Columns | January 04, 2011 17:23

The eternal argument

Chess, of course, is an abstract game. Its ultimate, objective truth is probably more mathematical than intuitive. Still, the game has so many subjective sides that it's almost impossible not to have arguments about the relative aspects of chess, such as the value of moves, variations and even rules. Which is just great.

The Creation of Adam, a section of Michelangelo's fresco Sistine Chapel ceiling painted circa 1511 In a recent blog post on ScienceBlogs, evolutionist David Sloan Wilson compares creationists who "protest that it is unfair for them to be ignored" to a chess player who "insists on continuing after his king has been taken." After all, according to Sloan Wilson, science, like chess, is a "contest situation":

The idea that it is unfair to be declared a loser and to be made to retire from the field profoundly misunderstands the nature of fairness in all contest situations. (...) In the ideal scientific contest, alternative hypotheses make different predictions that can be tested with empirical observations. When the predictions of a hypothesis are not confirmed, it is declared a loser and is made to retire from the field. New hypotheses are always welcome to enter the competition, including modified versions of rejected hypotheses, but science without losers would be as pointless as chess without checkmate and basketball without the final buzzer.

First off, I wholeheartedly agree with the above reasoning in principle: a discussion can actually - despite possible good intentions - be lost on pretty objective grounds. It's possible to rule out a perspective even though that perspective may be, in the eye of the beholder, noble or even religious dogma. Even so, I couldn't help thinking of the numerous times I've heard chess players (including myself) proclaim a win (usually by the opponent) to be totally "unfair". I've always felt that declaring a win to be unfair is a bit like declaring that losing itself can be unfair. The truth is, of course, that chess players -much like creationists - continuously lose despite good intentions. In fact, they often lose despite superior play! Imagine the last time you threw away a beautifully played game by one silly inaccuracy and you know what I'm talking about. The difference, I think, lies in the fact that chess, while ideally comparable to science in certain key aspects, is most definitely not only an objective enterprise at all. It is also a game of human emotion where justice and fairness can take on different meanings. (There are even chess players who claim it's "unfair" not to resign in a lost position.) In fact, I consider this one of the greatest beauties of playing chess: the constant tension between objectivity and subjectivity. Of course, it's easy to dismiss any talk of "unfairness" after a (lost) game as simply being a case of cognitive dissonance. After all, the winner is always right, no? Well, that's a valid point of view to a certain extent, but it's also a rather one-sided perspective. I once read an article by the philosopher Bill Martin in which he claims that if a chess player wins with the theoretically "absurd" move 1.h3, the result somehow makes this opening move less "absurd": an extreme case of the "winner is always right" position. Any chess player, of course, knows that things just aren't that simple. A more realistic approach would be the well-known assertion that he who makes the last mistake loses, but in any case, I think "unfairness" in chess is not such a straightforward concept as Sloan Wilson assumes it is. The idea that the course or the result of a game can influence our perception of its past is, of course, quite common in chess, and it's often a useful approach in the development of opening theory (though not when applied in the manner Martin applies it). But there are also wonderful situations in chess where the past and future are so intermingled that it's impossible to make a distinction between the two. The type of study where this idea plays a central role is retrograde analysis. I first got acquainted with this type of chess study after reading Tim Krabbé's superb book Chess Curiosities. The following position is featured in his book. Mate in 2 W. Langstaff 1922 In chess studies, castling is in principle allowed, unless it can be shown to be illegal. However, capturing en passant is only allowed if it can be demonstrated to be possible. Langstaff's study is based on this principle. White would like to play 1.Ke6 followed by 2.Rd8 mate, but then Black plays 1...0-0! and there is no mate. But wait, if Black can still castle, then what was his last move in the diagrammed position? It couldn't have been with the king or the rook (otherwise he wouldn't be able to castle!) so it could only have been 0...g7-g5 (the pawn had to come from g7 because from g6 it would check White's king.) So, White can just play 1.hxg6, right? Then 1...0-0 allows 2.h7 mate. Not so fast. After 1.hxg6 Black simply says his last move was 0...Rh7-h8 and there the legality of the en passant capture cannot be demonstrated. This of course shows White could have played 1.Ke6, but then Black simply castles and claims 0...g5 was his last move, ad infinitum. In Krabbé's words:

This leads us to the baffling conclusion that if Ke6 is the key, hxg6 isn't - but if hxg6 is, Ke6 is not. If White attempts one solution, Black has a defence which shows the other would have worked. Or to put it differently again: it is perfectly true g7-g5 and Rh7-h8 cannot both be Black's last move, but White (or the solver) has no way of determining which one was. Whoever feels giddy now should consult his local syllogism breaker.

(Langstaff's problem is actually filed under "partial retrograde analysis." The most famous composer in this genre is no doubt Nenad Petrovic, whose crazy 1965 study is heavily discussed in Krabbé's book. Those interested in retrograde analysis should definitely try to get their hands on Raymond Smullyan's two books The Chess Mysteries of Sherlock Holmes (1979) and The Chess Mysteries of the Arabian Knights (1981). They may also want to take a look at the Retrograde Analysis Corner website.) The relative side of chess is also felt, in a more mundane way, in chess annotations and publications. When does a move deserve an exclamation mark or a question mark? In the light of the "ultimate truth", it's tempting to assume a move is either losing, drawing or winning. A different point of view would be that a move either maintains the current status quo, or changes it, and that the degree to which the move changes the evaluation of the current situation determines whether the move should get !, ?, !?, ?! or even ? or ??. Others maintain that the symbols we attach to moves should also be used to explain entirely subjective aspects of the game: in this case, a perfectly normal move can be "bad" even though it doesn't spoil a winning position, simply because it makes the win harder or because it allows the opponent to set one final practical trap. (Yet another perspective is the one often chosen by kibitzers on internet chess servers, namely to attach question marks to any move not directly recommended by their engine.) In the end, it's all largely a matter of taste. Indeed, this is what makes chess such an attractive game for me: we're all allowed to have our own opinion on these matters. Personally, I think a chess commentator should try to be as "objective" as possible while not neglecting subjective or psychological aspects of the game's progress - but it has to be done with caution, and in moderation. People who reward their own moves with many exclamation marks and their opponent's moves with many question marks, and somehow manage not to win the game in Kasparov-like style, are definitely suspicious in my book. But there are many exceptions - some have to do with the credentials or the credibility of the commentator, some have to do with style. Alekhine and Karpov, for example, have a reputation for praising their own moves more than the ones made by their opponents. It's easy to forgive them, but with lesser gods we may not be so lenient. (I tremendously enjoyed a recent discussion on ChessVibes about this very topic, even though the commenters didn't reach a conclusion in the end.) Things seem to become less personal - less subjective - however, when the rules of the game are involved. Aren't the rules of chess fixed and undebatable? Not really. Anyone who's ever read International Arbiter Geurt Gijssen's column An Arbiter's Notebook on ChessCafe should know this is another huge misconception about chess. A rule may be fixed in that it is written out in the FIDE Handbook, but its interpretation is often subject to heavy debate. Bogolyubov-EuweChess rules have evolved over time, too. What's now considered to be rude or even against the rules may once have been perfectly acceptable. Just a few days ago I saw a great example of this phenomenon in a video released by the Dutch TV broadcast corporation VPRO showing Max Euwe and Efim Bogolyubov playing blitz in 1928. I noticed that not only did the two giants forget to press their clocks on several occasions, but that they also - shamelessly, we would now add - used both hands while moving the pieces and pressing the clock. Next time someone complains about this as a clear case of bad sportsmanship, it might be an idea to refer him back to the habits of the Fifth World Champion. Even some of our chess rules are largely subjective. Isn't there anything objective in chess, then, except its ultimate (and hitherto unknown) Truth? Surely the massive body of chess opening theory based on knowledge accumulated since the early 1500s - arguably the most impressive achievement in chess history - radiates more objectivity than anything else? But even here, things become fuzzy once you start thinking about it. What do we really know about chess openings? Can we finally say that the Ruy Lopez is "better" than the Italian or the Scotch? Isn't it all, again, just a matter of taste? Many years ago, a World Top Ten player told me the Ruy Lopez was "just a draw" after 3...a6 4.Ba4 Nf6 5.0-0 Bc5. This was, of course, the latest fashion then. I'm sure he thinks differently now. How many times has the King's Indian Defence been declared refuted? Doesn't the QGD always turn up in World Championship Matches, despite its unpopularity in tournament practice? Isn't it just a matter of time before the elite starts playing the Nimzowitsch Defence (1.e4 Nc6), as one of my club members likes to say? I don't want to belittle the progress we've made so far, but it seems to me those favouring Fischer Random chess are simply wrong when they make the argument that modern opening theory has killed our ancient game. There's still plenty of room for creativity and, indeed, subjectivity. Why don't they all just start playing - well, perhaps not 1.h3, but 1.Nh3 which, contrary to what Bill Martin thinks, doesn't strike me as "absurd" at all. The well-known Dutch master Philip DuChatel was quite successful with this move in the 1970s and 1980s. Surely the fact that nobody plays it currently, doesn't mean it should be regarded by definition as inferior? I think anyone who annotates it with ?! either isn't being objective or is simply being unfair. And the good thing is: we can keep arguing about this for as long as some supercomputer doesn't solve the game for us. What a great thing to look forward to.

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Arne Moll's picture
Author: Arne Moll


saturnz's picture

good article, I would have prefered it if the author somehow generalised the ideas to life in general, and not focused on just chess, since the lessons we learn from chess are easily applicable to that of life.

burnett's picture

Very pleasant reading so soon after the new year hangover. Happy/creative 2011!

Castro's picture

Yes, your revolt is understandable. You are right, but not because you can have two turns at solving it! :-) That's an hilarious good answer to those malicious confusion-throwers! But...

(Please see the discussion down...)

Castro's picture

The anti-anti-confusion hilarious counter-argument could be "If you can have two goes at solving, I can have two (also different) goes at defending, and now I say my last move was g5". Then you would be allowing entering the autor's "ad infinitum" confusion wish. I prevent that.

Anthony's picture

Chess is a result driven game. The goal is to mate the opposition. He who succeeds wins. Deservedly.

The confusion over 'unfair' results comes from the fact that each game involves a number of moves, about 40 on average. People who feel the result is 'unfair' probable payed on average better moves for a large part of the game. But a blunder, or a few second rate moves ruins the average over the entire game, resulting in a game played worse.

From my own experience I know it felt unfair if I was better during most of the game. I often ruined games having mentally already chalked up the point. That felt unfair. But this is merely subjective and actually delusional.

Mate, flag or surrender ends the game. Not the belief it was already won. The lower quality of the moves as a result of this faulty mindset is not unfair. It is a handicap that must be worked on.

Win's picture

Congratulations on your text. First class reading and a food for thought too!

I admit that myslef I regar chess as a highly objective game. Now I see its a bit more complicated than that.

Still I would not agree with few comments you made. Primarily with this statement:

"In fact, they often lose despite superior play!"

This is simply wrong to me. Its like saying that a driver who beat all the guys on the long rally but he made a childish mistake on the last very simple turn is somehow better. Truth is - this mistake cost him more than all he did to be ahead of the field. Its the same in chess. What you really need is to "add" all mistakes. If you make one which impact is much bigger than the impact of all of your beautiful ideas before you just lose.

Think of it in another way. If top GM blunders a piece despite playing an otherwise good game is he considered a moral winner? No, everybody is just saying that he made an extremely stupid move. Why we dont measure amateurs in the same way? Why amateur who played a good game and then spoiled it with one blunder is suddenly said to play this game better than his opponent?

"better despite blunder" theory also neglects one very important aspect of chess (and any other game). As much as knowledge and experience are important they are not the only qualities of a good chess player. Determination and focus are just AS IMPORTANT as pure chess skill.

test's picture

White allowed mate ten times but black never noticed. Black allowed mate once and gets mated. Who played the better game?

Mekhanik's picture

Errr, white. If black missed mate ten times he clearly deserves to get mated himself.

noyb's picture

This isn't even an argument! The player who wins played the better game. Period. That's why he is declared "the winner." He may not have played well, but in order to win you MUST have played better than your opponent, else your opponent wouldn't have lost.

kakashi's picture

There are other ways of looking at it. for example, if you have a better position out of the opening, and a winning position after the middlegame, it can be said that you played these phases of the game better than your opponent, even if your opponent wins because you blundered in the endgame. The opponent played the better game because he won, but you played the better opening and middlegame. Its a struggle between the subjective power of the many superior moves you make and superior positions you acheive vs. the one, solitary, game losing blunder.

test's picture

If I manage to swindle my opponent in a totally lost position after playing a bad game: I am still happy. But I won't claim I played the better game.

Marius's picture

Using both hands to play, is not only "bad sportsmanship", it is a violation of FIDE rule 4.1. And even chess rules that are "largely subjective" (which are all of them!) have to be followed!

kakashi's picture

The rule might not have been in place yet. If it was, it might not have been very widely known, seeing as FIDE was formed in 1924, just 4 years before this game. It was the 1920's, its not like they could just announce the rules on their webpage.

lefier's picture

Interesting about the relativism of chess openings.
One shouldn't be too dogmatic about the 'best openings', but be willing to study it's possibilities both objectively and as a door-opener to tactical play.
In this respect, among the top-players, Magnus Carlsen seems to do quite a lot of research, and is certainly willing to follow this relativistic approach.

Castro's picture

If you and Arne are right about the actual wording of the rules, then the problem should indeed be accepted as normal direct mate-in-x problems (and with a unique solution also), by the folowing reasoning: Castling is allowed, because it can't be proven to be illegal. Ok, that implies en passant to be proven to be legal, but that is precisely what the demand of 0-0 being legal whenever not impossible does! That could never be at Black's will! :-)

In fact, those rules are not ok. As I tried to explain, the rule that makes sense is no-castling-no-en-passant-unless-stated (and never in conflict, of course), and save exotic curiosities for exotic fields.

If, by "castling in the solution is allowed unless it can be proven to be illegal" is to be understood as "If not impossible, legitimacy of castling is uncertain", THAT would make things even more absurd, and it seems what is incredibly happening! Otherwise this problem should be considered "normal", by those rules.

Frits Fritschy's picture

In chess problems and endgame studies neither black or white has a will. The composer has. He makes it interesting for the solver: castling seems possible in a given position, but can you deduce that it is really so? En passant capture looks possible, but can you prove that black's last move was g7-g5? Many wonderful compositions have come out of this. Chess puzzles have a right to eccentricity, they thrive on it!
And when that does lead to inconsistencies, even better, that leads to philosophical mind breakers like the Langstaff problem.

Castro's picture

No one is denying those pleasures! I do love those eccentricities, you misunderstood me.
It's somewhat difficult to me to fully explain my idea, so I'll just say an example:
Do you remember those marvelous problems with some pawn promoting to an opponent's piece, or castling verticaly with a never moved, newly promoted rook?
Do you defend that the rules of chess should have remained that unclear? Have you heard about fascinating "chess" puzzles that require other pieces?
When the rules have issues, you get more than you expect. That can be good, but just for amusement. And I hope they'll never end!
The rule "0-0 and no e.p." is not a good one. It may amuse, but is contrary to reason, logic and economy.
Exactely! This Langstaff (and other) position(s) are precisely exploring the flaw in those rules. They prove what makes sense, namely that there are legal chess positions with "0-0 implying e.p.", which is the exact negation of the rules that absurdly seem to be "0-0 and no e.p. by defect".
In a (serious/legal) problem position, every legality of moves should be straightforward, and that is only achieved by forbiding special possibilities not literaly stated.
Leaving 0-0 as legal if not disproven by the position is asking for trouble, like if having a 3-fold repetition unless disproven in a draw study: White simply has to prove that the starting position could have happened for the third time, and claim a draw without moves :-)
Once Breyer published a position and asked the readers "Who stands better?" After long and difficult analysis, they discovered Black should win, but then Breyer informed that White (to play) draws, by "simply" demonstrating that there must have been 50 previous moves without a capture or a pawn move!

Frits Fritschy's picture

There is a clear difference between a possible en passant capture and possible castling in a composition: in the first you have to prove that something did happen to use it in the solution, which is doable, in the latter that something did not happen - normally impossible, because you can invent prove games either with or without rook or king moves.
For the rest: There is journalism, like competition chess, there is science, like in opening theory, there is prose, like in endgame studies, there is poetry, like in problems and there is experimental poetry, like in fairy chess problems, helpmates and even serieshelpstalemates (they really exist, look at the christmas puzzles of
All have their own rules and conventions, and all have their own beauty (and can be excessively difficult...). In the end, when it comes to compositions, it's the composer that sets the rules. If the result is pleasing to anyone, the composition is a succes.

Castro's picture


1. Beautiful analogy with writing! Only in what you call prose and poetry (studies and problems) you mustn't have conflicting rules. If you simply say that special possibilities are NOT there, by defect (that is, unless stated), you stand no chance of confusion.

2. "0-0 unless disproven" conflicts with every objectivity, namely with "no e.p. unless proven (or stated)", as Langstaff briliantly proves. Its a real FLAW in the rules!
If the rules are "0-0 AND no e.p.", it is potentialy possible (pleonasm? :-) ) to set a legal position where one of them depends from the other by a conflict-generator implication, namely "0-0 IMPLIES e.p" or, the same, "no e.p IMPLIES no 0-0", or, identicaly, "e.p OR 0-0". These 3 forms are identical, and Langstaff could materialise them. They are the NEGATION of the rules' demand, because that demand is absurd. There is a reason for having rules by default, with no ambiguity, and NO need to disprove anything.
One could ask GM Navara. He probably knows, as he studies Logic. I know I'm right!

3. In fact "0-0 unless disproven" conflicts with EVERY other rule about special posibilities, not just with "no e.p. unless proven"! It also conflicts (potentialy) with "no 3-fold repetition unless proven" and with "no 50 moves unless proven". What may be difficult is to find a position in which 0-0 IMPLIES one of those other special possibility that (as should be) is forbiden by default. Then the flaw would also manifest itself.
But even if, in practice, we were never to find real, concrete examples (imagine that even the Langstaff didn't exist, or even COULDN'T exist). It would always be a FLAW in the rules (for the serious discipline of problem solving, that is!) to mantain ANY uncertainity over which are the legal moves.

4. Retrograde analysis is other thing. There, other things are seeked. It is not acceptable that some problem reaches there DUE TO the rules for direct mate in x problems being incorrect!

5. Your 1st paragraph:
"There is a clear difference between a possible en passant capture and possible castling in a composition"
Apart from the obvious, you seem to be right, but you should't, in what rules is concerned.

Sorry my English, my repetitions, and my limitations in trying to expose things.

Castro's picture

“e.p OR 0-0? (the 3rd form) is wrong, and should be
“e.p OR no 0-0?

Castro's picture

Completely misunderstood!
OK, last try. Sorry for this seemingly arrogant recomendation: If you please, and wish, read very VERY attentively.

1. "we’re not there to suit the rules, the rules are there to suit us"
Fully agree! That is not the question and, if it is, it's you the one forgeting that!

2. Neither "guilt" has nothing to do, here. The law analogy does not refer to the issue!

3. You seem to believe I'm already not understanding how things work. OK, the rule says that 0-0 (inversely of all other special situations) should be considered possible, unless proven impossible from the very position (or the composer so states). I understand exactely the consequences, and also the beauty of the consequences! And it's not like this kind of beauty must end! Never! (more further down on this)

4. That ruling is (please read carefully) WRONG.
It STRONGLY should change, I assure you. (for chess tradicional "mate in x" solving). And with NO beauty loss whatsoever!
This is not an opinion, this is not philosophy, this is not a radical formalism or excess of rigour!
The situation is EXACTELY ( you read well) as when the rules for playing the game were vague enough for alowing (for instance) "enemy's piece promotions".
Should they have remained that vague (e.g. because of fear of losing beautiful studies exploring that theme? Of course not! Rules are enhanced, precisely to "suit us"!
Did we loose those studies or that beauty? Again, of course not!
They became recognised as belonging to a "Meta-theory", a "meta-chess", a "fairy" theme. Something along the lines "supose the rules have this reading..." And, meanwhile, the rules became (more) relyable!
That's how things go. Sure, of course there are good reasons (historical, logical unknown or others) explaining why we still have, until now, in traditional chess problems, "0-0 posible unless disproven". But it must change, because it makes for non-chess (really another game!) (which can be amazing and enjoyable, sure).

5. There are no composer or solver issues involved, let alone "criminal" ones! I'm glad there were this kind of rule flaws, and that it was (and will ever be) through beautiful compositions that they became recognized. And there will always be rules to enhance! Not doing it is childish, and it is NOT chess. Note that the Langstaff CAN NOT EVEN be presented as a legal chess POSITION (because 0-0 is neither legal nor ilegal!). And that impossibility is stupid.
It could (and certainly should) be both a fantastic "meta-chess"/fairy puzzle AND also a legal chess position (with few interest other than an easy mate in 2, ok, but still). It only becomes chess when you erradicate it from it very nature. The difference is having or not having good, chess, rules for chess problems, now that we conquered the beatiful theme (as many other before).

Frits Fritschy's picture

Last try.
In most law systems, you're innocent untill proven guilty. You don't have to prove that you haven't done anything criminal, that would be absurd. But when the other party can prove you've done it, you will hang.
When castling seems possible, you don't have to prove you've done something 'criminal', like moving your king or rook. So castling by the solver is only punished if the composer can prove the fact.
Now if the composer has done something 'criminal' by producing a position where black's last might have been a double pawn move, you're the one to prove the fact.

In the mean time, have some fun. Langstaff did, he found the only kind of position where law doesn't work. But we're not there to suit the rules, the rules are there to suit us.

Adolfo's picture

Hi... a single question, which thrilled me from your comment “…Do you remember those marvellous problems with some pawn promoting to an opponent’s piece, or castling vertically with a never moved, newly promoted rook...?”
How is this last case possible (the castling with a newly promoted rook)?, as I have never seen such thing.

Castro's picture

:-) Glad you ask!

The position is: White Ke1, Rh1, Re8; Black Kc1
Mate in 1!
The key is 1. 0-0-0-0-0-0-0-0 mate! (The rook had just appeared on the board by promotion, previously! It is a never-moved rook!)

In the past, the rule was vague. It was (something like) "Castling is consists of moving the king two squares towards the rook, and the rook is positioned next to the king, in the opposite side. For castling to be legal it is necessary that neither the king, nor the rook, have already moved. ;-) Nice rule flaw, and nice exploration, right? ;-)

Castro's picture

Sorry, I just wrote a string of "0-"s.
The move is 1. 0-0-0-0-0-0 mate (of course!)

Castro's picture


At least in my adaptation, the move has number 1. It's immediate mate (nothing too much demmanding :-) ).
Also, anyway you can (or even ought to) use "0-0-0-0-0-0" (six 0s), because each one stands for each empty square between K and R, right? (Of course one can use 4, meaning "the next", or "bigger" castling, but that is subverting the original meaning of the notation. One could, as well, use any other number, for instance "the age of the person who thought of that castling for the first time"... :-) )

By the way, as you're a "man of thought", and a real "man of chess", could you contribute to the discussion Frits/Castro with your (pls, very pondered) opinion?
Have you read it? I think it is of fundamental importance, and maybe you could help reaching it's conclusions to the right people?

Arne Moll's picture

You mean 3.0-0-0-0, Castro. The phenomenon was first suggested by the same Tim Krabbe in a (rather ingenious) study back in a 1972 in the Dutch magazine Schaakbulletin and was named "Pam-Krabbe castling". Krabbe writes in Chess Curiosities: "The FIDE rules nowadays do not speak of 'a rook' but of 'either rook on the same rank'."

Arne Moll's picture

I duno, Castro, it's a complicated subject. Do you know Petrovic's study that I mention in my article? It will give you guys more food for discussion for months to come. About 15 years ago I was really into these matters and had very interesting opinions about it, but to be honest I forgot them all. For what it's worth, my opinion is that without the ambiguity in the rules we would never have had those crazy problems so that alone is worth it in my book!

Castro's picture

But that is precisely one of the things I said! Glad there WAS ambiguity in the rules! Once conquered, one must seek different ones. Not losing anything, and (of course) correcting the rules. Or would it also be good to mantain the ambiguity about the rooks being (or not) of the first rank, or promoted pieces of our colour?
And notice that these two examples of mine, if not dealed with, would just have brought to our days chess as a slightly different game (maybe a good, interesting one!), whereas the Langstaff-type is worse (for chess problem solving). They make chess problem solving NOT related to chess itself, as played by rules that (obviously) leave no doubt about the full (and mutual exclusive) sets of legal and illegal moves in every position.
For instance, there is no legal chess position without, at least, both kings, right?
But why do you say that? Aren´t there puzzles without kings? Sometimes it's just a knight! Yes, but that AREN'T CHESS positions! And so, the CORRESPONDENT puzzle CANNOT belong to chess problem solving! (at least, from the moment the flaw is discovered.
If, as you say, they categorized (and very well, I suppose) these puzzles as belonging to "partial retrograde analysis", then (by the same move) they should imediately (the sooner the better :-) ) correct the rules.
For something's sake, my English cannot be that bad!

Castro's picture


Which rook gives mate doesn't matter to the notation! :-)
As the notation itself, either you didn't read my answer to Arne, or you're forgeting that 1. Either one wants to be in coherence with the notation, and it's meaning (and the number of zeros must be 6), 2. Or "anything goes". At least every integer different from 2,3 would serve, the meaning being ad libidum. For instance, 5 if it would be the fifth rook apearing on the board, 8 because of the opponent's eye movement caused, and so on. Have you though about why the king-side (the minor) castling isn't noted by one, a single, zero, meaning "the basic one"?

Adolfo's picture

Well, the 1.0-0-0-0# note was to support your notation on that (for the “number 1” matter) unlike Arne´s 3.0-0-0-0, which I did not know what he meant with the “3”. As for the four or six zeros issue, you may be right, I don’t know, perhaps each zero does mean those empty spaces before the castling move; I simply followed that Wiki article and Arne´s reference about it, I guess for a simplicity sake (I study economy BTW, so likely was biased to). Eventually, I don’t consider that important (the notation), but I do the potential inclusion of the rule. We tend to forget but sometimes happens that a quite late castling move decides the game. I remember some old Anand-Svidler in a Grunfeld where Vishy mated Peter with 0-0 passed the 30th move –and I am sure the record should be way higher, and someone king enough may be able to find it-, so why not passed, say, the 60th move.

Castro's picture


Sorry, forgot to add:

... And so, I was wrong when (some posts ago) I said those were rule-flaws of EXACTELY the same type. They aren't. I could live with 0-0-0-0-0-0, and opponent's piece promotions in chess (in fact, in some glorious way I do). :-)


Castro's picture


Ah, ok! You thought Arne erred the numbering! But he didn't he was refering to the seemingly original puzzle (note that I don't say "chess problem". But I could, if the rule stood as before that rule correction/enhancement!).
It was a mate in 3 composition (after all, haven't you follow Arne's links?), and the position before mate is similar to mine. Castling mates.

In fact, and contrary to Langstaff-dismounted flaws issues, we could have mantained that unclearness about castling, in chess (and that mate could still be a legitime chess problem). One thing is having "chess" as a slightly different game than we thought before: Other, unbearable, is chess not having a genuine, it's own, problem solving department (as the one that exists still imposes, as we found, positions where the legality of moves are not defined, hence not chess).

As for the record, I don't know, but my record is well above move 30, that I know!

Arie's picture


Your point is: "castling allowed unless disproven" in studies leads to contradictions with other special case rules like "no e.p. allowed unless proven", and is therefore flawed.

However, your alternative: "no castling allowed unless proven" would obliterate the use of castling in studies, since it is impossible to *prove* that castling is allowed (that is: to *prove* that there was no previous K or R movement) because - as Frits Fritschy pointed out - you can always start a proof game by moving your Rooks (just do 1.Nc3... 2. Rb1... 3. Ra1...4. Nb1 and this in all four corners to reach the starting position with no castling possible ever again).

So you have a choice: Rule out castling from all studies and problems altogether, or allow a paradox in some few extreme cases. Which do you prefer?

Castro's picture

So, could THAT be the problem (for you)? Well then it would be case imediately and easily dismissed!
The answer (I thought was already obvious) is: NONE of those!
Just procede like with any other special posibility, and just as BOTH logical rule-making praxis AND plain good sense demands:
The things that demand BY DEFAULT definitions are defined as having, BY DEFAULT the most trivial, basic, common, unspecial, etc. form.

(Note: Even way before knowing Langstaff-type "refutations", I was tought --- not so well, in a sense, it seems --- that castling was not allowed in problems, unless(...) And I also STRONGLY AGREED! Trying to teach me otherwise would have mean trouble, even if I wouldn't, still, be suspicious of a forced existence of a refutation. It would simply "stink"! :-) )

Of course castling must (from now on, don't be afraid!) be defined as non-legal, unless demanded by the very (chess --- it must be chess!) position, including in "position" the full information the composer may add, for instance "white queen-side castling valid". (This is as "Ruling out castling from all studies and problems altogether" as the corresonding for en passant, have you noticed?)
Don't be scandalized!!! That is made with every other special posibility!

Ok, luckily, the historical fact is that the castling rulling flaw was the one responsible for the exact type of beauty we came across (since Langstaff), and without which we would "merely" have it's (dozens of) similars in other fields. But that mustn't prevent us to correct flawed rules, which, by the way, is the ONLY way human kind really and fully apropriates the said beauty and logical meaning!
On the contrary!
Someone begun the right process: Sending the discovering, materialization puzzles to some kind of (suposedly right) "meta-theory". But didn't give closure! It's like not understanding!

Have you thought about the amount of themes (more precisely, of chess materializations of logic known themes) you are denied (beauty included) because of en passant being "non legal, unless stated or otherwise demanded"??

BY DEFAULT, "normal" rules must rule. And as good as we can make them! Uncovering flaws is a normal, sometimes endless, and usualy beautiful process. Mantaining them is the very negation of it! It points us to stupidity!

Arie's picture

Ok, understood. I do have two issues though, one practical, one more theoretical and along the lines of Frits's law-analogy.

Practical: Every study/problem with castling part of the solution needs to have an extra accompanying statement that castling is in fact allowed. Cumbersome, will be omitted, will spoil some of the solving fun, especially with retrograde problems. Not a big deal perhaps, but the general rule of castling allowed until disproven is more elegant and economical.

Theoretical: you state each definition should have the most trivial, basic, common form. There is a difference between castling and the other special cases you mentioned which I think make the current rules the most logical choice:

e.p. is possible *only* if something specific has happened
3-fold claim is possible *only* if something specific has happened
50-move claim is possible *only* if something specific has happened
Castling is possible only if something specific has NOT (yet) happened

If we get a study or problem position we are given no information about any specific events that led to it. Therefore it is logical and intuitively right (in my opinion) that we can make no inferences about any specific events unless they can be proven from the position (for instance by retrograde arguments).

This then implies that e.p., 3-fold, and 50-move are not allowed unless they can be proven, and that castling is allowed unless it can be disproven.

My point is, that a single, logical premisse (namely: we are given no information on the past) leads to a different treatment of castling compared to the other special cases.

Unfortunately (or fortunately, depending on your taste) this does lead to paradoxes in a problem/study niche. But "fixing" this paradox by obligating the composer to explicitly include information about the past with his study/problem is IMO a cure worse than the disease. But again, this is probably a matter of taste.

Anastasia's picture


Frits Fritschy's picture

Arne may not have been completely clear about the rules for solving problems and endgame studies. They are as follows:
- castling in the solution is allowed unless it can be proven to be illegal, i.e. from the starting position it can be deduced that either the king or rook must have moved;
- en passant capture in the solution is only allowed when it can be proven that the last move was a double pawn move.

It comes down to that you can't solve this problem, within the accepted rules for solving, unless you know black's last move.

The Sublime Distraction's picture

Interesting article!

Frits Fritschy's picture

Oh, come on, no-one of you ever had the experience, after winning or drawing against a much stronger player, of having been sleepwalking on the edge of a vulcano? That you hadn't seen a tenth of what your opponent had seen? That after a forced sequence of moves, surely leading to a loss, to your own surprise there was a sudden way out? Don't you dare to call that intuition!
Chess is a game of chance, becoming less so when you're getting stronger, but even then.

oliver's picture

The Langstaff problem is interesting but ultimately solveable. Ke6 ist not the key move (Black answers o-o) but hxg6 is the key, since if Balck claims hxg6 is illegal, because his last move was Rh7-h8, we calmly set the pawns back and play Ke6 with mate to follow.

Castro's picture

I could write pages (in my so beloved style, english and opinions :-) ) about such an interesting article. Lots of things to say, believe me. But I'm in the mood for just one minor point, now:

I have learned that, in a study, BOTH castling AND en passant MUST be anounced as (if) legal. If not anounced, by defect they are NOT legal.
As it is given, the wonderful problem given simply shouldn't be a problem :-) . Note that also, even if things were as you put it, the syllogism is easily broken (I'd say self-broken): Castling would be legal (because both not disclaimed and not disproven, right?). So, black's last was g7-g5, no doubt about it, and no Rh7-h8 move claim is possible! So the key is 1.hxg6 e.p., and 2.Rd8# or 2.h7#. Quod eram demonstrandum.

In spite of all beautiful and amusing compositions we all have known, exploring the unobservation of the above mentioned convention (no castling, no en passant), it is the one that avoids all misunderstandings, and hence the only scientific one (and in fact the only one that makes true sense).

Congratulations, great entering the decade, Arne ;-)

CapaBenko's picture

So everything is debatable and "lost" positions are not, in fact, lost. Someone should inform the grand evolutionists they aren't as brilliant as they believe. Science, religion, and chess...bring on the scotch!

A shame the third-rate introduction coloured an otherwise intriguing text on chess relativism.

S's picture

Why can't we have a thumbs up/down function on articles?

VladimirOo's picture

All very interesting stuff! You could make dozen of articles by expanding the ideas exposed in this article!

One excellent french forum (for those reading french, it is the fantastic suggested that we should not speak of "opening theory". As you point out, all this aspect of the game has nothing in common with a "theory", but more with fashion, belief, mimetism with the top, hypothesis: some player rehabilitate lines, some refutate lines, somes variations are considered trustfull, somme suspicious "according to a certain experience", certain games, or certain analysis done by a top player.

This "according to" does not define a theory: rather, this is a jurisprudence.

The real theoretical aspect in chess is at the other side of the game: in the endgame. Take Muller&Lamprecht, Dvorestky, or Nunn's book and here in these endgames with ultra restricted material you will have a real theory of the game, all scientificaly confirmed by the tablebase (for instance, the Lucena or Philidor positions). That is that you reach of stage in the game where you can mathematically demonstrate the outcome and in indifferently evaluate the position, not by giving nuanced evaluations such as white might have/has a slight/tangible/strong/major advantage, "white should win" (all subjective and still to be contested as the game proceeds) but by asserting "white wins".

lefier's picture

You are asserting that theory=truth, as certainly is the case with mathematics.
However, the term theory is used quite differently in other areas of science - like 'hypotesis' or even 'evaluation'.
So in this sense, chess is on common ground talking about opening-theory.
But of course, endgame-theory is closer to your deterministic understanding of the term.

Mike's picture

Great article..! It remembered me that, chess, as a matematical system, MUST be in accordance with Gödel's incompleteness theorems. Based on the absolutelIy defined axioms of the pieces moves and board geometry, you will never be able to create an infinite set of positions free of paradoxes! I loved to find this chess paradox..! Thanks...!

Castro's picture


"Based on the absolutelIy defined axioms of the pieces moves and board geometry, you will never be able to create an infinite set of positions" PERIOD! ;-)

Gödel’s incompleteness theorems has nothing to do with chess in that way. Everithing about the rules is finite, here. Mixing theory with meta-theory always yelds trouble, even with tic-tac-toe!

Castro's picture

... which, by the way, is of the exact same mathematical/logic nature as chess.

Mike's picture

Pls, read again my last post....I did not say, for the "demonstration" of my statement, that the board is finite! I assumed that the Langstaff's problem can be presented even if you consider an infinite board, which infinite columns x rows origin is placed just at the upper right square...! Remember that our beloved FIDE (real) chess game, mathematically speaking, is just a finite "window" of an infinite two dimensional game (or even multi-dimensional game), even if you assume the existence of a finite set of pieces and their corresponding finite moves rules (a limited set of axioms applied inside an infinite field or n-dimensional universe of squares). Mathematics is like this: Its is not possible to have any set of rules capable of creating a full consistent and complete logical system, because the universe is aways infinite and this also lead to the Heisenberg's uncertainty principle of quantum mechanics. So some judgement error can occur in this case, because people do not realize that the a.m. problem belongs in fact to an infinite 2D board....


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