proof

[Brunetti]

Not a proof

I never claimed it was.

Alex

[jefk]

there nowadays are various sorts of (mathematical) proof:

www.amazon.com/Proof-Pudding-Changing-N ... 0387489088

written by a mathematician.

Example initially the weak solution of checkers proving it's a draw but only found with empirical
results ie. number crunching may not have been accepted by some math fundamentalists.

yes tforce the tree of 'drawish' positions from ply 5,6,7 etc. is widening much much faster than
the tree with all possible lines leading checkmate positions; but you also need to be certain it indeed are drawish
positions (and not eg. positions after 1.g4? which can gradually increase the eval for Black if you go deeper).
Well in chess we nowadays have the results of Nnue evaluations, based on billions of simulations and thus really adding
some significant info to the eval (as has become apparent with the increase in strength with the Nnue engines during
recent years). And with such Nnue evaluations, from a symmetrical starting positions, it can be seen that
there always are more than enough drawish positions for Black to evade a forced draw. This reasoning can
be combined with (inspection of) the huge database with backsolved positions, and considering the drawing
margin of chess, an eval (preferably backsolved) remaining within e.g. +/0.3 or so and in addition possibly
observing the -flat- trend, we can determine from the start position that chess is a draw.
But this was referred to as a 'ultra-weak' solution by a certain IT project manager Colley (now out of
computer science) and later mentioned by Allis in his Phd thesis. Ofcourse the word 'solution' hints to
a requirement for a mathematical (rigorous) proof but the word 'determine' doesn't. As said the 'weak
solution' for checkers (and possibly Othello) also has not been 'proven' in a traditionally logical mathematical
way, but 'only' found by sound reasoning (eg using alfa/beta) and emperical results. The logic of the reasoning
for chess using the results of the Chinese database and the arguments i've given, possibly combined with other
evidence increasing draw margin at higher strength (100 pct draw results without book (for at least one side)
at relatively long time controls, etc etc only lead to one possible conclusion. I really don't care if shawn, viz,
and whiting keep on claiming there's no (rigorous) proof. I suggest they should read this book mentioned above.
Meanwhile i also don't exclude later on with similar reasoning the 'weak' solution (draw) can be found
without so much number crunching as was done for checkers. But i don't think i'm
going to present such reasoning and/or results. At least not here.

[shawn]

The amount of audacity it takes to compare your worthless claim to solving checkers...

[jefk]

'audacity' ?

just like Brunetti didn't claim he had a proof, i didn't compare my findings (*)
with the Schaeffer results. Can't you read ? Schaeffer and his team found a 'weak solution' ,
regarding chess i talke about an 'ultra-weak' solution. Different things you know.

Anyway going to end the 'discussion' (and avoiding the insults) here, one additional logical
fact corroborating the ultra-weak solution of chess is the much larger degree of freedom
for the (Black) pieces compared with the second mover in checkers. And checkers was
already shown to be a draw. In chess, knights can move to eight squares, forewards,
backwards, etc (well unless they are in a corner but even then they can get out again).
This intuitively confirms that there is no way White can induce a forced mate in chess.
Not in ten moves, not in twenty, not in hundred, not in two hundred. Because Black can
always avoid such a forced line. The reasoning behind this is about as simple (for me even
a lot simpler) than eg. proving the theorem of Pythagoras (or that tictactoe is a draw).

Anyway i'm not finished completely yet, but like i said, I will not post new findings
here on this forum anymore (guess why).

(*) based on > 25 yrs research in chess opening theory and btw found already that chess is a
draw about 15 years ago as comfirmed later with the Chinese database)

[shawn]

'audacity' ?

just like Brunetti didn't claim he had a proof, i didn't compare my findings (*)
with the Schaeffer results. Can't you read ? Schaeffer and his team found a 'weak solution' ,
regarding chess i talke about an 'ultra-weak' solution. Different things you know.

Anyway i'm not finished yet, but like i said, I will not post new findings here
(guess why).

(*) based on > 25 yrs research in chess opening theory and btw found already that chess is a
draw about 15 years ago as comfirmed later with the Chinese database)

1. Define your "ultra-weak solution". The Wikipedia definition does not apply to your supposed "proof"
2. I claim that there exists a 100-move maneuver that achieves a win for white. This maneuver is so deep and complicated that no correspondence player, chess engines, or cloud databases could even dream of finding it. Can you prove that I am wrong?

[jefk]

the wikipedia article just copied some text without any context and apparently added
some extra assumptions. Like i said the def of UWS was given by an amateur (It guy)
and later mentioned by Allis Phd ('determining the theoretical outcome from the start position).
Thus wikipedia is not the math bible (nor are you the chairman of some mathematical society
or so having sufficient authority to demand a more accurate definition of UWS).

As for your example of a hypothetical mate in hundred, apparently you didn't get my
reasoning, because such a mate can't exist. But i'm not going to repeat myself.

Some months earlier i promised ten thousand dollar for anyone who can find an opening
line for White which in all situations can lead to a win. Most knowledgeable people here (Kaufman,
Blass, jouni) wrote that nowadays it's obvious there is not such an opening line (best bet imo
would be a symmetrical English, starting from 1.Nf3 Reti but then you'll quickly find it's a draw.
r1bqkb1r/pp1ppppp/2n2n2/2p5/2PP4/2N2N2/PP2PPPP/R1BQKB1R b KQkq d3 0 1
other options is Slav, long positional play (with eg. Nxg6( but a draw in the end.
rn1qkb1r/pp2pppp/2p2n2/3p1b2/2PP4/4PN2/PP3PPP/RNBQKB1R w KQkq - 1 1

PS now going through this book 'proof in the pudding', in particular chapter ten
('beyond computers: the sociology of mathematical proof'); more examples
than a general discussion but nevertheless interesting.
- more interesting is chapter 13.2 with title "Why It Is important for Our notion
of Proof to Evolve and Change.

PS2 actually i don't even care so much about what some math purists think about my reasoning,
i'm a physicist and in physics (the earth is not flat and water is wet) we are not so masochistic to
constrain ourselves to such rigid requirements (as formulating ultrarigorous mathematical proofs
http://old.math.nsc.ru/LBRT/g2/english/ ... essary.pdf
proofs may remain necessary in math, but math is only an abstraction of the real world.
Just like chess (as described by the Fide rules) is more than a mathematical abstraction.
There are things as the no-touch rule (once a piece is touched it must be moved) and the
clock ofcourse. A player can lose on time; ask a certain father. And in correspondence
chess, once in a about every two hundred games a person makes an erroneous move
input, or once in a bout every two or more thousand games, he/she dies of old age
or otherwise. Only in such a situations it's not a draw, otherwise above master level
all games are drawn. guess why.

[shawn]

As for your example of a hypothetical mate in hundred, apparently you didn't get my
reasoning, because such a mate can't exist. But i'm not going to repeat myself.

Everything you have said are based on results are based on opening research, correspondence games, chess engines, or cloud databases. How do you know they haven't missed anything? The "i'm not going to repeat myself" sounds like a desperate attempt at saving your argument.

[jefk]

how i know i haven't missed anything ?
because I generated (or more accurately have let the computer generate) complete trees (just like the
Chinese database is almost a complete tree); and I'm not the only one (*) btw who has done such work but my
work apparently was bit more rigorous (except now when compared with the Chinese database).

Thereby you can quickly eliminate tactical mistakes (by both sides).

Left over are positional opening lines, like i already mentioned.
The result is a proof by exhaustion
https://en.wikipedia.org/wiki/Proof_by_exhaustion

and thereafter a proof by contradiction (if White cannot win then etc).
So indeed, not going to repeat myself
(there have been discussions here about the topic for years, and apparently
you were not involved in them).

Some people then are going to say that the chess tree becomes so large (even with alfa beta
pruning that an exhaustive search is impossible, but then - again- i mentioned reasoning with
backward induction (ok not complete induction like in algebra or control theory, i admit)
but nevertheless, a valid way of reasoning, with conclusion that Black can always
avoid a forced mate; because the further you go down in the tree, the easier it becomes
for Black to avoid such a mate because the nr of options for that has widened. simple as that.

And i'm going to end this discussion; feel free to (continue to) disagree, like viz et al or others
from the math inquisition (it looks you're an Mba and not even a math guy btw) i don't care,
2 months ago i proposed that at ICCF correspondence chess the thematic tournaments
should contribute to the rating(s); Kaufman made a proposal for a chess variant without
draws; such developments are more interesting then endless nitpicking about certain
logical reasonings being a rigorous mathematical 'proof' or not (yet). Imo there's no need
to repeat the same/similar exercise (number crunching) as for checkers for the game of
chess; nor for international draughts, i suspect, whereby it *would* be interesting to
see if here also the sort of reasoning(s) (to get to an UWS) could be applied (draughts
endgames are different btw, there's zugzwang etc. blabla; but there also are opening books
and by now Nnue draughts programs. In retrospect, with the checkersgui/nnue program i
suspect similar reasoning(s) could be applied possibly making the whole Schaeffer project
superflous in retrospect (yeah, the 'audacity' .... (lol).

(*) have a look eg. at the Kaufman opening books, 'advantage in chess for Black and White'
He worked with Komodo, and Idea, generating big trees. Thereby sometimes improving
a little on opening theory (as eg. in the Chessbase 'lets' check database). GM's have
analyzed a system as the Ruy Lopez Marshall gambit for Black for years, and found
it's a draw. Are you going to say all these people maybe have missed something ? (not)
But Kaufman and me (and the Chinese database) seem to be the most important who
looked at all openings. All ? Yes all, at least all relevant. From the start position there are
twenty opening moves possible. How i know i didn't 'miss' anything (hey, maybe there are
thirty opening moves possible ? Well not with the conventional rules of chess; like it or not).
Then for Black you can look at the most relevant defenses, whereby via alfa-beta you
can eliminate the responses (eg tactical mistakes) which are *not* relevant. Last piece
of the puzzle is reasoning that this endeavor by now is complete (Kaufman wasn't convinced
(yet?) of this but i'm 100 pct convinced you cannot win with an odd move as eg. 1.a4 or 1.h4
or whatever. Or similar, after a conventional opening move sequence as eg. 1.d4 Nf6 2.c4 g6
suddenly find a winning move as 3.h4!? (described eg. by GM Williams). Because such moves
should win in all situations and they don't. The Kings gambit doesn't win in all situations,
nor does the BDG. Like it or not. Ever heard of the program Alfa Zero ? From it's simulations
it must also have become obvious that chess is a draw (something not only Steinitz knew
more than a century ago, but most GM's acknowledge(d)/knew/know this).

[shawn]

how i know i haven't missed anything ?
because I generated (or more accurately have let the computer generate) complete trees (just like the
Chinese database is almost a complete tree); and I'm not the only one (*) btw who has done such work but my
work apparently was bit more rigorous (except now when compared with the Chinese database).

That's groundbreaking. May I ask how long it took you to generate the entire tree? chessdbcn is far, far from being a complete tree, just so you know .

Left over are positional opening lines, like i already mentioned.
The result is a proof by exhaustion
https://en.wikipedia.org/wiki/Proof_by_exhaustion

Again, show your proof by exhausion.

Some people then are going to say that the chess tree becomes so large (even with alfa beta
pruning that an exhaustive search is impossible, but then - again- i mentioned reasoning with
backward induction (ok not complete induction like in algebra or control theory, i admit)
but nevertheless, a valid way of reasoning,

So now you are saying that you don't have a proof by exhaustion, but rather a proof by induction. Interesting isn't it?

with conclusion that Black can always avoid a forced mate; because the further you go down in
the tree, the easier it becomes for Black to avoid such a mate because the nr of options for that
has widened. simple as that.

So the Grob is a proven draw because white has many moves to make? Noted.

(*) have a look eg. at the Kaufman opening books, 'advantage in chess for Black and White'
He worked with Komodo, and Idea, generating big trees. Thereby sometimes improving
a little on opening theory (as eg. in the Chessbase 'lets' check database). GM's have
analyzed a system as the Ruy Lopez Marshall gambit for Black for years, and found
it's a draw. Are you going to say all these people maybe have missed something ? (not)
But Kaufman and me (and the Chinese database) seem to be the most important who
looked at all openings. All ? Yes all, at least all relevant. From the start position there are
twenty opening moves possible. How i know i didn't 'miss' anything (hey, maybe there are
thirty opening moves possible ? Well not with the conventional rules of chess; like it or not).
Then for Black you can look at the most relevant defenses, whereby via alfa-beta you
can eliminate the responses (eg tactical mistakes) which are *not* relevant. Last piece
of the puzzle is reasoning that this endeavor by now is complete (Kaufman wasn't convinced
(yet?) of this but i'm 100 pct convinced you cannot win with an odd move as eg. 1.a4 or 1.h4
or whatever. Or similar, after a conventional opening move sequence as eg. 1.d4 Nf6 2.c4 g6
suddenly find a winning move as 3.h4!? (described eg. by GM Williams). Because such moves
should win in all situations and they don't. The Kings gambit doesn't win in all situations,
nor does the BDG. Like it or not. Ever heard of the program Alfa Zero ? From it's simulations
it must also have become obvious that chess is a draw (something not only Steinitz knew
more than a century ago, but most GM's acknowledge(d)/knew/know this).

Still, you can't refute my claim with this kind of crap evidence. Here's what I said again for your convenience:

I claim that there exists a 100-move maneuver that achieves a win for white. This maneuver is so deep and complicated that no correspondence player, chess engines, or cloud databases could even dream of finding it. Can you prove that I am wrong?

My claim explicitly states that this maneuver is unsolvable by any modern technologies or analysis. Using modern technology and analysis to refute this simply doesn't work.

[jefk]

'crap evidence'
(insult again, like previously the word 'audacity')

well again, i don't think you followed the historical discussion(s) about solving chess. Nor seem to understand what
i'm suggesting, whether i'm right or not. Namely that you don't have to generate the complete tree (not only because
of alfa beta because also because of transpositions such trees would be as huge as some previously
suggested, but that's another matter); because we (or a least I) can use backwards induction;
That's in fact what has been done with the Chinese database (and previously by myself as well
with the program Bookbuilder, developed 20 yrs ago), namely using minimax aka backsolving.

Some think the tree in chess is large to such a degree the search almost never hits the egtb;
wrong again. I've investiged many lines (eg with SF) and after a while noticed (eg. with flickering
of my external SSD) that the search was hitting the egtb's. And in such way Black of course
also can easier avoid a forced checkmate. Believe it or not.

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. And with backsolving it has been clearly shown a 'winning strategy' for White in
chess (building up an opening advantage) doesnt exist. My examples of avoiding checkmates was only the
cream on the pudding in other words an additional line of reasoning, but also using backwards induction.
After 1.g4? it's another matter (you misread or misunderstood what i wrote) and it's very well possible
that then there is a forced mate for Black after eg. 200 moves or so. Other matter. The chinese
database also suggests that Black has significant advantage after the wrong move 1.g4?? (that
this is a wrong move I -and many others- already knew some twenty five years ago, nothing new).
But White cannot get fundamental advantage with whatever opening move (and there are twenty
of them). *could* there be a 21th opening move for White complicated or not and then magically
inducing a forced win in 9872 ply ? Well sorry to disappoint you but not with current Fide rules
For the rest i'm not going to answer some other of your (almost rhetorical) questions anymore.

But again if you claim there can be a win in hundred moves, then you are wrong.
Unless you (or someone else) show(s) me the line which i will investigate and then will reward
you with ten thousand bucks (never gonna happen). Lol

This was the whole point of my earlier reasoning(s) wasn't it. But then I'm not obliged to 'prove'' that you're
wrong (with a suggestion there 'could'' be a forced mate). Define 'prove'. What kind of 'proof' would you like
to see. (hint: sometimes there can be multiple proofs, combined, proof by exhaustion and
backward induction can be combined, and this is what i've done, at least with some
logical reasoning, whether the math inquistion considers this a rigorous 'proof' or not).

Another empirical proof (repeating myself from about half a year ago_: let a Mcts search run for some
days, weeks, months, then you'll see the eval for White is going to zero. This imo would be almost as
solid reasoning as the Schaeffer method for a weak solution in checkers although many math purists
would disagree (getting used to it, and like i said i don't care, let them prove the earth isn't flat
(hey it *could* be flat no ? And it's only a hallucination if you think it's a globe).

With logical reasoning i've shown there's no forced win for White in chess ( a fact known in chess btw
since a century by anyone at Gm level or above (superGM). And if such a win would exist it wouldn't
be so 'complicated' btw. (Black can always avoid overly complicated positions btw, because there
are sufficient degrees of freedom for the chess moves, but then again i'm repeating myself;
and you imo continue to have some lack in understanding in this respect.
Ergo end of discussion. Good bye and good luck with your Wharton
Mba in Silicon Valley or where ever. What's your chess rating ?