? - threaten to win!

On the other hand, if White is lost at the beginning, than his task is simple: Now he can throw dice, and Black is spoiled for choice!

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What is a mistake?

A move is a mistake if it worsens the evaluation of a position by a half point or a full point (if the position considered permits this at all). There are no other mistakes. What should be wrong with a move that preserves the evaluation of a position?

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What is zugzwang?

A player is in zugzwang when he (to move) is lost and his opponent - if he were to move - could draw (at most). In such a situation, everyone would like to transfer the right to move to the opponent.

Both in the WWW and in chess literature, there are many examples, where the term zugzwang is used in positions whose evaluation is independent of the right to move. That is - with respect - nonsense.

In order to understand the differenz between zugzwang and right to move see f.e. Beispiel 5

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What is chess?

Chess is a two-player zero-sum game with complete information and alternate right to move. The outcome of the game is basically determined, i. e. the evaluation of any position can be preserved from the side to move till the end of the game: Drawn or (after at least one error) mate. This fact is often disregarded in the annotations of games and leads to contradictions (or statements that prove what the annotators want to be proven.) That's arbitrariness, and not funny at all.

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Theoretically yes, but practically no! Statistical methods (e. g. Monte Carlo methods etc.) are used in chess engines. With great success. But in principle they are out of place in a deterministic games like chess! There are at most winning, drawing or losing moves in a position. No more or less good or bad or otherwise attributed moves. Most of the often used special signs and symbols in chess literature belong more in the category "chess emoticons" than in the category "objectivity". In particular, if it is said that a series of moves decorated with exclamation marks leads to victory. Without identification of at least one decisive error made by one of the players, comments are nothing else but fairy tales.

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Are there simple, and at the same time effective and basic procedures - or strategies - in chess?

Sure, but with limitations, for example:

Attacking and preventing play: It is the aim of a chess to mate your opponent´s king. Therefore it is natural to manoeuvre your pieces in such a way, that there is a last check, your opponent can not escape. In return, the opponent tries to prevent that, and tries to mate your king. If the basic position of the chess game is drawn, these general "principles" will work only with the participation of the opponent (which is often forgotten in comments), the opponent must fail!

Playing for traps and prophylaxis: Oops is a fan of Mark Dvoreckij, although the comments in his chess books do not always withstand Oops view through the magnifying Zermelo-glass. This ultimately means that the annotations of Dvoreckij, as well as the annotations of many other chess commentators, are not tenable strictly speaking. This is Oops main criticism, if comments are not correct, what can they teach us? Mores?

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What help is a magnifying Zermelo-glass in practice?

It liberates us from dogmatic views of chess, and thereby stimulates us to set out on new paths. As long as it can not be proved that a seldom played move is an error, it can be played. Annotators call such moves innovations and mark it with the letter N(ew). But only if they are introduced by masters.

The chess practice is dominated by the rules and principles of chess masters, from the classical to the hypermodern and from the hypermodern to the ultramodern of today. Is this approach - that is, the view through the current magnifying Steinitz-glass - now obsolete?

Of course not! But a correction is necessary to achieve a congruence between the two points of view: Zermelos´s and Steinitz´. As long as the decisive errors in a chess game are not identified, one should be careful in saying that the „error“ was a violation of a rule or principle. Especially not if the rule or principle given for losing a game concerns a sequence of moves (or a plan). In order to show the correctness of a plan you have to know the correctness of every single move of the whole sequence (in the sense of the magnifying Zermelo-glass).

Even a threat (or counter-threat) called glue between two moves of a plan is no guarantee for the correctness of a sequence of moves (one without "holes") because: Even losing moves in winning positions can threaten to win! That sounds crazy, but is unfortunately true. Any comment (plausible explanation or story) must take this into account. If it does not, it is only of apparent utility.

In positions with many pieces it is obviously easier to tell a story, because the set of correct moves is usually quite large. It is easier to find words and move sequences in order to construct narratives and prosaic rules. With only a few pieces on the chess board, the rules become a bit sparse, but sometimes „more“ accurate (i. e. „The square rule“).

In principle, it is not at all certain whether there is a rule-based connection between two or more positions that goes beyond the rules of the game. If only because there are different ways to reach the different positions.

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What is the point of the coloured diagrams, causing confusion?

Yes and no! Clarification and confusion often occur together. Ultimately, however, information should replace uncertainties as much as possible. Looking through the Zermelo-magnifying glass brings to light things that are crucial in evaluation of chess positions, but are still overlooked or even not considered: The distance of pieces from the edge of the chess board or the radical change in evaluation of a position by displacement of only one single piece or the problem of evaluating a whole sequence of moves with the label "true". If the diagrams (s. menu item Examples) serve only one purpose, to show that it is extremely difficult to describe the characteristics of a position or the correctness of a sequence of moves or a manoeuvre in just a few words (rules, principles, manoeuvres, etc.), then they have done the most important thing.

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Often you hear comments like "White (or Black) plays to win". Is that nonsense?

Yes and no. It depends. Of course, White (or Black) may want to win. However, White (or Black) can not win without cooperation or help of his opponent. White (or Black) can support his intention to win by playing for traps, or in "quiet" positions by "kneading" his opponent. Mere waiting for an opponent's mistake certainly does not fit the „character“ of chess (but does not necessarily lead to losing thus relativising the statement heard just as often, White (or Black) lost due to „passive“ play.) It does not work, too. There must be a concrete error of the "passive" player!).

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Which statements form the core of the magnifying Zermelo-glass?

There is no difference in principle between 7-piece and 8- to 32-piece positions. In particular, the classic subdivision of opening, middle and end game positions is arbitrary. For this reason, terms should be used to describe any position (the 9 respectively - considering the right to move, 15 position types), which can be used without contradiction for all kinds of positions. That is currently not the case. The Steinitz-magnifying glass is based on terms like accumulation of small advantages, which, according to the correct Zermelo-magnifying glass view, do not exist.

In unclear positions {in those in which the Magnifying Zermelo-glass does not work, i. e. can not determine the exact positional state (X / Y) with X, Y either 1 or 1/2 or 0} are rules, whose scope is not exact know, at best heuristics that might apply, but mostly tautologies: they apply when they apply.

In practical play, we only have few options to choose a move: intuition based on acquired experience, or calculation of sequences of moves up to positions where our intuition or our experience works - for whatever reason. A guarantee for the correctness of a move, or a guarantee for the correctness of a whole sequence of moves, is only possible in such cases which end with a forced (!) mate. In all other cases, statements about the value of a move or a move sequence are pure speculation: fables, fairy tales and stories.

If no match can be won without an opponent's error, then this can not be justified by the fact that the winner has made one or more ingenious moves (to make matters worse, for example, decorated with two exclamation marks), or by clever use of the pair of bishops in order to queen a pawn, but because his opponent has made an error. Without identifying this error (of the length of a half-move) or at least speculating about it, the analysis of a game is not satisfactorily completed. Any justification that makes a special sequence of moves, a plan, rules or principles of limited validity responsible for the outcome of a game is without evidential value. In general, it is not clear what „glue“ between individual moves means - if it objectively exist at all: A plan? An idea? A manoeuvre? Or just a guess, a belief, a speculation?

Examples of frequently occurring, at least questionable formulations, partly using unclear terms. Oops uses his favourite author M. Dvoreckij because the playing principles expressed there (case play, prophylaxis, exclusion) under the Magnifying Zermelo-glass still look quite good, but nevertheless are problematic in concrete cases (The following examples are in the book (M. Dvoreckij, Recognising Your Opponent's Resources - Developing Preventive Thinking, Russell Enterprises, Inc., Second Printing 2016, short: RYORes-MD):

I. White lost quickly, without making any obvious positional mistakes. RYORes-MD, p. 250

Oops comment: Completely and utterly wrong. It does not work without an error. But what single move was the decisive one?

II. Only playing for zugzwang helps. (in position 2-17 of RYORes-MD, p. 168)

Oops comment: Nobody can be put into zugzwang without making an error before by himself.

III. A beautiful shot, reversing the evaluation of the position. RYORes-MD, p. 172

Oops comment: There are no ingenious winning moves. The evaluation of the position was turned upside down by an error of the opponent.

IV. The move 30.Td6!! sets insoluble problems for Black. RYORes-MD, p. 174

Oops comment: Only, if 30.Td6!! is a winning move. But in this case Black (!) must have made an error before!

V. It is important not to let his opponent consolidate, but to constantly create threats. RYORes-MD, p. 181

Oops comment: What is a threat? What means consolidation? There can be winning threats and consolidating moves in lost or equal positions. But they can only be decisive, if the opponent cooperates.

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