proof

[shawn]

Ever heard of the Zermelo Frankel theorem in game/set theory ? This says that if there's
no winning strategy for a game like chess (two player finite game with perfect information etc blabla)
then it must be a draw.

it's obvious that you are trolling at this point. If not then I do feel sad for you

[jefk]

not trolling, i meant Fraenkel.
https://en.wikipedia.org/wiki/Abraham_Fraenkel
The Zermelo game theorem was part of his work in set theory,
https://en.wikipedia.org/wiki/Zermelo%2 ... me_theory)
whereby the latter (set theory) was done to a large extent with Fraenke. The correctness of
some 'proofs' of his theorems were disputed for quite some time, btw, although a bit off-topic:
https://abel.math.harvard.edu/~elkies/F ... ermelo.pdf
They don't teach you this at Wharton, don't they.

So you feel sad for me, how empathic. As for you, as you're (to my knowledge).
not a mathematician, i can feel equally sad for you btw.
And you didn't reply us what's your chess rating (online correspondence or otherwise).
Anyway i won't be able to see it coz you're now on my 'foe' list; congrats. So you
were the one who is trolling. At least you're not very polite (understatement) i
must conclude and as said now to put on my ignore list.

[jefk]

PS although mr Xu won't see it anymore, found a chess player shawn
https://players.chessbase.com/en/player/Xu_Shawn/755071
https://ratings.fide.com/profile/39903982

age nine years old, so still a lot to learn (so he probably isn't the Wharton person i googled
earlier) a well i don't care anymore. As i'm by now 69 yrs of age and not going to argue
further with such kiddies, chess prodigy or Wharton business boy, actually i don't care
really; and they wouldn't win a correspondence game against me, i'm 100 pct sure of that.
100 pct ? yep 100 pct unless other things would happen than chess related.

PS2 explaining the term 'winning strategy' in Zermelo's game theorem, with an example
of how Black can win/must play to win against the (erroneous) move 1.g4?
Namely, by playing rather accurately, every move, first with 1.e5 or d5, etc. (not 1..f5?!)
And so on . Only wich such a winning strategy, Black could be able to win.
Not by getting suddenly a mate in 115 position out of nowhere. See what i mean.
That tactical winning chances usually only arise after building a positional advantage
was known already by Steinitz. Ofcourse you can construct strange aritificial mating problems
but such positions do not arise in a game with perfect play with both sides (like i said Black
can always avoid such positions). Indeed with some speculative players as Nezhmetdinov
and Tal (and sometimes Alekhine) sometimes tactical opportunities suddenly popped up
in a game as if out of nowhere; however this always was with *speculative* and not perfect play.
And i really don't think you need to have a Phd in math combined with a GM degree to understand
this (and the validity what i'm saying).
Nowadays such tactical situations also don't occur in high level correspondence chess anymore,
one players can go for a sharp line, sure, and the other player can ignore the SF output, but even
then a sudden mate in x won't occur, at the most you get a transition to a won endgame (for
Black or White); whereby one side always in retrospect can be shown to have made a mistake
(or more, often two or three minor mistakes).
best situation a
Amen

[mosfel24]

I think we can extend your wonderful proof to prove that Connect Four is a draw.

No wins in 1 move.
No wins in 2 moves.
No wins in 3 moves.
No wins in 4 moves (as other side can prevent any attempts easily at a four in a row).
Etc.

And since the game tree is expanding and there are many choices to avoid loss, Connect Four is a draw.

QED

[towforce]

I think we can extend your wonderful proof to prove that Connect Four is a draw.

No wins in 1 move.
No wins in 2 moves.
No wins in 3 moves.
No wins in 4 moves (as other side can prevent any attempts easily at a four in a row).
Etc.

And since the game tree is expanding and there are many choices to avoid loss, Connect Four is a draw.

QED

[jefk]

obviously this mr Moshe Felman (real name or not (**) also has misunderstood my reasoning,
and quoting /misattributing things completely out of context.
Note that for 4-in-a-row contrary to chess (and checkers) it's crystal clear that there *is* a winning strategy,
namely, starting with the first move in the middle. Then after a few moves the tree for the other side (second mover)
-trying to avoid a loss- is narrowing (in chess it's widening). This again complies with the Zermelo theorem that if
the first player can always win there must be a winning strategy (with the four in a row comp programs such
a winning strategy was quickly found, just like with 1.e3 in losing chess).

Didn't i write that there indeed may be (and probably is) a -forced win for Black in chess after 1.g4 ?
Even although this win isn't there yet cq obvious yet after ply 3,4,5,6 etc. So why the ridicule ?
Just like suggesting i think all swans are white; it's insinuating and insulting Bs and out of proportion.

But for the normal starting position in chess , the situation is different, and it's not a matter
that there is *no* win in 4,5,6 etc, after 1.e4 d4 or whatever, it's 1) because black can *always*
avoid a forced win (mate) in ply n because the tree of drawish opportunities (contrary to 4-inarow)
is widening and thus also in ply n+1. Using backwards induction. and 2) from backsolving (and Nnue) it's
clear there's no winning strategy and thus no win (Zermelo). Repeating myself in 4-in-arow the game
of Chomp and numerous other games which are not ' balanced' such trees (for the second player)
are not widening but narrowing and thus as a result there then can be a forced win for the first mover.
Not in the game of chess. Not in checkers. And not in Othello (although there the reasoning again
would be slightly different i guess). Balanced are intrinsically stable, a concept in mathematical
control theory, and although drawing margins can be different, in chess it's rather high and you
really have to make big mistakes in correspondence chess if you want to lose (and as utterly
superfluous comment, ofcourse in 4-in-a-row) you don't have to make such a mistake, because
this game is *not* 'balanced'; although this may be difficult to understand for nine year old
kiddies, chess rating (with new Fide ratings i presume) >1800 or not. And what's your chess rating
mr ' Felman' ? Just being curious. Ever played computer assisted ICCF correspondence chess ?

For some other math purists (and the inquistion), as i wrote several times now, there are
different sorts of proofs; even in math. There are formal proofs, and informal proofs (*).
https://staff.fnwi.uva.nl/d.h.j.dejongh ... proofs.pdf
it's also on wikipedia btw
https://en.wikipedia.org/wiki/Proof_the ... rmal_proof
Now i suggest that the computer kiddies here, mathematicians or not, all go and
mail wikipedia and tell them that informal 'proofs' are not a 'proof'.
Good luck and have fun.

In the past i wrote about cumulative evidence in relation to physics (and law), and it
was again regarded with scorn and disdain because this wasn't real 'math' etc etc.
Well sorry to disappoint such math kiddies again, but there's a concept of
Bayesian reasoning and in the field of computer assisted proofs such Bayesian
reasoning, in particular the accumulation of evidence plays a significant role
https://en.wikipedia.org/wiki/Bayesian_inference
And computers are nowadays often used in finding proofs, whether some oldfashioned
math purists may like it or not
https://en.wikipedia.org/wiki/Computer-assisted_proof

Concluding, instead of reacting to my constructive arguments with immature and agressive ridicule, scorn
and disdain like this 'shawn' kiddie did, I suggest to produce a counter argument, namely a forced win
for White in x moves (otherwise you'll soon end up on my foe list as well, if that's what you wish).
Good luck and have fun again.

Meanwhile i'm not going to continue in educating math purists and computer kiddies here anymore in
the general principles in the philosophy of math and science, first do some proper reading and
background study i suggest, then present yourself with real name (**), education and chess rating,
and then i might give you a mature reaction (but probably not coz i basically gave up on this forum
at least regarding this discussion; most people simply don't seem to be able to understand it,
and worse, then smell blood when the math inquisition start their attack, and like sharks and
hyena's blindly follow the scorners trying eg. to make silly counter examples or otherwise
suggesting that i might be wrong; again, only way you can show i'm wrong is by showing a forced
win for White; if you can't do that then shutup and don't collect ten grand; bad luck thus)


(*) see also:
https://news.ycombinator.com/item?id=12 ... g%20enough.
and:
https://kevinsullivan.github.io/cs-dm-d ... ludes.html

(**) only could find a ' moshe felman with a reference regarding the holocaust, so it's
probably not a real name (hint, moderators). Maybe it's Feldman though dunno but
also there is no chess player named M.Feldman -nor mathematician- to my knowledge

[jefk]

to add to my infallible (although apparently not always understandable) logic:
In the situation that Black wins against the move 1.g4, the tree of moves for White after ply
5,6,7 avoiding checkmate also is widening slightly, but not to such an extent that a checkmate
in the end can always be avoided. This is also plausible because of the quick - possible- mate
for Black after 1.g4 ? e6 2.f3 Qh4 mate. As earlier hinted, it's a matter of 2d topology, not strictly
complete induction. It was -i can admit- 'only' a(n) -additional- qualitative argument, and in the situation
of White avoiding a checkmate after having started with 1.g4 is clearly much more difficult (than for
avoiding the checkmate(s) after the normal starting position (we would have to count the exact
nr of possibilities in both situations and investigate the degree to which the trees are widening
to make a fair comparison; simply a hint for further research). But nevertheless,
it was posed as additional argument in a computer assisted reasoning (informal
proof) that there is no forced win for White.

And i can also be sarcastic: so computer assisted proofs are not proofs ?
Then why are the called' proofs' ?
Yes, there also are non surveyable 'proofs'
https://en.wikipedia.org/wiki/Non-surveyable_proof
hey also not Proofs Ofcourse ! (is the Math Inquisition shouting at home testing their
engines on playchess and having their fourth beer of the day)
Really ? well, then why is the word ' proof' used? Just wondering; Lol

ok, it's a controversial matter, i admit, as clear from articles as this
https://www.sciencenews.org/article/how ... ical-proof
personally, as may be clear from earlier statements, i disagree with this
article; by now it's clear some computer assisted proofs (as eg. the Schaeffer
weak solution for checkers) also are valid 'proof's. Just like the Chinese database
in combination with backsolving, NNue and Zermelo's game theorem. So simply shouting
that the application of Zermelo's game theorem in chess is not a 'proof' like
many here have done and apparently still are doing, is making a fool of yourself.

First of all the burden of proof for obviously balanced games as chess is to the
math purists from the math inquisition to show (Prove) it is *not* balanced.
Just as i asked them to Prove that the earth is not Flat.
Second, to show the ' validity' of their proof(s) computer assisted or not
is to show us a force mate for White in x moves. If this is not done then
chess is a draw. just like checkers. with perfect play at least.
(*) , a validity which i can always deny on this forum as long as i live and even thereafter (because
it's not valid because we can always find a counter example where Black is not checkmated by force)
QED
The latter at least as an informal ' proof' . And thus a (preliminary) -possibly valid- step
towards a weak solution even without number crunching, thus some sort of 'proof' .
whereby the UWS has already been found with logical reasoning. Whether
some here may like it or not (and then copy each other with loose and unfounded
(unproven) statements as ' not a proof' , 'not a proof' , not a proof' , 'not a proof' ,
not a proof' , 'not a proof' , ' not a proof' not a proof' , 'not a proof' , ' not a proof'
not a proof' , 'not a proof' , ' not a proof' not a proof' , 'not a proof' , ' not a proof'
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not a proof' , 'not a proof' , ' not a proof' not a proof' , 'not a proof' , ' not a proof'
Not a Proof !!!!
etc.
ad nauseam
In other words, not a style of discourse which would be normally accepted in a civilized scientific
forum, whether it would be about physics, philosophy or even math maybe. But then this is not
a scientific forum but mostly a chatbox for chess kiddies playing with Fritz and SF apparently.

[shawn]

Anyway i won't be able to see it coz you're now on my 'foe' list; congrats.

I am honored

[jefk]

continuing my reasoning to mr felman,

while my argument(s) that it's not about not being mated but the (extremely) fast increase of options
avoiding to be mated when going down the tree (contrary to the situation afte 1.g4 for Black
or in the 4-in-a-row game), like i said, the degree of freedom, such argument can be fortified by
looking at the nr of tactical *mistakes* instead of just mate positions (an idea partly inspired by the
tforce idea of having an eval without search). In 4-in-a-row the nr of options avoiding tactical mistakes
is decreasing the further the game is progressing; similar for White after 1.g4? after ply 4/5/6
(although that would need to be investigated with practical examples and counting).

For Black in chess in a normal game, the nr of options of *avoiding* a tactical mistake (eg.
losing one pawn) is increasing immensely fast the further you go down the tree. Thus maintaining
the drawish nature of the game from the start with ease.
So then a few math purists can (continue) shout (and repeat ad infinitum) 'that is Not a proof'!
No, it's not a rigorous proof yet, who cares, first of all a rigorous proof is not needed (imo the
burden of proof is for those thinking White can always win) secondly it's an informal, computer
assisted proof. That it's probably a non-surveyable proof (maybe not definable with extremely
formal math logic) is irrelevant because of ideas -and research- such as this:
https://mizar.uwb.edu.pl/trybulec65/8.pdf
Counter example:
The idea that suddenly magically there will arise a position at ply x (lets say ply 245) forced
in all lines where Black cannot avoid a tactical mistake to such a degree that the game is lost,
thus is impossible (cq insane). But if Black can always avoid such 'tactical mistakes' then Black
can*not* lose the game of course. QED

PS the concept of tactical mistake (rather than avoiding mate) ofcourse can/should ideally be
specified a bit better; losing one pawn may not be the best option (for further research) because
of gambit ideas (and positional compensation) but this of later concern as far as i'm concerned.
And like i said, i'm not going to explore this here any further. Chess is a draw and (UWS)
if you think that White can always win then show me i.e. us in this forum the line(s),
with complete analysis, until the egtb results. hint: do not start with the move 1.g4, (nor 1.f3).
Good luck and have fun.

[RubiChess]

As i'm by now 69 yrs of age

That may explain something.