How close can we come to proving that white draws?

[mmt]

If black blunders at any time then your constructed opening book should allow white to win, if you are proving that black cannot win.

My book just needs to let white draw, not necessarily win.

[mmt]

If we can prove this, I think it would be an important result in chess. The most important theoretical result up to that point in time. Somebody can get a paper published (cite my post! ) and it would be in the Wikipedia main chess article and it's much much much easier than proving that black draws, so I think it's a good discussion to have. My OP is about trying to estimate when there will be enough computational resources to do this.

[Madeleine Birchfield]

The other factors that many people are not considering is that these experiments and proofs do not happen in a vacuum. How much hardware do you need for proving your opening book? How are you going to be able to afford it; how are you going to replace the hardware as parts of it wear out? How much storage do you need to store the opening book database? How are you able to guarantee that you are able to continue your project in the case that Russia goes to war against the United States and launches nuclear weapons before you are able to finish, or that modern society doesn't collapse due to climate change or running out of oil? (Scientific reports and the UN have indicated that we only have about 10 years to solve climate change) What happens if proving that white draws takes longer than you are alive; do you have a plan to find somebody else to continue your task, or are you the only person interested and the project dies with your death? Do you want to establish a foundation like the Gates Foundation whose sole task is to prove that white draws in chess? The foundation might draw resources that could be used on other aspects of society like curing cancer and ending poverty. Perhaps the world should abandon everything else so that we could dedicate all the world's energy and resources on proving that white draws for chess, good luck convincing the world's leaders and politicians who cannot even agree whether taxes should be raised at all. So many outside factors that can determine whether we are anywhere even close to proving that white draws, and I don't think it possible on a human timescale with current national and international politics.

[Alayan]

The former is physically impossible as the number of positions in chess greatly exceeds the number of subatomic particles in the universe

This is repeated by many people, but it's completely false.

It's based on Shannon's estimate of the number of possible games. Which is much much much higher than the number of possible positions, which is all that really matters.

This thread is about finding draws, not proving losses.

Your problem should be equivalent to evaluating 2-folds and TB draws as wins for white, then solving the resulting game as a win for white.

It is still ludicrously hard.

[jefk]

MB (and DC) ok i'll be more serious now:

First of all, i'm also aware of the existence of mathematical game theory,
ofcourse and such definitions as of a solved game (and the need for
proofs if you want to 'solve' it); but when someone wants to prove White
can draw, something which for me is obvious (just don't play 1.g4, and or
maybe a few other lousy first moves). So i became a bit ironic
in my writing i guess and referred to (book/tree building) experiments;
which if done properly (eg with an strong) NNUE engine
already say alot, leading to conjectures, albite not 'proof's.
Not going to quote myself (*) but i mentioned that there quite
a lot of conjectures in math which are accepted as most likely
(or maybe even evidently) true.

Second, repeating myself, but now mainly for info of MB,
in game theory you don't have to always prove things by
brute force, while the Zermelo theorem i mentioned is insufficient
indeed for chess to derive a proof, in future years i don't discount
the possibility a proof can be found, in steps if necessary. At
the moment i can only think of a method such as 'complete induction'
(for which the chess rules would to complicated i guess) but
there are other methods as well. do your research i suggest,
here's just an introductory example :

and here more in general (other games than chess)

the latter blok mentions the Nash equilibrium and others
have thought about that for chess:
https://www.sciencedirect.com/science/a ... 5X11005085
https://www.hindawi.com/journals/gt/2013/534875/
considering the latter article, it looks complicated stuff indeed.

As for the DC position, while Arasan may have won, i'm convinced
that in correspondence chess i could draw with Black (especially
against Arasan btw, as long as it's not Nnue).
In general, there's no threat of a draw death of the game of human
chess, as we know. But in (ICCF) correspondence chess we are
approaching this (i.e. more and more draws at top level);
nowadays still sometimes White can win, when being lucky, which
often means that Black didn't go for e.g the Marshall attack in the RL,
but tried Breyer or Zaitsev (or Chigorin), especially when playing
such a variation in a suboptimal way.

PS so while making plans to 'prove' that White can draw, etc
don't discount the experience of correspondence chess players, i
would suggest. The initial value in my Aquarium base (with SFNnue)
the advantage for White is approx 0.24, and stays that way,
with 'perfect' play. Which is not enough for a win in the endgame.
Now i also know ofcourse about positional play, even strategies,
pawn structures, etc. but even then i strongly suspect that
Black will keep enough options (currently against e4 being 1...e5,
French, Sicilian and against d4 or Reti, the QGD (incl Catalan or
Bogo-Indian), Slav, and Gruenfeld (the latter i have not analyzed in
detail but i believe mr Kaufman in this respect). Meanwhile, people
as the mentioned Larry K may continue to find 'theoretical' /computer
improvements for White but even then i think Black will continue
to hold its base (example, the RL Marshall attack (a defense in fact)
has been analyzed almost into a draw dead; as a human i wouldn't
play it, but for a GM it's a rather easy to a draw. Then ofcourse
you can play an anti-Marshall, but this is diminishing the advantage.
Also Black can go for the Berlin and then also even with the Re1
variation there's not enough winning advantage in the end imho.
For the rest i suggest to do your own (opening) studies.

(*) DC i didn't mean that you shouldn't quote me, but quoting
my whole (long) message seemed a bit superfluous to me;
but oops, i now see your a moderator, so i have to be careful,
i guess (which i now tried to do already in this message btw,
especially in content, whether you (or MB) think its naive or not.

[towforce]

If you follow elite correspondence chess of last few years, it is now well over 90% draws, and entire events are decided by a single win. Most wins and losses are actually not due to the chess, but technicalities such as time losses. The writing is on the wall.

Do we have any way of estimating the elo rating of top level correspondence chess (TLCC)? Since affordable computers became better than humans, has the gap between TLCC and tournament control computer chess been constant?

The correlations in this post suggest that chess becomes drawn at elo rating 5237 - but I'm guessing that TLCC has not reached that level yet?

The ICCF only gives "over the board" ratings - link.

[jefk]

those ICCF ratings are not Otb,
they are calculated on the basis of correspondence games,
but there's quite some rating 'deflation' there,
because the level of the games played at top level
are like with hybrid (man/machine aka centaur ) chess and
thus at levels approaching at least 3600 or so i guess (if you
would compare it with games played at otb time controls)
So can add approx 1000 points in my (rough) estimate.

PS In such a situation, as Iccf CCM my rating is approx 3330

[towforce]

those ICCF ratings are not Otb,
they are calculated on the basis of correspondence games,
but there's quite some rating 'deflation' there,
because the level of the games played at top level
are like with hybrid (man/machine aka centaur ) chess and
thus at levels approaching at least 3600 or so i guess (if you
would compare it with games played at otb time controls)
So can add approx 1000 points in my (rough) estimate.

PS In such a situation, as Iccf CCM my rating is approx 3330

In that case, chess computers, on their own, and at tournament time controls, are probably closer than we'd realised to being unbeatable. You say correspondence chess is "at least 3600", and, allowing for the imprecision, that's probably not far away from where the top chess computers are (CCRL ratings link).

[jefk]

top engines becoming almost unbeatable ?
yep, certainly against humans, when using fast hardware,
and equal (human vs machine) time controls
(which is a reason the humans nowadays sometimes get some
pawn odds, or the engine even playing with eg one knight less.

In such situations, opening theory ie 'book' (unfortunately also
for the engine) becomes irrelevant, whereby we know that at
the highest levels, normally the importance of opening
theory becomes larger (well known amongst
Iccf correspondence Gms btw)

Therefore personally i would prefer man/machine duels to be played
with different time controls, eg. normal (slow) for the human
and fast for the engine (to give the human at least a slight chance)

As for the Tcec tourns, i'm not knowing the current situation,
some time ago i noticed some strange openings, i must say,
but played for both sides. A better idea maybe is to use
the 'unbalanced opening' book by mr Pohl (for both comps).
If haven't figured out that themselves already,

PS someone here estimated the top Elo at about 5000,
but in my estimate (using almost perfect opening books, it will
be lower, maybe 4100 (to maybe must maybe- 4600 or so; my 2cnts again.

On Iccf you already can see it becomes very hard
(almost impossible) to reach 2800, but then again,
those ratings are depreciated compared with 'real life'
because it's only calculated within it's own (iccf) bubble

[Alayan]

Entering an unassisted engine in ICCF could be a good way to gauge how strong ICCF players are relative to it.

Do we have any way of estimating the elo rating of top level correspondence chess (TLCC)? Since affordable computers became better than humans, has the gap between TLCC and tournament control computer chess been constant?

The correlations in this post suggest that chess becomes drawn at elo rating 5237 - but I'm guessing that TLCC has not reached that level yet?

The ICCF only gives "over the board" ratings - link.

I explained to you in a previous post why this 5237 value is deeply flawed. Not +-100 elo flawed. Flawed to the point of uselessness.