Chess will never be solved, here's why

Almost everything after "for all practical purposes" is garbage...(highlighted red)

https://youtu.be/3EkBuKQEkio?si=7XJZ2fTs34BMs4OP

Anything could be 'weakly solved'.
Cure for cancer - hey most people die before 90 anyway - and nobody gets to 130.
There. Cancer just got 'weakly solved'.
Reverse time travel?
Lots of movies making many millions of dollars about that.
There. It just got 'weakly solved'.
How about zero to sixty in under three seconds?
Is it 'solved'?

Yeah - apparently cheetahs can do.
Beating out muscle cars and fighter jet aircraft.
But Suzuki bike even faster.
Now that's Solved.
Want zero to sixty in under a second?
Yeah sure - a bullet in a barrel of a gun.
There you go.

It seems surprising to me that you, as a chess player, can't understand that at many, many places in the entire tree of analysis generated by one of the sides, there are moves that are simply ignored after a zero ply analysis. Billions in each game. Trillions in a set of 102 ICCF games, I would estimate. Guessing they don't matter is acceptable (and necessary) for a chess player playing a game and trying to maximise the (statistically) expected result, but is fatal to any claim of weak solving. Not only is there no such thing as "for all practical purposes" in proofs, what you describe is trillions of nodes away from being well-described as such.

In the solution of checkers, there were NO such loose ends. That's because those who did it understood what weak solution meant and were well-aware that doing a half-arsed job and saying "we're sure the result is a draw" would be worthless and not even merit publication. They used a thousand years of powerful CPU time - much more than that in an ICCF match, although the speed of hardware has greatly increased - because it was necessary. You are saying it needs LESS computing power to weakly solve chess than checkers!

No.

The branch of mathematics in which I finally specialised at University was mathematical analysis (building on real and complex analysis and topology to do differential geometry on manifolds, topological groups (an abstraction of Lie Groups) and functional analysis (essentially analysis in infinite dimensions, motivated by the fact that classes of functions form infinite dimensional vector spaces with metrics). So in that sense I am precisely a mathematical analyst.

That being said, it's the more elementary analysis - such as calculus in multiple dimensions - that I use all the time. Such as now, so bye.

All of which will mean nothing at all to @Optimissed because he was obviously badly frightened by a surd as a child and is now incapable of facing anything of a mathematical or logical nature.

I think it's reasonable for anyone not to be familiar with most of that!

But it is characteristic of @Optimissed that he chanced upon the term - mathematical analyst - that happens to be most precisely describes me, and then said the opposite. (I presume he was not even thinking of "analysis" in the mathematical sense, referring to the branch of mathematics that developed out of calculus).

Chess has not been strongly solved for all positions of 7 men or less as you are well aware. Why don't you update your cut and paste files?

Chess has not been solved in any sense for many positions with rooks and not strongly solved for the majority of all positions of 7 men or less under competition rules. (Indeed with the definition of "position" that you insist on for competition rules even ultra-weak solutions do not necessarily exist.)

Hmm. This seems a bit too pedantic. The 3-fold repetition rule is a convenient addition to the rules rather than being of fundamental interest. It settles games when neither player can work out how to win - even giving them a couple of shots to realize a position is not getting them there. Chess with a 50 move rule suffices entirely to avoid infinite play, and Syzygy tablebases suffice to deal with this.

The only fundamental difference is to distinguish when earlier faffing around in a game - visiting at least one (basic chess) position at least twice - has managed to reduce a win to a draw by blocking all routes to the win.

How many times have you seen chess problems or other positions of interest published, where they list all the positions that have been previously visited two times because this is crucial to the result?

To be fair, it is worth emphasing the variant of chess that is being addressed. The fundamental one - basic chess - can be theoretically "fixed" by saying the lack of a finite route to a win is a draw. [Note that this is what tablebases do. They work out all the forced wins - there is a hard cutoff when no new winning positions are added for a move of retrograde analysis - and then infer that what is left is drawn].

This can be easily kept a finite game for theoretical purposes by specifying a large maximum number of moves (after which it is a draw). While FIDE might prefer a 50-move rule, a mathematician might lazily use something like the number of distinct positions (say a 10^45 move rule) because if there is no route to a win in the number of distinct positions, you can be sure there is no route to a win!

So while it is true that the precise treatment of the repetition rule turns chess into a monstrous game vastly larger than basic chess and way less amenable to analysis, the main focus of interest is the more amenable versions.

Simply put, under competition rules, Syzygy will lose you points in some actual positions if you take it's recommendation and with @tygxc's definition of position as a FEN with no ply count will give undefined results in any position that is a non terminal win under basic rules. What you say has no bearing on whether these positions are strongly solved according to the definition.

I believe Syzygy can only lose you points in the curious situation where you have been playing a game not using it, make a double repetition, then start using it and run into a triple repetition in the same position. If you had used it throughout, the initial double repetition could have been avoided since no optimal route to a win returns to a position.

Admittedly there are more absurd variations. It is theoretically possible that your opponent only has the chance to blunder and lose in a position that is theoretically drawn and has been visited twice, but visiting that again makes it a draw.

None of this is very interesting!

The most interesting and virtually universal simplifying assumption about a position is that NO positions have been visited twice. Without this assumption most chess problems do not work. If the first move in the problem is not a capture (or other irreversible move), you can't be sure making it does not immediately result in a draw.

You expanded it. I'll post some answers.

How many times have you seen chess problems or other positions of interest published, where they list all the positions that have been previously visited two times because this is crucial to the result?

I've posted one or two and seen a lot of published draws by repetition with sufficient preceding moves. Strictly speaking all printed positions should include that. There is, I think, an unwritten convention that all printed positions should be taken as ply count zero unless otherwise stated or provably not, but that doesn't apply to the game of chess - you can't have a very long game that consists only of pawn moves and captures. 

Yes of course. But isn't that the whole point of the definition? I'm just pointing out that it fails the definition of strong solving, which is distinguished from weak solving by precisely that. I'm not talking about using it in practical play or connecting it with any sort of solution of chess from the starting position. The Syzygy solution is a weak solution under competition rules of all the positions it covers (currently positions without castling rights less than 8 men). That is not the same thing as a strong solution under competition rules (it is under basic rules).

Yes. My point is that the strong solution dominated by the 3-move repetition rule is way more intractable and less interesting that the versions for slightly modified versions. It's like for tablebases, you have ones for basic chess and for chess with an n-move rule and I can't recall much discussion of 3-fold repetition versions except here!

I'm not usually very interesting. I'm just pointing out that when @tygxc keeps posting that the Syzygy tables provide a strong solution under competition rules he's wrong. And that's just a fact.

You can't have a whole game like that, but most basic chess positions can have a zeroed ply count. And when analysing them after that, repetition is only relevant to achieving a draw - if there is a win, an efficient win does not repeat positions.

Yes I know all that. I repeat none of that changes the definition of strong solution and the fact is that we don't have strong solution of winning positions even without castling rights for 7 or fewer men under competition rules. Which is exactly where we came in.

Are you disagreeing with that?

I'm not disagreeing with what you said, but nothing currently (or probably ever) tells you what that efficient non repeating win actually is for general competition rules positions, which would be a strong solution. Syzygy just says TSMYOYO.

I am not sure what a TSM yoyo is , but the point is that the interesting thing is one that has not been done, but which is least intractable. Especially when the practical significance is so little for the more intractable version. That's why people are interested in an 8-piece Syzergy tablebase.

Let me underline that. Solving FIDE rules chess is simply not as interesting as solving chess without a repetition rule, and the purest form of chess is really the one without the 50-move rule either (at least replacing it by a big enough number not to ruin long mates!)