Chess will never be solved, here's why

@13491

"a bare minimum of 4.5 candidates per move in classical chess"
++ That gets smaller if transpositions are taken into account.

@13494

"1000+ move games"
++ The 112 ICCF WC finals draws, >99.992% certain to be perfect games with optimal play from both sides end in certain draws in average 39 moves.

@13478

"the same narrow pool of engines" ++ Some may use Stockfish, some LC0, some Komodo...
There is also a difference in hardware, e.g. the Russians have worse hardware because of sanctions. Nevertheless 4 of the 17 finalists are Russians.
It is also possible to tune the engine, e.g. change the parameter 'contempt'.
The time control is 50 days / 10 moves, but one player may spend 2 days on a move and the other 10.

"Nobody has an advantage in playing strength"
++ Over the board 2 of the 17 finalists are IM, 1 is FM, and others untitled.

dude its so funny seeing optimissed getting middle school math concepts completely wrong. I dont even need to argue against them he makes a big enough fool himself.

optimissed thinks that there is some sort of disagreement when elroch and the others are listing what are known for over 100 years to be mathematical facts.

optimissed claims there's theoreticians that disagree, but where are they exactly?

since when is high probability accepted as proof in mathematical journals?

The person who's 'failing' to distinguish - is O. Not Elroch.
O - always obsessing over his misinterpretations of intelligence.
It doesn't even 'seem' to have crossed his mind that Elroch understood exactly ...
with O doing a kind of tygxc ?
Failing to understand mathematical objectivity?
Having disdain for same?
More like - O just trolling again - looking for any semantics opportunity to do so. What percentage of his own personalizing nonsense does he actually believe?
Probably very close to his name. O percentage.
Whereas others - not having his insecurity - don't need to lie and therefore don't.

This is the only kind of person who supports Elroch. A person who has been making completely irrelevant arguments on this thread for years now and who argues contiinually that what rules we play by makes a difference. Well, it doesn't make an important difference except for a few dozen powers of ten regarding the magnitide of the numbers of games which need to be evaluated, if chess is to be "strongly" solved.

The argument here was about the numbers of positions to be evaluated. No-one seemed to have the intelligence to understand that each position has to be assessed like a game. Obviously there's a lot of overlap and redundancy but the storage space is massive, meaning that there's zero possibility of solving chess without the use of algorithms.

Elroch argues strongly against algorithms since they are not deductive but more inductive. The kind of people who habitually protect Elroch in his ventures into the unknown and not the kind who are capable of understanding what's going on. If, say, there are five people trying to protect him, one onders how many different people that comes to in reality. A lot of people prefer not to live in reality but there are other reasons I mentioned that.

For someone who continually uses the supposed insult of "narcissism", because I know I'm a LOT more intelligent than Elroch in that my IQ is much higher than his, this use of of the endearing epithet can only be a case of projection. Of course he will know why it springs to his mind so readily, and will be only too keen to keep that knowledge away from others. It certainly makes one thing, considering that Dio and player also try to smear their targets in the same way. Those of us who keep our eyes open will know very well why they use the word so readily.

I'm sorry but you are an toidi spelled backwards. One of those I referred to. Your opinions here don't count and you have never displayed any knowledge which wasn't obviously A.I. (because it was so out of character for you and so blandly composed). No-one who supports E has the ability to understand what is actually going on here and elsewhere. Many won't even be real.

It isn't that Elroch doesn't have the intellectual ability to make an argument to support his case. Yes, he's a good example of a person who will use knowledge to deceive people rather than using intelligence to convince them. Anyone who has much more of the former than the latter may be tempted to do so, where their self-concept is at stake. It's too late now to worry about what others think so it's only self-concept that's being protected.

However, Elroch ONLY JUST has the intelligence to know that a deductive argument to support his case is completely impossible. We know how he attacks arguments made by others to support their cases, when they're not deductive, which is one of his weapons: alarmingly disturbing double values. I think by now he knows I'm a LOT brighter than he is and that I will dismember any argument he tries to make. That conclusion isn't the result of anything but honest observation and honest reporting.

So, let's get this straight. Every time some ignoramus spouts nonsense denying some part of mathematical knowledge, proclaiming that all of mathematics is wrong because he is a self-proclaimed genius and therefore complete ignorance of the subject and lack of any useful intuition is no barrier to the superiority of his proclamations, there is an immediate obligation for others to overwhelm the massive barrier of his ego and lack of understanding and to convince him of textbook facts?

No, there is no such obligation.

Despite that, here is a brief introduction to cardinality and why you should understand that different infinite sets have different sizes. I've even provided handy links to definitions of very basic mathematical terms.

First, lets define a relation >= on the class of all sets by:

A >= B means that there exists a surjective function from A to B

[Exercise for reader: show that this relation is transitive and reflexive. This makes it what is called a preorder]

This relation (like all preorders) generates an equivalence relation on the class of all sets by the definition:

A == B means that A>=B and B >=A

[Exercise for reader - verify that it is an equivalence relation]

There is a famous theorem that shows that for any two such sets there is a bijection between the two sets (I had to look up the name of the theorem but I could recall the neat proof).

This equivalence relation defines cardinality. If two sets are in the same equivalence class - i.e. there exists surjections in both directions - then they are of the same cardinality, i.e. size. This definition applies to all finite and infinite sets.

All that is left is to show there are two infinite sets with different cardinality.

Take the set of natural numbers and the set of decimal numbers between 0 and 1. If there was a surjection between the natural numbers N and this set of decimal numbers S, say

f: N -> S

then define a new decimal number x as follows.

if the n'th digit of f(n) is 7, let x have an n'th digit of 8

otherwise, let x have an n'th digit of 7.

It is easy to see that x is NOT one of the list of numbers (it differs from the n'th number at digit n, so it differs from all of the numbers, and there is no risk that it has a sequence of 9s or 0s afterwards (the only way that a decimal number can be the same as another with a different set of digits).

[Exercise for reader - make a similar, but neater proof showing the set of subsets of the natural numbers has bigger cardinality than the set of natural numbers]

This is first year undergraduate stuff (at least where I studied) and is not difficult (and nor are the necessary parts referred to. We don't actually even need the Schroeder-Bernstein theorem.

So now, @Optimissed, you have no valid excuse for not understanding the basic fact that different infinite numbers have different size.

With regard to the last statement in your last post, the truth is that while everyone is aware that you have a extraordinarily high opinion of your own intelligence, you often refute your own claims and are actually rather dull-witted by comparison with say a decent undergraduate mathematician. I suspect that you will be unable to understand the above (or to fix this by independently studying something which could be just part of a single lecture).

Fisher 960 exists 😎

hey opt, how about you answer the extremely basic and falsifiable question instead of childish insults? surely if you had any sort of, worth, you would have addressed it?

Elroch, you seem to keep forgetting that optimissed has likely never covered, or completely forgotten abstract math language of any type, and because of his narcissism, will choose to not try to understand it because he cannot accept the fact that someone would know something he doesn't. I can predict with almost complete certainty that optimissed will fail to understand the concept.

his claim that an infinity's magnitude needs to be "Assessed" to determine differences is literally self contradicting. The infinity is literally the magnitude. in addition, it's not even true of even non-infinities.

its funny how he claims no infinity can be countable when there is literally a class of infinity called "countable infinity". the fact that optimissed's language includes "Elroch believes that the infinite can be counted even though "infinite" literally means "cannot be counted", since finite means countable." means that he has no understanding of infinities or what it means for something to be "countable".

While maths uses precise language, the vagueness of @Optimissed's language is an issue. He is very likely using "countable" incorrectly as a synonym of "finite". It is likely that he never has understood or even known the correct definition. To my knowledge, he never clicks on a link like that to fix the inadequacy of his basic knowledge.

@13470

"Only if you want to ignore reality"
++ You are the one who ignores reality. With unlimited thinking time the unguided engine reaches the depth to find the forced checkmate.
Thus the error rate at unlimited time is zero. So you fitted the wrong curve.
You should fit a curve with an asymptote error = 0 at time approaching infinity.

The 17 ICCF World Championship finalists at 5 days/move would play this endgame perfectly even without table base or computer. Troitsky did and he had no computers.
It is no coincidence that the late GM Sveshnikov first asked for good assistants and only then for modern computers. Give me five years and I will solve chess.

"Thus the error rate at unlimited time is zero. So you fitted the wrong curve.
You should fit a curve with an asymptote error = 0 at time approaching infinity."

the curve was determined by the datapoints, he didnt choose the curve to fit his argument. also, the curve you propose is literally what you are trying to argue as the truth, so thats a circular logic fallacy.

the whole point is that our machines arent programmed to approach chess with mathematical certainty in every position, not that our current machinse cant be modified or made powerful enough to achieve perfection in some positions, or all positions if set to analyze the whole table base. but thats not what the engines do.

Sveshnikov never mentions the word "solve". he says "close". hes not talking about any mathematical solution, and you would realize that had you both:

a) any understanding of mathematical proof. b) read the article you cite.

I mean playing strength, in terms of engine analysis. The ICCF competitors are all almost certainly using the top engines available - which means all the players are performing at the same level.

Which means that draws are practically inevitable.

I don't believe human playing strength matters at this point, due to how high engines have climbed.

A 2300-rated human won't have anything to offer, in terms of chess understanding, to improve the playing strength of a 3600-rated engine.

Just as a 1500-rated club player won't have anything to offer, in terms of chess understanding, to improve the playing strength of Magnus Carlsen ...

Now to be fair, I do believe chess is a draw. So if that's your argument, then I completely agree with you. It should be a draw, anyway - that's how the game is designed. Both players should begin on equal footing. Otherwise, the game would be flawed.

But I don't consider ICCF games to be proof that chess is "solved". I consider them proof that humans using top engines will draw against other humans who are using the same top engines.

It's ... not exactly a surprise outcome ...

theres a thing where russians reportedly have reduced hardware but played well, although during the timeframe where it was confirmed that russians had reduced hardware (ie the timespan of the interview tygxc cited) russians played considerably worse.

@13526

"The ICCF competitors are all almost certainly using the top engines available"
++ Different engines, different tuning, different hardware (the Russians have worse hardware because of sanctions, but nevertheless 4 of the 17 finalists are Russian), different time per move (50 days per 10 moves, but one may take 2 days on a move and the other 10 days).

"I don't believe human playing strength matters at this point, due to how high engines have climbed." ++ 4 Russians qualified for the World Championship finals, despite worse hardware.

"A 2300-rated human won't have anything to offer, in terms of chess understanding, to improve the playing strength of a 3600-rated engine."
++ 'the key is planning, which computers do not do well — Petrosian-like evaluations of where pieces belong, what exchanges are needed, and what move orders are most precise within the long-term plan.' SIM Jon Edwards wins 32nd World Correspondence Championship

'How many ideas can you interactively throw at the computer in one hour is the key question'
'It takes chess wisdom to escape with a draw even though Stockfish and co have calculated 2+ scores most of the middle game.'
Interview with ICCF 26th World Champion

"chess is a draw" ++ Yes

"Otherwise, the game would be flawed." ++ Losing Chess and Connect Four are first player wins.