Does anyone know of a game that was drawn under the mandatory 75 move rule?

In fact, computer simulations of chess are chess in accordance with the FIDE laws. Not of any particular implementation but certainly for an abstract flawless computer interface which supports all the relevant FIDE laws. First of all this is true because FIDE has intensely engaged in disussions with the digital community on the integration with the OTB environment. That has resulted in the articles on 75M and 5R terminations which were inserted on the request of that community. The fact that FIDE has found it unnecessary to provide separate laws for playing under computer interfaces indicates the two are considered compatible on the parts where they overlap - most parts outside article 4. Which can only work when the non-overlapping parts operate as closed modules in their own environment - just as a library function in a computer program. Nobody cares how and where it is executed. It only connects to the program by the exchange of defined data objects.

I only mentioned the idealized computer as a logical reduction of the effects of article 4. If executing a move in a computer interface is a simple thing for a player then the OTB move must be an equally simple thing by result. The human stumbles and cheats are to be resolved inside article 4 and will not change the format of the outcomes. 

Note that there is no externally relevant alternation of colour in article 4. The only relevant colour is the colour of the player on move since he is the one in control. In one move turn, only one player decides between the options given by the rules.

Perhaps I phrased it badly. By "if it is postulated that the series of  legal moves is a possible game continuation", I intended to mean, if the relevant rule (5.2.2 etc.) postulates it.

By saying "... neither player can checkmate the opponent’s king with any series of legal moves", my contention is that the 5.2.2 as it stands does postulate it, because it would naturally be taken to mean, "can checkmate by playing on under the rules in force". So the answer (to "does the series of moves ... alternate") would according to the current FIDE rules be simply "yes".

On the other hand if 5.2.2 were replaced by, "The game is drawn when a position has arisen in which no series of legal moves exists ending in checkmate", then the new rule would not postulate a possible game continuation, because a series of legal moves by itself is just a series of moves satisfying 3.1-3.9. No player is defined to have the move at any point except the start of the series and there is nothing that implies the series must alternate in colour. So if 5.2.2 were replaced as you propose, then according to the resulting set of rules, the answer would be "not necessarily". 

I hope that clarifies.

@Arisktotle

"In fact, computer simulations of chess are chess in accordance with the FIDE laws."

None of the ones I've seen. All mine enforce a draw after 50 moves even if the losing player doesn't claim and, as you say, don't even document what corresponds with touching and releasing a piece for the purposes of article 4. 

But even if they did perfectly simulate the rules they are clearly irrelevant to interpreting the rules.

And the fact that a series of moves occurring in a game must be by pieces of alternating colour is  dependent entirely on articles 1.2, 1.3 and 4, so why do you say, "nothing we do or evaluate in chess with regard to things as legality and move series can ever be dependent on article 4"? For legality I would agree (but not for licitness).

Most certainly the expression "in which no series of legal moves exist" would imply alternation of colour. For the reason that I wrote it and like FIDE I coudn't imagine that anybody would ever read it in any other way. Also keep in mind that the proposition contains a negation. If a series leading to checkmate does exist then it is indeed playable, the game can continue and there is no discussion about legality. The negation is a decent logical trick to prevent having to provide an algorithm in cases where the position is dead. Which is OK for a definition but at the same time leaves the question unanswered on how to find it out. Intuitionists did leave the room some time ago .

Well I would read it to mean exactly what it says. Alternation of colour is determined by the articles I referred to and these take no part in the definition of "legal move". If it is so read without pre-suppositions the phrase would most certainly not imply alternation of colour.  If you were to phrase it "no playable series of legal moves ..." that would be different. It would then correspond with the FIDE rule. Here "playable" would mean licit under the rules and would include arts. 1.2, 1.3 and 4. (But again it should be no series of legal moves playable in the absence of this rule.)

Yes, I suppose many computer programs draw at 50M. I haven't investigated it but I have also seen reports of players telling you have to claim it - on a computer. It would be weird to ask FIDE for an extension to 75 moves and at the same time continue drawing at 50. Also the example games provided a while ago went till 75M. How could they arrive there without a computer executing the rules correctly?

The computer is not relevant to the interpretation of the rules but it helps in cutting through the article 4 red tape to evaluate the scope of that article. It's a reduction trick similar to showing that you can't checkmate a king with 2 knights by retracting 1 move from checkmate positions with that material. For someone who already understands what article 4 is about, the computer parallel doesn't add anything.

On a point I will discuss later "legal moves" constitute possible state changes in a sequential system. Article 4 defines or affects none of these predefined possible state changes. It only deals with the manner in which these changes are realized in a physical game space. Which is totally irrelevant for any other article. The wedding planner might concern him- or herself with the wedding dinner, the dress codes and all the interactions between the wedding couple and the guests. At the same time he/she might be completely oblivious to how the guests arrive at the wedding or how they get their outfits. The rules only state you gotta be there properly dressed in time. How they do it is up to the guests. That's article 4. Ultimately, the players could violate all conditions of article 4 and still play a perfect chess game provided they effectively played complete legal moves before every move turnover. Moves are not actions, they are state changes.

@Arisktotle

"Article 4 affects none ... Which is totally irrelevant for any other article."

Not if that article postulates that all the rules (including art. 4) are to be in effect for some condition as in art. 5.2.2. (In fact 5.2.2 is he only such article in the Basic Rules section I think.)

Note that my version of 5.2.2. was a rewrite of the orginal article showing that self-reference can be avoided. I left the part that was not contentious (to me) unchanged if only not to place emphasis on an element I didn't want to address.

Probably I will only change your mind when I can demonstrate that the expression "legal move" is not defined in the chess rules, not intended to be defined and not required to be defined because it belongs on a different level. But that story is too long for this post.

When the wedding planner says you gotta make your own travel arrangements doesn't mean it matters to him/her how you do it. It's a confusion of the how and the what. Article 4 is relevant to the outside for what it accomplishes but not for the how which is all the article is about. You need not know or read any part of article 4 for application to 5.2.2. beyond the fact that it produces a legal move in a physical game space - the one thing article 4 doesn't state or define explicitly! This is the nature of modular designs.

Probably, when you look at it formally, article 4 can be removed. Article 3 precisely describes the legal moves and one might leave it to the players on how to execute them. Arguably article 4 was only added to battle cheating and bring some order in the house.

@Arisktotle

Your rewrite avoids self reference. The problem is that FIDE decided to define "legal move" with reference to a restricted set of articles. This means that in the rules it doesn't mean what you always thought it meant.  (I think FIDE didn't include arts. 1.2, 1.3 and 4 in the definition of legal move to avoid the problems of then interpreting 4.7 "When, as a legal move or part of a legal move, a piece has been released on a square, it cannot be moved to another square on this move. The move is considered to have been made ... " which would leave you a problem deciding whether or not it was a legal move or part of a legal move. (It's a legal move if it's been released as a legal move which is true so long as its been released as a legal move ... .) But what you are really trying to say in your rewrite is "a series of licit moves" where "licit moves" means what you always thought "legal moves" meant before FIDE redefined the term. Were you to substitute "licit moves" in your rewrite you would re-introduce self reference.   

No. You need to know that it produces a move of a piece of the intended colour, which is mandated only by art. 4. What I suggested we call a licit move rather than the defined legal move. Without that the first diagram I posted in #197 would not be dead under the rule. I think it's dead under the FIDE rule but not with your proposed rewrite (or, at least, not if you think checkmate has meaning as the result of a series of moves that is not assumed to be made by players - I would say that strictly speaking all positions that are not already checkmate would be dead).

Article 4 is only activated when it is known that the game is alive and which player is on move. Though article 4 speaks of "the player on move" as if it might address both sides, it effectively does not. Where it states that "only the player on move can adjust the pieces" it merely confirms that only one player is control of the game in this phase. But article 4 doesn't know who is on move, it needs to be told by a father process which runs the game flow. The father process provides the alternation of the players and reactivates article 4 after the move turn. This is part of the base setup for sequential games. It is also necessary because other steps must be made after a single move before turning the move over like - you guessed it - the DP evaluation. That's why article 4 cannot produce an uninterrupted move series. 

In my approach to 5.2.2 checkmate is not an issue. It is always legit to qualify a move series as one that could be played by the players before they do it. Since it doesn't concern a dead position, the assumption is valid! Unless you propose to eliminate the word could from our language.

Yes, I shouldn't have used the word "only". It is of course arts.1.2, 1.3 ad 4 in combination. But this doesn't invalidate my point.

Btw. it actually states 

Only the player having the move may adjust one or more pieces on their squares, provided that he first expresses his intention (for example by saying “j’adoube” or “I adjust”.

Which is one of the problems I referred to with section 4. It refers only to misplaced pieces on their squares. I think there should be a rule, "only the player on move can touch the pieces on the board". 

I extended my previous post with a few lines to illustrate why article 4 is not the one alternating move turns.

The added lines on checkmate obviously assume alternation in the "series of legal moves". At some point it should occur to you that where you get in trouble, my approach delivers a consistent and workable version of the chess rules - with just minor amendments.

In my approach to 5.2.2 checkmate is not an issue.

?

It is always legit to qualify a move series as one that could be played by the players before they do it.

It is legit so long as you do qualify it, which you didn't. In fact the difference between the FIDE wording and the proposal seems to be only that you removed the qualification. But then if you were to so qualify it without explicitly saying "could be in the absence of 5.2.2" you just reintroduce the self reference.

Since it doesn't concern a dead position, the assumption is valid! Unless you propose to eliminate the word could from our language.

I think here you're saying that the qualification should be understood without explicit mention. I disagree, but in any case that would just give you an implicit self reference instead of an explicit one. 

But maybe I misunderstood. I don't understand your final sentence.

In some contexts the phrase "legal move" refers to the change accomplished by the move, in others it refers to the playing of the move (e.g. article 4). It's a consequence of the multi-functionality of the "move" word. As a noun derived from a verb, it sometimes refers to the action, sometimes to the change aspect or both. You will not address such concepts because you believe that the phrase "legal move" is defined only in its entirety. Not true, in fact, it is just an english language shell concept - with a touch of game theory - which is valuated in the context of chess or another place but not defined. Therefore the interpretations of "legal moves" follow the options available to us in the english language and sequential move games. Which generates quite a lot of freedom for the interpretations of the component parts "legal" and "move". Be back on this in a separate reply.

Thus, the statement that "no legal move exists" should be viewed as stating that "no move can be legally played in the position under investigation and the right player on move" - referring to the action aspect of the noun "move" in combination with the contextual address of the adjective "legal". A move always needs to be a well-formed move but you may define it any way you like as long as all legal state changes are somewhere in the finite set of possible moves. That is why all formal mathematical systems include descriptions for their wffs (well-formed formulas). These are necessary to randomly enter the complementary system space and make it available to logical reasoning, e.g. by RAA - reductio ad absurdum.

The objective of a game has no bearing on discussions of the rules because it is outside the formal rule system. It is a meta condition in itself accompanied by its own logic; for instance, many compositions go by the same rules of play but have different objectives. Identifying checkmate is only detecting a named termination point (the game terminated with black being checkmated) which is a formally accessible target. Like my approach to 5.2.2. it is defined by FIDE in a complemententary non-algorithmic manner. Only if no legal move exists - and with the king under attack - the game is terminated in the state "checkmate". This is OK because it leaves the legal moves with the positions/histories where the game can be continued. The heuristic step of negating the conclusion is one all humans make effortlessly because they do so thousands of times in their lives when solving ordinary decision problems. In an axiomatic approach you can use the knowledge that only a finite number of state changes exists. When the axioms produce none of the finite number of changes, then you may conclude that none exists and declare checkmate. The system itself cannot conclude that but we can by reflection. This process is trivial and belongs to the neural knowledge of most human beings. FIDE avoids such a formal approach because most of us are not mathematicians. There is more than one way to communicate with humans though.

Another shortcut to the "series of legal moves". Chess consists for I guess 90% of simulations of series of legal moves which we call "thinking". These moves are not played but they produce the same (simulated) outcome as the moves when they are played. You would be mad to consider including or rejecting a move because the rules suggest there is a difference in appreciation between the moves you think and the moves you play. That would mean that the system you simulate fires back on the simulation which becomes circular. This applies to the evaluation of conditions such as checkmate or stalemate. It does not completely apply to dead positions because the moves we need to consider in these evaluations are potentially beyond termination which gives problems. That is why we need to amend the rules of play for analytical DP playouts - if we demand an algorithm. I suggested the scenario with a shadow board where the game-analysis is continued with different rules.

My point is this: the only function of the activation of a "series of legal moves" is to produce a simulation of some type. The simulation is invisible to the chess system which cannot say things like "this rule applies to moves which can actually be played and not to simulations". It cannot say that because the simulation asserts that all its moves can be played in the game and game section it simulates". When the simulation follows different rules from the standard chess rules then its outcomes must be reinterpreted in a way dictated by the standard chess system. After all, the simulation is only a service device.

Note: most simulations are partial and only emulate the parts required for the resolution of an issue at hand. For instance there is no need to address the content of article 4 when analytically deciding about possibly dead positions, even in an OTB game.

On legal moves

A few decades ago - before dead postions were introduced to the FIDE laws - nobody would
argue about the meaning of the phrase "legal move". Since the "move" part clearly refers to
the action of "moving" or "playing" and "legal" to its legitimization by the laws, a "legal
move" could only be "a move you are permitted to play" - given a particular game state. As
witnessed by for instance by the articles 3.8.2.1 and 3.7.4.2 the legal moves are evaluated
as "changes one is allowed to make to an actual game position" and not as "the isolated movement of pieces on an otherwise empty board or in a theoretical diagram".

In terms of definitions, article 3 mainly focuses on the extensional aspects of "the legal
moves" which corresponds to the "maximized list of move choices available". There is however
also an intensional definition of "legal moves" (or simply "moves") which applies from theory to the whole category of "sequential move games" (like chess, tic-tac-toe, draughts, go ..). It says that a move denotes all the actions of one player in a single turn. So moves are not about "pieces" but about "player actions". Two other intensional characteristics of moves stand out:

(a) By the choice of the player on move, a move takes one known game state - addressed as a position - to the next game state. These game states are quite complicated as they involve (besides the obvious piece configuration) all properties which might affect the future of the game - like conditions on castling right, e.p. right plus 3rep, 5rep, 50M and 75M progressions. For simplicity one is advised to forget all these individual property states and assume instead that every move is added to the full game record which represents the current positional state in its entirety. So we define the game state as "the full game record up to now" optionally supplemented by a diagram. This way, all information for the execution of future moves is always available if required. In fact, that is why arbiters require you to keep the game record in an OTB game. For them it is the only sure-fire method to resolve every game-history related query. Most importantly, the game record always reveals who is on move by application of the alternating move logic. A (legal) move can therefore never be a move by the "wrong" player. This fact is reflected by article 1.2 which takes care of this intensional aspect of the "legal move" in "sequential move games".

(b) No legal move can be made when the game is in an "end position". "Stalemate" and "checkmate" are obvious examples but end positions also occur after "draw agreements" or for instance in "a dead position" or after a "5rep". Note that it is simply a rewording of the principle that the "game rules no longer apply when the game is finished" which is trivial for any sort of formalized game.

One might argue that pieces of game theory ought to be included in the rules if one expects
players to abide by them. That is only partially true. The alternation of moves between players
is indeed in article 1.2 though everyone already knows it from the days they learned tic-tac-toe. That the rules of a game stop functioning after the game stops can not be in the rules of chess or any game except as a clarification. It would be paradoxical to specify a game rule which says of itself that the rule is invalid - at the point of its relevant application. It's a truly universal meta game rule!

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So where did the trouble with legal moves start? It was with the introduction of the rules on "dead
positions":

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 .....

This rule is not formally incorrect but most confusing! I would have much preferred to use a different formulation:

5.2.2: The game is drawn when a position has arisen in which no series of legal moves exists leading to checkmate. The game is said to end in a ‘dead position’. This immediately ends the game .....

The following issues might be encountered with the current FIDE version of 5.2.2:

(a) One might believe that this article suggests there are legal moves you can or cannot play even though the position is dead. Well, it does appear to suggest that but it does not say that. Once the position is dead, not a single legal move exists, let alone can be played (see the paragraph on the intensional properties of moves). So what? If the position is not dead you can certainly find a checkmate with legal moves. But how to find out that a positions is dead? Well, any way you like and which will convince the arbiter. Even if you could play legal moves in a dead position, playing all the possible lines (possibly millions) to prove there is no checkmate anywhere is undoable. You will need heuristic reductions anyway. The FIDE article does not force you, your opponent or the arbiter to produce a particular proof so you might all agree to an ad hoc procedure. For instance, both players get the opportunity to produce a checkmate by playing arbitrary moves for both sides on a duplicate board position for 5 minutes. When they both fail, the position is considered dead. Note that my formulation for article 5.2.2 is better than the FIDE version but the proof problem is the same. So the available approaches are the same. In time, somebody will write a computer program to do this job with 99.9999% accuracy.

(b) In pure despair one might attempt to assign a different meaning to a "series of legal moves" for instance by randomly mixing black and white moves as if they are broken loose from the game. That would simplify the analysis to find a checkmate somewhat but it is in direct conflict with the intensional properties of the "move object". Since a legal move by article 1.2 must comply to the "who's turn (who is on move)" alternation, its definition leaves no room for such frivolous interpretations.

Note: The cause of FIDE's poor formulation of article 5.2.2 is the desire to primarily address game players and arbiters with concepts all will understand. Those who read 5.2.2. with common sense will see that a conditional analysis is required and care less about how it was formulated. And I bet most of them do indeed get it right. Whatever you believe, it is unthinkable to break with all game theory by legalizing moves after game end positions. That would only propagate in discussions and differently domains - such as compositions -  where these misassignments can have significant effects. My personal view is that one could erect a class of analytical moves for out-of-game analysis.

Note: In tournaments players may continue to play after a position is dead or after a 5-fold repetition of positions or a peaceful 75-move series. They play these moves outside the game scope because they are not aware these conditions occurred and have no time to check them. These situations should be addressed by FIDE in the same category as "what to do when a bear enters". They have nothing to do with the rules of chess only with the uncontrollable imperfections of its environment.

i guess its 50 in USCF and 75 in fide