Chess will never be solved, here's why

My point is the laws don't say that.

They do say:

12.1 The arbiter shall see that the Laws of Chess are observed.

If the laws of chess are observed in that case, both players win.

5.1.1 The game is won by the player who has checkmated his opponent’s king. This immediately ends the game, provided that the move producing the checkmate position was in accordance with Article 3 and Articles 4.2 – 4.7.

5.1.2 The game is won by the player whose opponent declares he resigns. This immediately ends the game.

@Optimissed

I'm sure something of the sort would happen, but the arbiters would be violating 12.1.

The laws themselves say unequivocally that both players win.

I just copied it verbatim from the handbook. You'll have to write off to FIDE and tell them they're dishonest.

Endgame problems don't generally specify the number of moves to mate, so slower solutions are normally acceptable. 

Just look at the link. I believe it's the most up to date version.

The laws taking effect from January next say the same.

Again you'll have to write off to FIDE and tell them they're illogical. (You might be right.)

@5912

++ The same weak solution without the 50-moves rule also applies with the 50-moves rule.
"Is that what you mean by your above statement?"
++ No, a weak solution of chess is a strategy for the initial position to achieve the draw against any opposition. Your 5-men position is strongly solved in the 7-men endgame table base and cannot result from the initial position by optimal play from both sides.

++ The game as described in the Laws of Chess. https://handbook.fide.com/chapter/E012018
"There are at least five games described in your link." ++ No, there is one only.

"why then are you bringing ICCF and TCEC into it when they have different rules?"
++ Because they share the same weak solution.

"The games I posted are interest to me" ++ Not to me. All 7-men positions are strongly solved. Weakly solving chess is from 32 to 7 men. I await your drawn KRPP vs. KRP.

"What rules are you going to assume?" ++ The Laws of Chess.
"all of them?" ++ Yes.

@5917
"most people would identify "position" and "game state""
++ No.
Diagram = position of all pieces.
Position = diagram + side to move + castling rights + en passant possibility i.e. FEN without ply
Game state or node = position + evaluation + history

Actually, it depends on which ruleset you are using.

Even in chess with a repetition rule and a ply count without irreversible move rule, the game state only requires the history back to the last irreversible move.

Which brings to mind that there is a minor imperfection in the FIDE rules in that the repetition rule says:

The game is a draw if a position occurs (at least) three times during the game. (Intervening moves do not matter.) It must be claimed by the player with the turn to move. The claim is made:

(a) If the position is about to appear for the third time, the player making the claim first writes their move on their scoresheet and notifies the arbiter that they intend to make this move.

or

(b) If the position has just appeared for the third time, the player with the move can claim the draw.

Positions are considered the same if

(1) the same player has the move,

(2) pieces of the same kind and color occupy the same squares, and

(3) the possible moves of all the pieces are the same.

This certainly looks like it refers to the possible IMMEDIATE moves of all of the pieces. As such it could fail detect a loss of castling rights that would make it a different state. The reason this is important is that loss of castling rights changes the possible future paths, sometimes crucially, and this could be an achievement by one player.

The rule could be improved by saying "the possible future moves..." instead of "the possible moves..."

@5932

"As such it could fail detect a loss of castling rights that would make it a different state."
++ No. This is the actual wording. 9.2.2.1 and 9.2.2.2 treat castling and en passant.
9.2.1
The game is drawn, upon a correct claim by a player having the move, when the same position for at least the third time (not necessarily by a repetition of moves):
9.2.1.1
is about to appear, if he first indicate his move by writing on the paper scoresheet or entering move on the electronic scoresheet, which cannot be changed, on his scoresheet and declares to the arbiter his intention to make this move, or
9.2.1.2
has just appeared, and the player claiming the draw has the move.
9.2.2
Positions are considered the same if and only if the same player has the move, pieces of the same kind and colour occupy the same squares and the possible moves of all the pieces of both players are the same. Thus positions are not the same if:
9.2.2.1
at the start of the sequence a pawn could have been captured en passant
9.2.2.2
a king had castling rights with a rook that has not been moved, but forfeited these after moving. The castling rights are lost only after the king or rook is moved.
https://handbook.fide.com/chapter/E012018 

Looks like I was referring to a version of the rules that was replaced in 2018.

12.2.2 

12.2 The arbiter shall:
...
12.2.2 act in the best interest of the competition,

doesn't prohibit two people winning the same game.

If the game is played under basic rules an arbiter has no jurisdiction and art.12.2.2 doesn't apply..

If the game is  played under competition rules art.12.1 mandates that the arbiter must declare the game won by both players in the circumstance I mentioned. If you feel that is not consistent with art.12.2.2 in that circumstance then you feel the FIDE laws are inconsistent. That doesn't mean the rule prohibits both players from winning.

FIDE might feel that art 10.2

10.2 The total score of any game can never exceed the maximum score normally given for that game. ...

is enough to resolve the inconsistency in that case. Both players win and each scores 1/2 point in the tournament. (Or maybe it's scored 1-0 or 0-1 depending on the arbiter's mood.)

 FIDE, just to be inconsistent, don't have a ply count without irreversible move rule. You can castle into a 50 or 75 move rule draw.

@5938
"You can castle into a 50 or 75 move rule draw."
++ Yes, you can, but not in a perfect game with optimal play from both sides.
Both players can aimlessly hop around with knights for 75 moves to trigger a 75-move draw with all 4 castling rights intact, but that is sure not to be a perfect game with optimal play and it would not oppose to the draw.

https://www.iccf.com/game?id=1164365

Here is an example of a game > 99% certain to be a perfect game with optimal play by both participants. It is the most recently finished ICCF WC finals game. It is exceptionally long: 65 moves and it ends in a 7-men endgame table base draw. The 50-moves rule was never even close to being triggered. There was always compelling reason to move a pawn or capture a piece. Not moving a pawn or capturing would not be optimal play and could cause a loss.

@5940

"You are certain that two tempi provides a win for black in the following position?"
++ No, that is still a draw. White is up 1 tempo in the initial position, which is a draw.
If white loses 2 tempi, then white is 1 tempo down.
To win you need an advantage of 1 pawn or 3 tempi.

"No way is the result clear." ++ This is very clear: a draw.

"you are now relying on samples of size 1 to "prove" results about chess in general"
++ That is one example of 1104 perfect games with optimal play from both sides.

But you can see this has got the wrong answer. After 1. Nf3 d5 2. Ng1, black is clearly better off than white in the opening position! Black gets two good moves in while white has moved nothing (net).

The problem is that the terminology "one tempo up" is slightly misleading. You could really say white is 0.5 tempi up at the start because, as the game progresses, white alternates between having made 1 more move and 0 more moves, averaging 0.5 more moves.

By this better quantification,  black has 1.5 tempi advantage after the moves above. This comes from 0.5 - 2.

Likewise what is called "3 tempi" really means 2.5 tempi advantage (alternating between 3 tempi ahead and 2 tempi ahead).

@5944

"After 1. Nf3 d5 2. Ng1, black is clearly better off than white"
++ Black has gained 2 tempi, thus 1 tempo versus 1 d4. That is not enough to win.
For example 1 e4 d5 2 exd5 Qxd5 3 Nc3 Qd8 is playable despite the lost tempo.
IM Basman has often played 1 h3 d5 2 a3 like in the British Championship, which is like 1 Nf3 d5 2 Ng1. You could argue if the moves a3 and h3 are assets or liabilities.
https://www.chessgames.com/perl/chessgame?gid=1026336 

"You could really say white is 0.5 tempi up at the start because, as the game progresses, white alternates between having made 1 more move and 0 more moves, averaging 0.5 more moves."
++ White is 1 tempo up, than after black plays 0, then 1, then 0. It averages 0.5, but white has an extra punch of 1 move. Like 1 e4 e5 2 Qh5 Nc6 3 Bc4 Nb8? 4 Qxf7#

"Likewise what is called "3 tempi" really means 2.5 tempi advantage (alternating between 3 tempi ahead and 2 tempi ahead)." ++ 3 tempi is 2.5 tempi average, but 3 tempi punch

You're right.

Some people keep saying Syzygy is a strong solution of 7 man chess under competition rules.

@5946
"Syzygy is a strong solution of 7 man chess"
++ Syzygy or Nalimov, do not care. 7-men chess is strongly solved.
You seem really obsessed with the 50-moves rule.
The 50-moves rule plays no role in solving chess.
It is just a practical rule to prevent games to last too long.