proof

[JacquesRW]

As for me claiming to have a proof (for an ultraweak solution), if you would read accurately enough
through the reference i gave for abductive reasoning, you could point out that such reasoning is
usually not giving such 'proof's. quoting from the wikipedia article :

Abductive reasoning, unlike deductive reasoning, yields a plausible conclusion but does not definitively verify it.

This is entirely my point. You can't claim to have an ultraweak solution if you have not proven it.

[JacquesRW]

key point (repeating myself, but for clarity) was the combination of 1) Black can avoid forced checkmates
from ply 3,4,5,6 etc. and 2) because the 'tree' (of possible checkmates lines) is (exponentially) widening,
there's 3) no way White can force a mate after ply 10,11,12, etc ad infinitum. QED

This reasoning does not work. You only need a single forced checkmate line to contradict it. Making an argument that it is highly unlikely is not enough to conclude that there is no way white can force a mate.

[jefk]

You can't claim to have an ultraweak solution if you have not proven it.

my point is that an 'ultraweak solution' (UWS) doesn't have to be proved.
In the game of Hex it was shown with some strategic arguments it's a draw.
In the game of chess by now it's known that the end result is a draw with best play.
Just as we know that the earth isn't flat (yes i claim that without proven it).

But if it's known a game is a draw then this is similar as having an UWS depending on the
definition of course. Apparently you want to use your own definition (have you read that
Phd paper, and the context of the later quote by vd Herik ? Just wondering. You like
syzygy a year ago may claim it was *meant* with UWS there must be mathematical
rigorous proof that the outcome is certain (to be a draw, win, or lost). This imo
is just speculation, mathematical/wishful thinking.
But i can agree to disagree. Depending on the definition of an UWS, i'll put it on hold;
yet i still maintain that it's 100.000 pct certain with current rules chess is a draw with best
play. Ofcourse the math inquisition or other thought police now likes to hunt me
as if i'm math enemy nr one because for them it's not proven that it's 100.000
Ok, lets say then 100.0 happy now. Actually 99.9999(etc) will converge to 100,
this is well known in math, a limit theorem and it's proved as well btw. Lol

[jefk]

You only need a single forced checkmate line to contradict it.

well that's the point, there are no such lines (*).

can you find a force mate in two for White ?
(hint, doesn't exist).

(*) up to a certain depth it can be seen that such forced mates don't exist. And second part of
my reasoning was the widening of the 'tree' (of possibilities of avoiding checkmate; a slightly more speculative
thought i admit, but such thinking is not uncommon in eg. mathematical control theory where forecasts are
being made with math models and based on that strategies are derived to eg. stabilize the process.
Also referred to sometimes as 'dynamic programming'.
https://en.wikipedia.org/wiki/Dynamic_programming
And it works, it's being used, although it's not always easy. Musk failed with three rockets trying to land down
again without crashing, the fourth time he succeeded. But maybe you like to mail him and tell him it's
mathematically impossible because it has not been 'proven'. Well good luck then and have fun.

[JacquesRW]

my point is that an 'ultraweak solution' (UWS) doesn't have to be proved.

I'm not sure why it would be, or why you would want this to be the case. You can have an ultra weak "solution", and it can simply be wrong? The only way to verify that it isn't garbage is proving it anyway?

yet i still maintain that it's 100.000 pct certain with current rules chess is a draw with best play.

I'm not disagreeing on that - I believe Chess is a draw.

[JacquesRW]

You only need a single forced checkmate line to contradict it.

well that's the point, there are no such lines (*).

But you aren't justifying that they don't exist, you are only saying that it is unlikely. As I said in that post.

Not sure how long I can bear to continue to engage in something that seems like trolling, but I'd like to point out that this thread is called "proof", and you've now said that actually you don't need to, and have not, provided a proof. lol

[jefk]

it's not (meant as) trolling.
Regarding 'proof's there are various sorts of proofs. Mathematically rigorous proofs, sometimes
still with one or two flaws (as in the first proof by Wiles about the Fermat conjecture
mathematical less rigorous proofs, in the process of later possibly becoming more rigorous.
In addition in science there exist real world findings, eg. that the earth isn't flat.
In jurisprudence, aka law (*), it's sometimes stated that it was proved that someone
was guilty. But for you such proofs are never rigorous because they are not with
100 pct mathematical certainty. Well luckily we now don't always have mathematicians
in court rooms otherwise it would become an annoying mess.
A game as chess is much more than only the mathematical abstraction; game theory is
just only a subset of reasoning which can be used for certain purposes. With knowing that
chess is a draw, it's irrelevant whether this has been proved (rigorously) or not (yet)
in mathematical game theory. Utterly irrelevant. You can try to prove the earth isn't
flat by comparing it with a globe, then using 3D euclidian dimensions (eg. making a model)
and so on, a method often used in physics (together with measurements and reasoning.
Then when you're finished and declare the earth isn't flat, after which you will be
hunted by the math inquisition because your 'proof' wasn't mathematically rigorous
for whatever reasons(s) eg the earth isn't perfect globe, it's not 'proved' that there
are only 3 spatial dimentions (hey maybe there are 4?). And so on, ad nauseam.

(*) a year ago i posted a link with a principle of cumulative evidence (used in law) after
which i got some derogatory comments from a math guy suggesting that apparently i'm
not able to see the difference between law and math. well i do but apparently some
math fundamentalists can't see the world often is more complex than their math models.
Again, try to find that Phd thesis (where UWS was mentioned), it's much broader than only
giving proofs; the UWS definition was later copied out of context in a wikipedia articles,
suggesting this is the absolute truth ergo one and only definition of an UWS (not).
Because in the original Phd thesis, it was stated that UWS means 'determining' on beforehand
(if a game is a draw or win/lost). The word ''proof'' was Not used (although one example was
given for -one variant of- the game of Hex, in which situation it indeed was a like a proof).
Nevertheless, it's for some years now determined that chess is a draw thus an UWS.
Whether you like it or not, or consider it trolling, or whatever.

[JacquesRW]

it's not (meant as) trolling.
Regarding 'proof's there are various sorts of proofs. Mathematically rigorous proofs, sometimes
still with one or two flaws (as in the first proof by Wiles about the Fermat conjecture
mathematical less rigorous proofs, in the process of later possibly becoming more rigorous.

Those are called "incorrect", Wiles' proof was incorrect, and wasn't accepted until it was corrected.

(*) a year ago i posted a link with a principle of cumulative evidence (used in law) after
which i got some derogatory comments from a math guy suggesting that apparently i'm
not able to see the difference between law and math. well i do but apparently some
math fundamentalists can't see the world often is more complex than their math models.

We're talking about Chess here, a formally defined game. A theoretical result about Chess has nothing to do with the real world.

I don't think many people disagree that in practice chess is a draw. But this isn't new or interesting information.

EDIT: This is the second time you've edited a post in this thread with significant changes, can you just make a new post instead? I post a reply only to see something completely different to before.

[jefk]

This is the second time you've edited a post in this thread with significant changes,

yep maybe you reacted a bit (too) fast.
While usually the time for final editing of a post isn't so long (10 mins or so) if i notice
something written wasn't clear or incorrect, i prefer to edit it rather than making a new post.

In some situations a new post could suffice, but it might also cause extra confusion.
no big deal, i suggest to be flexible.

Chess being a draw is no big news anymore, but in the past i got responses -like now from you-
that this wasn't proved yet etc. (thereby then also seeing suggestions to reduce the draw rate in (ICCF)
correspondence chess eg. by Nickel, Kaufman and myself as being not really required (yet).
The latest correspondence chess world champ Jon Edwards wasn't convinced at least one or two years
ago the game is a draw (and apparently still thought he could get advantage with the Glek system.
But by now the paradigm (usually more prevalent in physics than in math) indeed is towards 'draw'.

Chess is more than the basic rules e.g mathematical concept but when discussing it's a draw
game theory indeed becomes an important element. What i was trying to say is that
imo mathematical game theory anno 2024 isn't so well established as you might think and that it's
not always necessary to use 'number crunching' like they did for checkers to determine on
beforehand the fundamental result aka theoretical outcome of the game.

PS here's the Phd paper i referred to earlier (1994) by V.Allis
http://fragrieu.free.fr/SearchingForSolutions.pdf

And here's the vd Herik paper (2001)
https://pdf.sciencedirectassets.com/271 ... 7/main.pdf

[JacquesRW]

PS here's the Phd paper i referred to earlier (1994) by V.Allis
http://fragrieu.free.fr/SearchingForSolutions.pdf

So the definition is given as

ultra-weakly solved
For the initial position(s), the game-theoretic value has been determined.

and it seems your whole post is predicated on it not saying "AND PROVEN"?

What i was trying to say is that
imo mathematical game theory anno 2024 isn't so well established as you might think and that it's
not always necessary to use 'number crunching' like they did for checkers to determine on
beforehand the fundamental result aka theoretical outcome of the game.

I'll state clearly the only point I want to get across:
Unless it is proven, you have not determined the game-theoretic value, as your believed value **could** be wrong.

This doesn't inherently have anything to do with game theory itself, in 2024 or not. I'm quite confused as to how you've determined "anno 2024 isn't so well established as you might think" as I haven't given any opinion on the state of mathematical game theory.