If white plays a game without any mistakes or blunders...

Also, as to the mathematical breakthroughs section of your argument, I don't find it particularly compelling evidence for chess being unsolvable through some mathematical technique that it has not been discovered yet. Humanity has not yet solved all mathematical problems of note and progress is very emphatically not slowing down yet.

@ProgrammerAngrim

I think we both agree that it’s possible, with our current knowledge of physics, to store a 13-piece tablebase on this planet. Whether such a tablebase ends up being the size of a notebook or the size of a car does not change the general conclusion.

The question is this: How big do we need to make the opening database to have it so any possible move by Black (we can choose how White moves) will lead to either checkmate or a winning position in that currently imaginary 13-piece tablebase.

I have made a study to give us an idea how big such an opening book would have to be:

Here, Black completely blunders the Scandinavian: 1. e4 d5 2. exd5 Qxd5 3. Nc3 h6?? 4. Nxd5 and now, how long can Black survive? Black can survive for 40 more moves until White finally gets checkmate. We can see the forced checkmate on move 37, so we could probably have our opening database have: “37. ... e5: White mates in 8” and not store moves 38-44 in the database. Even so, we need to have a database showing all Black replies from the time Black blunders his queen until a known forced checkmate is seen 34 move later.

So, for us to prove that Black can not draw or win with perfect play by White after 3. ... h6?? (hanging his queen), we need to store all possible Black moves for around 30 turns. Being optimistic, if Black has only eight moves per turn which do not result in a forced mating sequence by White until move 37 (we’ll assume lines are pretty much forced after move 33, but in the actual game, Black has at least three moves without a known forced mate on move 36), our database will need to store 1.7 * (10 ^ 72) positions. That’s a lot more than the number of atoms in the Earth; we would need a database the size of Jupiter or one of the other big planets to prove that 3. ... h6?? is not a draw or win for Black.

Now, is 3. ... h6?? a line where Black has drawing chances? To use the “Russell’s Teapot” line of reasoning being presented in this thread, we would have to develop science fiction technology to before we could say “After 3. ... h6??, White with perfect play can always force checkmate”. To not do so would be us not having an “open mind”. This “open mind” nonsense is a very poor argument.

It is the general consensus that Black can not avoid checkmate after hanging their queen without compensation. I have shown this argument to be true by making a game played by very strong computer opponents (who can defeat any person in the world), where, after Black hangs the queen, White forces checkmate.

For someone to argue that 1. ... h6?? is anything but a defeat for Black, they would have to show me a game where Black wins or draws after hanging their queen, and then we would then study the game to ensure that White did not make a blunder.

The database to prove that White wins after 3. ... h6?? would actually be about the size of an ocean (1.3 * 10^36) , not a large gas giant. The general point still stands.

Dude I'm not sure where the disconnect is in your brain that makes you incapable of understanding the difference between absolute statements and heuristics, or the difference between proof and suggestive evidence. In fact, your statement "It is the general consensus that black can not avoid checkmate after hanging their queen with no compensation" makes no sense in the light of any sort of formalism. You introduce some nebulous and exception ridden notion of compensation to cover your ass in the case that the specifics of any given position invalidate your general rule. This is fine when we are learning to play, or analyzing games, but it is completely useless in teaching us about the underlying structure of the game.

At the end of the day, every single position in chess has exactly one forced result. The result for white is defined exclusively as:
"The result for white in a position with black to move is the best result such that result of every position after black moves is equal or better." That definition is applied recursively from each and every checkmate, threefold, 50 move rule position, etc etc etc. No matter how much handwringing you do about consensus, or general rules, those are not proof for absolute statements about chess.

The starting position has not been shown to be a win for either color or a draw. There is suggestive evidence that it is a win for white. There is suggestive evidence that black has drawing chances. There isn't much evidence that it is a win for black, except the existence of zugzwang positions as possible in chess.

Also, your concept that we only need a 13 man tablebase + an opening book to prove that chess has any given result is completely ridiculous. What we need to prove that is a 32 man tablebase comprising only of positions which can be acquired legally. If our plan is to brute force compute all the positions in chess, that is the only acceptable standard of proof, given that it is not acceptable to write off positions as hopeless if you cannot prove they are hopeless. Otherwise, we would need a non-constructive proof based on that definition of the result of a game to prove any sort of outcome.

Proving things is not just saying your opinions louder. When we talk about chess, which is a perfect information game about which absolute statements an be proven, those statements must be proven to be called fact. Otherwise, they are opinions. They could be good opinions, expert opinions, important opinions, extremely likely opinions, useful opinions, etc. But they are not facts, and it is arrogant to assert them as such.

“the disconnect is in your brain”

When the other person resorts to personal insults, you know you’ve won the argument.

“You introduce some nebulous and exception ridden notion of compensation”

Compensation is a standard term in Chess: https://en.wikipedia.org/wiki/Compensation_(chess)

“There is suggestive evidence that [the starting position] is a win for white.”

Please show us your evidence which indicates that Chess’s opening position is a win for White.

“a 32 man tablebase comprising only of positions which can be acquired legally”

Please estimate how much space would be needed to store a full 32-piece tablebase. Show us the math used to come up with the estimate.

“it is not acceptable to write off positions as hopeless if you cannot prove they are hopeless”

Then show us the evidence that 1. e4 d5 2. exd5 Qxd5 3. Nc3 h6?? is anything but a forced win for White.

I have shown that it’s not computationally feasible to show this position is a win via brute force, and would require science fiction technology. Therefore, we need to show it’s a win for White via common sense and fuzzy heuristics: King + queen vs. King is a known (and proven) forced checkmate, and adding 27 other pieces to the board won’t change that (unless there’s a forced mate, which there isn’t after 3... h6)

“those statements must be proven to be called fact. Otherwise, they are opinions.”

Actually, they are what are known as scientific theories: https://en.wikipedia.org/wiki/Scientific_theory

Science is the process of taking a theory (e.g. White is winning after 3. ... h5), coming up with an experiment which can prove or disprove the theory (having two strong computers play out the game from that position), and updating our knowledge based on the results of said empirical experiment (White won).

Now, we can change the current theory (and, yes, you have stumbled on why scientists call it a “theory” and not “fact”) by performing a new experiment: Start at the 3.... h6? position, have two strong computers play it, and have Black win or draw. Until this can be shown, the current theory that being a queen up without compensation always leads to checkmate for the other player (if the game is played correctly) stands.

And, in the real world, the majority of science is based on “theories”. These “theories” are good enough to give us revolutions in technology and medicine which previous generations have not seen. Developing a vaccine in only a year? That would had been unthinkable only 50 years ago, and it all comes from theories based on empirical evidence. That’s also why we had to wait a year before the vaccine was available; the theory had to be thoroughly tested before we were confident the vaccine was safe and one which reduces the risk of getting COVID-19.

Again, to state that we if can’t prove something isn’t true, it might be true is a form of the old argument, that since we can’t prove there isn’t a teapot between the Earth and Mars, there might be one there. At which point, I bring out Hitchens’s Razor: https://en.wikipedia.org/wiki/Hitchens's_razor Or, as they say in Latin: quod grātīs asseritur, grātīs negātur

Standards of proof are different in different domains. Particularly, the study of chess falls well within the domain of game theory, where the normal standard of proof is a rigorous mathematical proof and statements based on heuristics are referred to either through what is provable about those heuristics or they are rightly identified as unproven conjectures. I'm done replying to this thread because you seem to refuse to engage reasonably here.

Even with pure mathematics, saying something like “There might not be an infinite number of twin primes” does not correctly represent what we know. Saying “We believe there are an infinite number of twin primes, but this hasn’t been formally proven yet” is more accurate. There’s no particularly good reason to believe there’s some twin prime set that’s the largest twin prime pair, and we’re getting quite close to a formal proof that there are an infinite number of twin primes. https://en.wikipedia.org/wiki/Twin_prime

It is true that sometimes what looks like a number sequence which goes up to infinity ends up not being one upon further examination: https://en.wikipedia.org/wiki/Fermat_number (i.e. (2 ^ (2 ^ n)) + 1 is only prime for n = one of {0,1,2,3,4}) Indeed, this is a case where, while we haven’t found a Fermat prime bigger than 65537, there’s no reason to believe there is one.

Come to think of it, we can come up with a heuristic for “how closely does this engine play perfect Chess?”: We give the engine a bunch of positions with known solutions (namely. positions with 7 or fewer pieces, for which tablebases are available) and compare the move the engine makes with the actual correct move in the tablebase. Partial points are given for “not the correct move, but the position is still won” This will give us a reasonable heuristic for how accurate the engine plays positions which are too complicated for us to readily have a tablebase for.