Understanding Dead Reckoning - Hard DRexit versus Soft DRexit

Dead reckoning has been with us since a few decades after FIDE decided to introduce the dead rule in game chess in a make-up I rate as Hard DRexit:

(Hard DRexit) article 5.2.2: The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game.

"Dead reckoning" is the associated term in the composition field to designate all evaluations to determine if positions are dead. The purpose of the dead rule was to prevent aimless manoeuvering until closure by 50M(oves) or 3R(epetitions) claims without the possibility of checkmates on either side. Simple example:

However, there was an unintended while harmless side-effect of the dead-rule related to stalemates. Occasionally a position would end in a "dead" draw one or a few moves before a stalemate occurred. That was uncalled for since the rule was only introduced to abort the senseless move series which might follow the preceding diagram and not the few moves before manifesting a stalemate such as in the diagram below:

Then another thing happened. Two new rules were introduced to make draws automatic after 5 repetitions and 75-moves (without pawn move or capture). And they proved to be new places where the dead rule could terminate a game before it was due. Example:

This position is dead as no move sequence exists that allows a checkmate before the 75-move forced draw kicks in. Since the premature draws only shortens the duration of the game and do not change the outcome, the game issues are mostly theoretical.

Outside the game domain there were more serious issues. Already in existence were many composed problems based on stalemate draws but also on automatic 3R and 50M terminations. The dead rule provided many opportunities for new creations but also appeared to destroy a number of existing problems (amongst which one of my own best), especially those with duration numbers on them like "=3" (forced draw in 3 moves). They were now flawed beyond repair because the dead rule shortened parts of their solutions. The Composition Federation tackled this with a new article which has many drawbacks of its own but which is not the subject of the present comment.

What I want to suggest here that there is another way for FIDE to define dead positions by returning to the original concept and bypassing the collisions of deadness with the other drawing rules. This approach which I named Soft DRexit would not terminate positions close to drawing borders but still perform its duty as eliminator of senseless prolongations of drawn games (as in the first diagram).

(Soft DRexit) article 5.2.2: The game is drawn immediately when a position has arisen in which neither player can checkmate the opponent’s king within 1 billion moves and there is no certain stalemate within 1 billion moves - under the basic rules of play,

[Note: I argued in another post that a billion-move rule should be added to complete the basic rules of play which makes the formulation of Soft article 5.2.2 logical; there are however alternative criteria to achieve the same]

This article effectively says that - without changing the rules of play - you should make your DR-analysis by assuming that 3R and 50M and 5R and 75M do not exist because they are not in the basic rule set while stalemate is explicitly ignored! As said, I am convinced this is in line with the orginal intent of article 5.2.2.

Does this mean that we must abolish the Hard DRexit article 5.2.2 which exists now? No of course not. Some problem composers will love to use it alongside the Soft DRexit version I described!

Another discussion is which version of article 5.2.2 should be activated by default in which composition category (like endgame study, orthodox problem, retro problem). Whatever we pick, my prediction is that we'll still end up with both DRexit versions in use in several categories. Both have their plusses and minuses!

[Note: Letting the dead rule ignore 3R, 5R, 50M and 75M is not strange. These rules were themselves carefully designed to ignore one another! Imagine that a position repetition would require that you are at the same move count of a 50M series. Would effectively destroy the repetition draws!]

Update 14/11: first version was unclear; now extensively edited.

Well written my friend!

Thnx! It is tough to write about a subject which people hardly ever address on purpose, but they nevertheless stumble over when composing chess problems. And those who really target the DR theme are a small specialist group with a low profile on this site. Except for the king of DR, Andrew Buchanan, who occasionally visits us!

Hi guys,

I've only just spotted this article.

First, I am relieved that after 20 years DP rule seems to have bedded in for over the board play. Yes occasionally a GM may play a zombie move, but no-one really cares. I guess I should be sad that they don't mind, but it actually it's good because if they did care then they might change the rule to stop the beautiful unintended consequences!

I am of course more interested in the composition world. Before DP was nerfed by a convention, it was very clean: the issues were that the conventions are so scrappy, both (1) inherently, and (2) in their flexibility as they were stretched beyond their initial intent by DP.

For example: "Castling is permissible unless it can be proved that it's not permissible." Surely the second "permissible" should be replaced by "legal"? I guess the reason "permissible" is not defined further is that we need something which makes sense across RS, PRA and other protocols (Touch-Move anybody?). But how could it interact with DP? Suppose the game is alive if and only castling is legal. Are other moves apart from castling permissible? Robustly, I might say yes, but the convention was never designed for such contingent use, so I enjoy saying no.

I won't get drawn into the chaos of how multiple occurences of the castling & en passant conventions are combined in the conventions.

Or take 3Rep. "A position is considered as a draw if it can be proved that an identical position has occurred three times in the proof game combined with the solution." If the position was repeated three times in the past, then obviously the game *wasn't* drawn, because we are still playing. I am ok with it's forward application, and I'm ok that if we have a choice in histories, we avoid the ones in which a position occurred three times. But if a position must have occurred *three* times, then clearly the imaginary players did not choose to draw. The convention goes too far: a game sequence that is legal over-the-board becomes "unplayable" in a composition. And we need to say that capturing a rook removes castling rights, because at the moment this is a hole in the rules.

Why do some people assume that DP rule must have visibility of the convention which says that the game must mandatorily end? This seems completely up in the air. I was surprised many years ago when old Arisktotle said that his wonderful composition (and it is sublime) was broken by DP depending upon DP, because I still have no idea how he is so sure that DP knows about the convention.

There's a similar issue with the 50M convention, but worse. "Unless expressly stipulated, the 50 moves-rule does not apply to the solution of chess compositions except for retro-problems." The 50M convention is incredibly vague: it doesn't even get rid of the notion of score-pads, players, clock etc, which are meaningless in the context of a composition. But do you know the reason why this rule is still so vague? This is the best joke. This is the kind of thing you only discover if you actually try to clear up the conventions with WFCC. You find that some people say castling zeroes the count, while others look at the actual rules and say no it doesn't. And this is all because there are a couple of problems by Plaksin which depend upon castling and his fans can *bear* the thought that these problems would no longer work. So everyone has to suffer because it is necessary that the convention remain vague enough to allow both interpretations. But most people assume the convention is written as if it was written sensibly like the 3Rep convention.

With both 3Rep and 50M conventions there should also be an explicit statement about what one may assume about the history of the game. 5Rep and 75M rules do not form part of the conventions today: they are potentially interesting in that they are actually mandatory, but the current conventions cut in first, so their impact is just in things like: what's the longest possible game of chess. And if 3Rep & 50M were going to be adopted, then some assumption ought to be written about what one may assume about the prior history, as with 3Rep & 50M.

So there is all this boring nonsense. To separate myself from this as much as possible: I think (and have almost always thought) that DP is part of the chess game. Step 1: We do all the reasoning we can about the game, including application of DP rule. Step 2: If we need to go further, then we go to the conventions, and then we make a move forwards or backwards and we can go back to Step 1. This approach would destroy a couple of good problems (including one of Michel Caillaud's) and it would salvage a few (including Arisktotle's). You're welcome, Arisktotle! This is my interpretation of how things work: the Anselan interpretation. If you want to have DP know about the conventions, then fill your boots, but that's someone else's interpretation, and they can give it their name.

But then DP was nerfed. But I can't be offended, because I'm so happy that the endgame community realized that there was actually an issue (unlike many other problemists who were just in denial). The fix is curious, because it depends on deciding what is a retro composition, when this has deliberately not been defined. However that is an interesting challenge, and "restrictions breed creativity" is one of my mottoes. It is a challenge because some forward problems require to have something added to give them a reverse flavour. Maybe a retraction, or application of my second-favourite convention: Art.15: If the first move does not lie with the conventional party (examples see Footnote 9), this should either be indicated in the stipulation or deducible from retroanalysis. Similar games are possible with the 50M rule, as Rocky Wong has shown in a couple of his columns here. However there are some problems which have suffered: notably Ronald Turnbull's forward DP problems.

The Anselan interpretation says that DP is always ignorant of the impact of the conventions. I am Anselan, so it will not surprise you to learn that I don't feel the need to make push for any complex changes to the current FIDE rules. They are working fairly well, thanks to continual maintenance. The same cannot alas be said of the conventions but this is work in progress.

I do have an idea called Golden Age Principle (GAP). For any problem, you look through the chess timeline and if there is any period when rules or conventions made the problem sound or a record-holder, then it is to be considered sound or record-holder. In the case of records, it means that there can be multiple record holders. The intent for this is to protect past composers' rights so that people are upset if anything changes. No idea if it could work, but I want to try it on the castling zero issue

Welcome back, Anselan! Trust you had a good time between chess.com visits. Well - as good as possible on a planet in limbo.

If you'll continue searching chess.com, you will be surprised to learn how many articles and comment posts I wrote on varying aspects of DR in the past year! This one is rather formal in the sense that it offers an alternative definition of the dead rule which resolves many discussion points that have arisen at one time or will arise in the future. It's aim is simply to retain the dead rule for its original purpose by eliminating the interaction with rules which only incidently come across it.

Soft DRexit is not about conventions, it is not about competitive rules (which are now strictly separated from the basic rules) but only about a basic FIDE law definition which prevents potential collisions with rules in one extension of basic chess or another. Under these extension come e.g. (a) game extensions such as in the competitive rule sets with repetitions and 50m/75m (b) conventions as they apply to various standard composition types (c) all the existing or new fairy and retro types.

As described in an earlier article, a formal system like chess requires decidability and this is hardly the case under the existing basic rule set. I added the "billion move" rule to make axiomatically decidable (by playing chess moves) whether or not a position is a dead draw. In the leading article I showed how the billion move rule could be used for a different approach to DRexit, namely the soft DRexit. The idea is that we then have a choice of dead rules which might be used in competitions (not all that relevant) and compositions (most relevant). And perhaps everyone will eventually unite on the soft version?!

Note: Perhaps soft DRexit achieves precisely the formalization of your own thought line by creating independence from all other time management rules - 3rep, 50m, 5rep, 75m.

The points you discuss in your post are most issues in the hard DRexit and not in the soft DRexit. Some are the subject of other recent articles and comments I posted. While writing them I also reviewed - in my mind - the rules and conventions relating to DRexit and my compostions. I can now prove that my 3rep 41.5 move proof game is indeed flawed under hard DRexit. The reason we'll continue to disagree on it is that we can never simultaneously retain our own mental retro constructs while including some of the other. I don't know about your paradigm , but mine is a complete uncompromising package where all concepts, definitions and actions are inextricably linked together. It's not an incidental collection of modules - though there are some free choices and infinite extensions.

Things such as GAP may be useful but are no focus in my paradigm. One should always provide sufficient context to define (the rules of) the problem. That is what the stipulation field is for.

Another note: you probably wondered why I tackled this from the angle of the FIDE laws. The answer is that games have the same issues compositions have. For instance the competition rules on chess.com feature an automatic 3R draw. If chess.com could evaluate dead postions - it currently can't - then indeed you could never play my 41.5, 3rep proof game on it! It would draw on 41.0 unless it received additional instructions to apply soft DRexit. The issue is real in gameland as much as in compolalaland and is therefore a natural inhabitant of the chess laws and not the conventions. The chess.com engineers will be very grateful for bringing this to their attention for the time they are ready for it. Computers don't buy stories, only algorithms.

Hi Arisktotle,

Why (oh why) is there a "k" in your name?

I am glad that DP rule continues to interest you as much as it interests me.

I can see why you might want to separate basic rules from other categories: I like that.

But the DP rule is a unique annoying artifact found lying on the beach: if we start having artificial flavours and versions it loses its appeal. I happily pay the price of Article 17A convention, and keep the variety of situations that it applies to in the retro world, rather than have your version which throws out stalemate altogether even for retro problems. There is no real difference between your soft rule and no DP altogether: you might as well just allow the pieces to flounder on until 5Rep or 75M intervenes. There's no point to it.

What I like about DP is what you can enable with it. So for example, in Chess960, you have a position with K & R on the first rank. We need a convention to say if they are on their starting squares (how do you opine there?) as well as the regular convention to say whether they've moved. DP rule can say: these guys are on their original squares and they have never moved, and look at the #5 they can execute now. The other thing I come to like increasingly is the retroactive nature of DP: that we can have both forward and backward play, with the same pieces doing a different dance. This all needs the stalemate interaction.

How exactly does DP rule + Arisktotle paradigm engage with 3Rep to break your problem? Maybe just point me to the link, please.

GAP is because the rules change. If your paradigm doesn't allow for rules changes over history and into the future, it seems rather fragile

The first site where I tried to enter my real name - Aristotle as you know  - refused it and I quickly concluded there are as many Aristotles as Napoleons on planet earth. So I went for the safer "A risk total".

Do you prefer "genuine disagreements" over "artificial flavours"? As you know I like comprehensive formal definitions as a solid source of reference. It's for the computer programmers. For the public we need something a lot more user friendly. Also see the last paragraph in my previous post which I edited heavily.

If you think there is no DP left, you misunderstood me. K+B vs K+same squared B is still DEAD as are many, many other positions. How to handle stalemate is complicated since it is also in the basic rule set and it is a fundamental termination state. Both including and excluding it in DP evaluations has its consequences. I made some very interesting problems combining stalemate and DR to illustrate their weird interaction. I'll try to trace the link (done! see addendum).

Chess960 is a perfect system to demonstrate the power of my paradigm because it is fairy (OK, was fairy) and my system is made for fairies. I haven't cared to look at it in detail but I know that the trick is to define as little as possible. The rest must be done by the generic operation of the applicable logic(s). Example: you simply permit "castling" between any king and rook as long as not inconsistent with preceding action. The original positions of pieces follow from the actions taken and are free for the remainder. That is why I always advocated RS as the default logic. It is much harder to handle this by PRA logic though not impossible. And, as often said, the logic type is not something to discover by a crazy convention; it should be specified in the stipulation or by a conventional default.

No I can not explain to you why my proof game is flawed. Either my explanation is too short and you won't swallow it, or it is extensive and you can't swallow it. I wrote it in fact a few years ago in terms of 2 alternative rule/convention concepts and I now know know that one of them leads to inconsistencies. It's not in itself intricate but it is the top of a pyramid where all concepts are unnatural to you.

(on GAP) In my paradigm, the applicable rules are an attribute of the problem. The road towards identifying them is in the stipulation, for instance "Circe". If the rules of Circe change at some point, then the rules attribute of the problem in the database ought to be modified to reflect the changed rules, e.g. to "Circe pre 2020". Of course, alongside, a public resource should exist describing what the rules of "Circe pre 2020" were. A database problem with all its rules and instructions should be portable but that is not always simple to achieve. The burden is mainly on the composers and the composition community not to make changes to their systems which endanger the understanding of older creations. That's another reason why I object to conventions such as "detect the applicable retro-logic by evaluating the solution". In some years that convention may change again and nobody gets what to do in which problem.

Addendum: Here is the link to a 'simple' problem that queries all the conventions on retro, stalemate and DR and some more. It is (a) =2 and (b) =1.5. The answers are in the last post of that thread and quite elaborate though not necessarily clear

https://www.chess.com/forum/view/more-puzzles/mate-in-two-634#comment-44992764 

Hi Ari: I'm very busy with work at the moment, but Die Schwalbe have just accepted my article with Andrey Frolkin on Passenger Rooks hurray. So the next recreational item is to finish a long-stalled article on DP, larded with many new compositions. Again I'll work with Andrey on this. Very keen to include some of your new compositions, and to reflect your perspective. Do you have a list of relevant threads you have posted in here?

There are some broader mathematical issues that I also want to address in the new article. Do you have an assessment of decidability as it applies to chess? If you need to bound the number of moves you are talking about infinite board, yes? Not sure that is so relevant to chess programmers.

When you write " In some years that convention may change again and nobody gets what to do in which problem". This is part of the 3rd problem curse: loss of contextual history. See a recent problem with me and Lohman in PDB where I describe curses and how to approach them

Don’t forget me as the guest star, the world’s #1 and maybe only expert on dummy pawns!

There is no DP+DP composition... yet

To be concrete: can you make an h=1 problem where the solution is 1. z1=P Jxz1=, where z is a file, and J is an officer? I.e. the position must be dead if promotion is to Q,R,B,S, but still living if promotion is to P. Obviously the first move is allowed to be a capture too. Such a Dead Pawn Schnoebelen would be quite a coup. The initial vanilla version might be pure forward chess (i.e. need to declare Dead Position rule in the stipulation), but a later version might have retro aspect so the stipulation can be simplified, as per Art. 17A.

See https://pdb.dieschwalbe.de/search.jsp?expression=k=%27dead%27+and+k=%27schnoebelen%27 for prior art.

I skip your last post because I don't get it (may be RewanDemontay does). I set up a paradigm for fairies but I commonly do not compose fairies except as examples for the theory.

The issue of decidability is a critical one in chess, especially given the increasing demand to have engines and interfaces play a role as chess companions to humans. It all starts with the rules and conventions. As long as joking conventions exist like "DR applies if it is a retro problem - without specifying what a retro problem is", complete decidability is totally out of reach. As you found out yourself, the 50M rule+convention is weird, much more so than its repetition nephew (it's asymmetrical at the 50M borderline). Can't get decidabilty in such muddy waters. Note that Plaksins 50M problems are generally correct when you know they are retro-problems under RS-logic. Just logically simplified versions of my infamous #7.

Finite state systems are always decidable in principle. It is however uncertain that chess is finite unless you limit it by hard boundaries such as the repetition rule or the billion move rule. The reason is that the full states in chess are defined by full games and not by diagram positions. It changes when you introduce a fixed goal such as checkmate. Without that goal, a more illusive goal might be defined such as "weave a game that produces the values of a hyperbolic mathematical function by some metric" which may have infinite states. It's not the checkmate state that makes chess finite but the checkmate goal. You can play forever while avoiding checkmate and endlessly repeating the same "positions" but the total game pattern may continue to vary forever like the decimal digits of pi. What we see on the chess board generates the illusion of seeing a "position" while it's actually a "cluster of positons" with different game histories and different future options. Fundamentally there is only a finite number of chess diagrams.

So nothing I wrote is about infinite boards. It's about 8x8 boards where the number of states can be finitized by reducing them effectively on the basis of achieving a "diagram" goal such as checkmate or by artificial hard boundaries.

The state of "draw" is similar to that of the "Gödel formula". It is axiomatically undecidable (axioms are moves) except when you permit the introduction of a model with non-axiomatic information such as "all games which cannot produce a checkmate are a draw". It is a 2-valued logical conclusion derived from knowing that "all games end" and there is no excluded middle for them (intuitionism: LEM = law of the excluded middle). Every finished game is either checkmate or draw. It is a similar poperty to "provability" in the modern version of the Gödel formula. We know that every formal sentence is either provable or unprovable but an axiomatic formal system knows not. It can only attempt to exhaust all options for axiomatic proof and it fails because they are infinite. In our reduced version of the chess system the number of axiomatic states are finitized but still impractical for evaluation. That's where 3R, 50M and the billion move rule help out.

On top of that, there actually is an excluded middle in chess. When players can still checkmate in theory but alfa-beta minimax prevents them from ever getting there, what then is the outcome of the game (without boundary rules)? People think it's a draw but no one knows because there is no axiomatic point where you call in the arbiter to decide this for you. Just as in the Gödel formula.

Written off the cuff. Sorry for the typos and the brainos. Had no prepared article for this. Now I have. The next version will be better!

Currently have no interesting problems for you except the simple one linked in my previous post. I am still a low volume composer though I produced a good number of orthodox problems recently.

Gotta stop now.

Addendum:

Of course, a lot may be said on the decidability of issues around the retro-logics such as RS and AP but it is of little use until we know everyone understands them in the same way. I believe they are all algorithmizable types though not necessarily approachable with First Order Logic.

Addendum 2:

Regarding the "if it is retro-problem" conventions. Since the Codex was "enriched" with the pre-decision convention on RS/PRA logics, it has gone downhill as I feared. I have argued against it on the basis of "why then not bundle all direct mates in one stipulation such as fastest mate?" In the current context I can add undecidability to that. But there is an even more fundamental argument. Why do you think all the conventions referring to the past come under the heading of Miscellaneous conventions? The answer is that they were not designed to create a category of retro problems but to recognize that all diagrams are incomplete and in need of extra information whenever and wherever the demand crops up. All compositions must be retro-analyzed to some degree to verify that default assumptions can be confirmed or rejected. By this very clever approach these conventions became an extension of FIDE laws and the creation of a special retro rule category was unnecessary. Obviously, while all problems were still in print and not digital, anyone would recognize the typical retro-problem by a (subjective) appreciation of its content and by an (objective) appearance in the retro-column of a magazine. Besides the orthodox problems with retro aspects (the hybrids) there were also retro-problems with special rules and they were clearly indicated in the stipulations.

Then the reductionists arrived. Nobody knows why (well, besides reduction) but they decided to withdraw the original intention of the miscellaneous conventions to supply missing diagram information to orthodox problems and replace it with a new and alien pre-assignment to first figure out which rules apply. Initially based on "workable solutions" and later on "retro-problem type". Meanwhile, the net had arrived as well. Before the net, the retro-problems were indentifiable by the neat retro-column in the chess magazine. But now suddenly the "retro-problems" were copied and posted everywhere requiring the assignments and rules to be portable. No column or environment to identify the types and the rules. Which meant we went in the diametrically wrong direction. Instead of supplying more information as appropriate for portable objects, the reductionists provided less information.

And now we landed in the situation which the miscellaneous conventions always intended to forestall. To find out how to solve a problem with orthodox instructions (such as white wins) you first need to determine whether or not it is a retro-problem even when it follows all the FIDE rules. With any "luck" your next assignment is to reject the logic which could not possibly deliver a satisfactory solution and finally - if you didn't die from fatigue - you may progress to actually solve the problem. It's a good joke but it is also the universe on its head.

Yes I pretty much agree with Addendum 2. Do you know that the WFCC agreed in Vilnius to move to the latest version of the FIDE Laws, but then failed to announce it? The result is lost! The chair of the rules committee is well known for not answering emails, so it might as well not have happened. Madness haha

BTW I think 3Rep & 50M are basic rules too. The *implementation* over the board is complicated and requires machinery as specified in Section 9

I am not sure what you agreed to. All of it ??? I just added and edited a second addendum!

No , they are not in the basic rule set. It stops after section 5. In the older (I think pre 2017) version of the FIDE laws, the basic rules cross referenced to the competition rules which effectively made them one body of rules. Now they are clearly separated allowing for the replacement of one competition rule set with another!

No I meant they conceptually *are* basic chess rules for me. Good old 3Rep & 50M. Obviously I know that in the current layout of FIDE rules they are stuck in section 9, but if you are building one grand set of rules for the ages, you wouldn't want to be hung up on that

Btw you cannot move to the latest versions of the FIDE laws without amending the composition codex to deal with the FIDE 3R, 5R, 50M, 75M complex.