Will Chess ever be "solved"?

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Avatar of DiogenesDue
FirstMarch wrote:

...What? Hahahahaha are you insinuating that the use of my profile picture is racist? It's a popular meme of an NBA player (you literally don't even know who it is, so hilarious) making a confused face, and I'm using it because it's personally funny to me for opponents to see whether they win or lose after a blunder. This is how you know you're out of touch, old man... And no one cares about what flag people use, Zimbabwe is simply my favorite country, excluding my own. To suggest that one is a "fake profile" because they put a random flag and profile picture is just incredible to behold, not to mention your abhorrent use of buzzwords to sound smart. Stick to your lane, bud. You made an absolute fool of yourself butting in, not even talking about the original topic at hand trying to white knight a random dude posing as a woman. Cringe!

I am not white knighting...perhaps you didn't grasp what I actually said in my first sentence and understand the implications of "just as fake".   The difference is I would not have any particular beef with Nikki's behavior.  I was just pointing out the hypocrisy involved in yours.

Time will tell about your motivations and the longevity of your account, and who may or may not be a fool.  It's not a unilateral declaration you can just decide on.  Though some here do try that tactic often...3rd parties actually make the determination over time.

Let's just say given your current body of posts, I'm not overly worried wink.png.  

Avatar of FirstMarch

@btickler

Again, cringe! Hope you realize that anyone stumbling upon your posts and reading the way you type will instantly recognize what kind of a person you are, and how ironic it is that you choose to be the way you are. You don't even play chess on a chess website and sit on the forums all day... Unironically all day... and every day. What a waste. Way to not even address how you thought my picture = racism, lmao! Hope one day you learn that you won't be able to win any arguments on the internet as long as you, as a person, exist. That's how sad the situation is.

Avatar of DiogenesDue
FirstMarch wrote:

@btickler

Again, cringe! Hope you realize that anyone stumbling upon your posts and reading the way you type will instantly recognize what kind of a person you are, and how ironic it is that you choose to be the way you are. You don't even play chess on a chess website and sit on the forums all day... Unironically all day... and every day. What a waste. Way to not even address how you thought my picture = racism, lmao! Hope one day you learn that you won't be able to win any arguments on the internet as long as you, as a person, exist. That's how sad the situation is.

I hope you realize how sad this all sounds coming from an anonymous troll wink.png...and how futile,  given that your posts will probably be gone sooner than later.  

I don't sit on the forums all day.  Nobody does.  You see, in this modern age we will live in, the internet is a virtual construct that allows for multitasking, and these forums sit open on a single tab among a couple of dozen tabs I am working on at any given time.  Do you consider yourself to be "sitting on the forums all day" when you check the forums between making telemarketing calls?  "Unironically", prior to this past week I had not been posting much at all of late anyway.

I guess next in line comes the basement dweller attack? wink.png

Now, it's true that I am retired and may have a lot more leisure time than you...but that is something to be proud of, not to ridicule, unless you're just too wet behind the ears to know any better (and your usage of "cringe" does trend in that direction).

Avatar of binomine
-BEES- wrote:

I don't think anyone expects the Berlin or Grunfeld to be anything else but a draw. I fail to see how that would change anything. However, sidelines and variations that are theoretically uncertain would be affected. Some would be vindicated and some would be killed.

Let us assume there is a position, the Q position, which is a guaranteed draw or win for white during perfect play. 

Now, and this is the really difficult part, let's assume white can reach this Q position no matter what black plays. 

Then if both of these are satisfied, chess would be solved, without needing to resort to checking any other position. 

The fact that by move 3, it's possible to reach a position that virtually guarantees a draw hints that the Q position could exist. 

Avatar of Justs99171

If we had a computer which was capable of computing every possible move/position, which is a ridiculously high number - so high it's essentially abstract, would this same computer be capable of evaluating every single possible move/position.

It's entirely possible that the device or program, which has quantified every possible position, misevaluates numerous moves/positions.

At this point, chess wouldn't actually be "solved."

Now imagine if there are numerous computers/programs able to quantify the total number of possibilities, and all are assigning varying evaluations. It's entirely possible, given the discrepancies, that none of these computers/programs are 100% accurate, yet inevitable that one from the group is superior to the rest.

At this point, even then chess still hasn't been "solved."

Avatar of tygxc

#122

Many positions probably are guaranteed draws with best play from both sides, thus many positions are "Q positions". 1 e4 e5 2 Nf3 Nc6 3 Bb5 Nf6 and 1 d4 Nf6 2 c4 g6 3 Nc3 d5 probably are "Q positions". That is not however a proof. Chess has for decades been conjectured to be a draw, but it has not yet been mathematically proven.

Avatar of tygxc

#123
No this is not the case. There are only 3 possible evaluations of a position: draw / win / loss. We could even simplify to 2 possible evaluations: draw / no draw.
If there were a computer that could calculate from the initial position to the end, then chess would be solved, but such a computer is totally unfeasible now.
Likewise if we had 32 men table bases, then chess would be solved, but 32 men table bases are unfeasible we now have 7 men table bases and work on 8 men is in progress.
A more realistic approach would be to generate sufficiently large table bases e.g. 13 men and then calculate from the initial position towards that table base. That would solve chess in the same way as checkers has been solved.
Even that is beyond present capabilities, but is likely to come within reach before the end of the century as technology advances.
One promising technology that can achieve that is quantum computing.

Avatar of binomine
tygxc wrote:

#122

Many positions probably are guaranteed draws with best play from both sides, thus many positions are "Q positions". 1 e4 e5 2 Nf3 Nc6 3 Bb5 Nf6 and 1 d4 Nf6 2 c4 g6 3 Nc3 d5 probably are "Q positions". That is not however a proof. Chess has for decades been conjectured to be a draw, but it has not yet been mathematically proven.

Yes, many positions fulfill the first part, but not the second. 

It's possible to get a draw or a win from a lot of positions in chess, but it is not possible to enter those positions without consent from your opponent. 

The theoretical Q position would be inescapable.  

Avatar of DiogenesDue
Justs99171 wrote:

If we had a computer which was capable of computing every possible move/position, which is a ridiculously high number - so high it's essentially abstract, would this same computer be capable of evaluating every single possible move/position.

It's entirely possible that the device or program, which has quantified every possible position, misevaluates numerous moves/positions.

At this point, chess wouldn't actually be "solved."

Now imagine if there are numerous computers/programs able to quantify the total number of possibilities, and all are assigning varying evaluations. It's entirely possible, given the discrepancies, that none of these computers/programs are 100% accurate, yet inevitable that one from the group is superior to the rest.

At this point, even then chess still hasn't been "solved."

Traversing backwards from mate (which is how tablebases are built) precludes the need for any evaluation of the type you mentioned...there's either a brute force mate, or there isn't.  Any position that is not a forced mate is a draw by omission/exclusion from the tablebase.

Engines create evaluations by having human-derived and tweaked valuations (traditional engines) and/or engine derived learning (machine learning engines).  These are relatively useless in terms of solving chess.  They are only good for "scoring" the imperfect play of humans and current engines wink.png.  But that scoring is inherently flawed. 

Avatar of tygxc

#126
There is not one single "Q position", there are many. Neither white nor black presumably can avoid landing in one of the many "Q positions"

#127
An engine is not useless for solving chess: it is useful to calculate towards the table base to drastically reduce the number of positions needed to look at. Checkers was solved with an engine "Chinook" calculating towards the 10 men table base.

Avatar of Optimissed
Justs99171 wrote:

If we had a computer which was capable of computing every possible move/position, which is a ridiculously high number - so high it's essentially abstract, would this same computer be capable of evaluating every single possible move/position.

It's entirely possible that the device or program, which has quantified every possible position, misevaluates numerous moves/positions.

At this point, chess wouldn't actually be "solved."

Now imagine if there are numerous computers/programs able to quantify the total number of possibilities, and all are assigning varying evaluations. It's entirely possible, given the discrepancies, that none of these computers/programs are 100% accurate, yet inevitable that one from the group is superior to the rest.

At this point, even then chess still hasn't been "solved."

I agree with this assessment and I made a similar argument on the "is chess a draw" thread, contra the idea that all we need to have is a full tablebase of all moves. Disregarding the difficulty or even the extreme improbability of ever achieving such a tablebase of all moves, there would be no actual proof that somewhere in the enormous mass of calculations, a mistake hadn't been made. It could never be shown that a mistake hadn't been made and, therefore, that route can provide no proper proof of whether chess is a draw or win.

Whether the tablebase, which is highly improbable in itself, is generated using a forwards search or a backwards search (or a forwards and backwards search that meets somewhere in the middle) all we could do would be to surmise that a mistake wasn't made within a certain percentage of accuracy. So the situation, after all that, is no different from what it is at the moment. We may be sure that it's inherently drawn, of course.

Avatar of tygxc

Computational proofs are accepted in mathematics:

https://en.wikipedia.org/wiki/Four_color_theorem 

Avatar of aarnavhps

yes

 

Avatar of aarnavhps

i code a bit

 

Avatar of aarnavhps

i can confirm that you can

Avatar of Optimissed
tygxc wrote:

Computational proofs are accepted in mathematics:

https://en.wikipedia.org/wiki/Four_color_theorem 

Such as "if the calculations are correct then the proof is too"? This kind of tablebase proof isn't a mathematical proof, however.

Avatar of tygxc

Yes it is.

Appel and Haken let their computer color 1834 maps to prove their mathematical theorem.
Likewise the proof that checkers is a draw is a mathematical proof as well.

Avatar of Optimissed

EXTRACT
<<<An unavoidable set is a set of configurations such that every map that satisfies some necessary conditions for being a minimal non-4-colorable triangulation (such as having minimum degree 5) must have at least one configuration from this set.
A reducible configuration is an arrangement of countries that cannot occur in a minimal counterexample. If a map contains a reducible configuration, the map can be reduced to a smaller map. This smaller map has the condition that if it can be colored with four colors, this also applies to the original map. This implies that if the original map cannot be colored with four colors the smaller map cannot either and so the original map is not minimal.
Using mathematical rules and procedures based on properties of reducible configurations, Appel and Haken found an unavoidable set of reducible configurations, thus proving that a minimal counterexample to the four-color conjecture could not exist. Their proof reduced the infinitude of possible maps to 1,834 reducible configurations (later reduced to 1,482) which had to be checked one by one by computer and took over a thousand hours. This reducibility part of the work was independently double checked with different programs and computers. However, the unavoidability part of the proof was verified in over 400 pages of microfiche, which had to be checked by hand with the assistance of Haken's daughter Dorothea Blostein (Appel & Haken 1989).

Appel and Haken's announcement was widely reported by the news media around the world, and the math department at the University of Illinois used a postmark stating "Four colors suffice." At the same time the unusual nature of the proof—it was the first major theorem to be proved with extensive computer assistance—and the complexity of the human-verifiable portion aroused considerable controversy (Wilson 2014).

In the early 1980s, rumors spread of a flaw in the Appel–Haken proof. Ulrich Schmidt at RWTH Aachen had examined Appel and Haken's proof for his master's thesis that was published in 1981 (Wilson 2014, 225). He had checked about 40% of the unavoidability portion and found a significant error in the discharging procedure (Appel & Haken 1989). In 1986, Appel and Haken were asked by the editor of Mathematical Intelligencer to write an article addressing the rumors of flaws in their proof. They responded that the rumors were due to a "misinterpretation of [Schmidt's] results" and obliged with a detailed article (Wilson 2014, 225–226). Their magnum opus, Every Planar Map is Four-Colorable, a book claiming a complete and detailed proof (with a microfiche supplement of over 400 pages), appeared in 1989; it explained and corrected the error discovered by Schmidt as well as several further errors found by others (Appel & Haken 1989).>>>

Avatar of Optimissed
tygxc wrote:

Yes it is.

Appel and Haken let their computer color 1834 maps to prove their mathematical theorem.
Likewise the proof that checkers is a draw is a mathematical proof as well.

But the prospective "solution" of chess does not seem feasible and in the very unlikely event it were achieved, it would be impossible to prove that it were correct because it would be impossible to prove that an error hadn't been made. In contrast, the four colour problem, which seems intuitively correct, is capable of being proven and has been proven by raw "brute force". Also, I think the difference in magnitude makes the two "proofs" qualitatively different from one-another. At best, it seems to be a difference of opinion, since I think we agree that a deductive proof that a potential solution of chess is correct is impossible.

Avatar of tygxc

#137
Proving chess a draw is much more complex than proving checkers a draw or proving that 4 colors suffice to color any map. However conceptually it is the same: for the proof you write a program and let it run on a computer. A peer reviewed paper is then published that explains the method and the results and that is then accepted as the proof. You could even argue that a computational proof is easier to verify than a pure mathematical proof. The pure mathematical proof of Fermat's Last Theorem is no easy read. There have been several "proofs" of the Riemann Hypothesis, which had to be retracted afterwards. The 4 color theorem proof was also challenged by Wilson, but then corrected. That is how mathematical proofs go nowadays.