I hate the threefold repetition rule

In the issues with a 75-move rule positions you mentioned the positions are not even dead (because an unlimited number of moves have checkmate as a possibility). You can look at such positions as becoming drawn, but not yet drawn. There is some confusion with the term "dead drawn" but that is not the term applied to a dead position (the term refers to positions that are almost hopelessly drawn with even only moderately skillful play, but I've won, and occasionally lost, positions that were generally considered dead drawn).

MAR, the king and pawns position you posted earlier is dead not because of a move counter, but because even with an unlimited number of moves there is no way for either side to deliver a checkmate.

I didn't say it was dead because of a move counter.

I believe it's dead because neither player can checkmate the opponent’s king with any series of legal moves. That's the FIDE definition.

I posted it as an illustration of the flaw in your argument 

Note that the 75 move rule says "9.6.2 any series of at least 75 moves have been made by each player without the movement of any pawn and without any capture. If the last move resulted in checkmate, that shall take precedence."

The key words are "have been made", NOT "will be made".

The stalemate rule is similarly worded, "has no legal move", NOT, "will have no legal move".

If you apply the same logic to the king and pawns position you refer to, then the position is not dead (contrary to what you just asserted). Both players have legal moves and the fact that they will have no legal moves when stalemate occurs you would deem irrelevant. 

In the issues with a 75-move rule positions you mentioned the positions are not even dead (because an unlimited number of moves have checkmate as a possibility).

What the FIDE rules refer to are series of legal moves and whether either player can checkmate the opponent’s king with any of them.

I'll issue the same challenge to you as I did to @anselan.

Here it is:

I challenge you to produce a series of legal moves whereby either player can checkmate the opponent's king from that position under FIDE competition rules.

Failing that, I challenge you to explain how it's not dead under FIDE competition rules according to

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, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7.

You can look at such positions as becoming drawn, but not yet drawn.

I can, and do, look at them as dead, hence yet drawn, under the FIDE competition rules. (Obviously neither dead nor becoming drawn under basic rules.)

There is some confusion with the term "dead drawn" but that is not the term applied to a dead position (the term refers to positions that are almost hopelessly drawn with even only moderately skillful play, but I've won, and occasionally lost, positions that were generally considered dead drawn).

But that of, course, has no bearing on the subject.

@MARattigan: I predict that anselan will have no problem meeting your challenge - since a legal move need not be a playable move by his personal "Little red book". So he will simply play past the 75M-automatic draw and hand-out a checkmate.

Neither player could checkmate with such a series, so the challenge would not be met. I think you would probably agree with that.

But your prediction is a "strawman". He has not so far done that. We should wait and see. 

By the way a legal move need not be a playable move by my personal "Little red book" either. So far as the FIDE laws are concerned it's just the moves that correspond with the definition of "legal move" in art. 3.

I once proved to you (in a set-theoretical context) that "a series of legal moves" must always be "playable" but the unplayable legal move has been deeply engraved in anselan's mind for many years and is made a cornerstone in his retrograde theories and terminology. FYI.

But I didn't follow your proof at the time and I don't believe the conclusion is correct. I would regard a seriesmover mate, for example, as a series of legal moves. In English a series of legal moves would necessarily be a playable sequence, in fact would mean that, but the term "legal move" must be taken according to the FIDE definition in interpreting the laws.

Right, let's wait and see! I just wanted to spare you the confusions I had in the past when communicating with him about "legal moves". Of course the challenge would be met by ignoring the 75M stop and continue with an unplayable legal move.

The challenge was to find a series of legal moves with which either player can checkmate the opponent's king under FIDE competition rules. That would not be met by a series of legal moves that included any unplayable moves.

That is the whole point of having unplayable legal moves! Though you need it for another purpose.

I acknowledge that the phrase "any series of legal moves" in 5.2.2 would include series with unplayable moves; these would all fail the criterion in that rule that a player could checkmate with the series. 

Note that there are no "series of legal moves" in the FIDE laws except as part of dead- or half-dead evaluations. That is precisely the context in which one could project a future where you can claim to use an unplayable legal move to manifest checkmate potential.

Noted. In each case accompanied by a phrase indicating that a player cannot checkmate with such a series, ruling out series with unplayable moves as a counter-examples.

And, I am disappointed you still believe in unplayable legal moves. It shows you never got the unassailable proof I delivered on the significance of understanding the term "series" much more than the pretty trivial "legal move".

Ah well, 'fraid so. The term"series" has no definition in the FIDE laws so I just take it as English. (Actually because of a background in mathematics, I keep typing "sequence" instead and having to correct it.)

I've done this today, and the problem is obviously fixable by modifying the stipulation to "Game drawn by repetition" instead of "Game drawn". Coincidentally, I published another problem with the same modified stip for the French retro solving tourney, where the more specific stip was felt to be clearer for the solvers. In both cases the content is intact in what might otherwise be a grey area.

Considering the subject and the fact that "series of legal moves" only feature in DP-situations, I thought it was fair to answer the challenge in that context. If you want to make a point with it, that would be the next step anyway. Otherwise I bring it up again when we are there.

"Unplayable legal moves" will never manifest in an actual game - obviously - but might be adressed for analytical evaluations to open or close doors - like a DP evaluation, like a retro-logical-analysis. In fact, the playable legal moves are the only ones which could exist in our reality to produce a legal checkmate. That is why scenario's based on unplayable moves should be completely eradicated from the DP evaluation process.

They are already.

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, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7.

6.9 Except where one of Articles 5.1.1, 5.1.2, 5.2.1, 5.2.2, 5.2.3 applies, if a player does not complete the prescribed number of moves in the allotted time, the game is lost by that player. However, the game is drawn if the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves.

In both cases a player cannot checkmate the player’s king by any possible series of legal moves if that series is unplayable. Obviously.

(Actually not quite obviously, but it applies to any legal position as defined in the laws.)

The FIDE description is not algorithmic but everyone reads it that way - except mathematicians of course

Which brings us to math for instance about terms like "series". All of chess is completely abstract and mathematics. At the same time it is played by "common people". I wrote some posts ago that a reasonably complex game absolutely requires a "system manual" and a "user manual". Whether or not these manuals exist and how good they are, changes nothing about the fact that chess is 100% math. And that is the only level we should address it on on this level of discussion.

The term "series" has precisely the same meaning in natural language as in set-theory. The related property of "ordering" is probably the central property of sets. Almost all sets are well-ordered before the math community gets interested.

?.

Lots of mathematicians talk about, e.g., regions in the Euclidean plane without worrying about any particular ordering of the points.

Precisely as the word "series" in natural language, it identifies a collection of items and an "ordering rule" which orders all of them. The basic "series" in chess is the "chess game" which is nothing but a "series of legal moves", the ordering rule is "the order of play".

Disagree here. Neither the dictionary nor the FIDE laws say anything about that - you just made it up.

The ordering rule is just the order you write them. The series may or may not be playable.

It's arguably true that if a move in such a series is an immediate successor of some other move in the series people might interpret it to mean it should be a legal move from the diagram left by that move, but this interpretation isn't assumed by the above rules, nor in my opinion correct.

In fact I don't think either the dictionary or the FIDE laws even assume a series has to be well ordered. Players obviously cannot checkmate with any series of moves that is not well ordered, so these are automatically excluded as counter examples to the above rules.

There is not a single doubt that the word "series" has the same structure and use in english but the people using it tend not think too much about it. It's rather simple and there are "series" everywhere. We think about it because we have a higher mission. I have written that story before and there are some more steps which I will omit now to prove that legal moves must be playable.. Only this to show there is nothing exotic going on with "series".

Note there are more places where parts of math are disguised in the rules. An interesting one are the basic FOL (first order logic) expressions used to describe the retro conventions, e.g. on castling and e.p. moves or repetitions.

Btw, chess features some of the most interesting subjects in foundational math: non-determinism (plus model theory) and the axiom of choice. Most of it awaiting a decent "system manual".

The axiom of choice would only be relevant to infinite series of moves. If an infinite series of ω moves is either prescribed or postulated under the axiom of choice there is no last move therefore no final position.

You could call that a stalemate because, with no position neither side has any legal moves (those are defined as a relation between diagrams - no diagram no moves) and, of course, neither player has a king in check - for that youl'd also need a diagram. 

Under FIDE competition rules no infinite series of moves is playable, so the question doesn't arise. 

It's worse than that. In the range between 50 and 0 plies from the 75R mark all moves are "fake" in all games since either side could have claimed a draw on every move. What they were doing in that stretch looks more like "playing chicken" than a serious chess game. Nevertheless, it turns out that GMs do play these games - up to and even beyond the 75M mark! That in itself makes DP and the draw rules meaningful for arbitration!