Chess will never be solved, here's why

#2166
"There are non-mathematicians and non-mathematicians.
You are obviously one of the latter."
I am pretty sure I know more about mathematics than any of you, including the man with the 2 degrees.
Mathematics has since ancient times been applied to solve all kinds of problems, not to demonstrate that nothing can be concluded.

I assume you're referring to Gödel there.
Induction and deduction are the two main pathways of any science.

Do you really think any of your 4 curves represents the fraction of decisive games versus time?

No, but I thought you, as the World's greatest living mathematician, might.

Coming back to deriving the error rate E from the fraction of decisive games D, it is obvious that E =~D provided D is small enough.

Proof:
At 1 min / move the paper gives D = 0.021.
Under the generally accepted hypothesis that chess is a draw a decisive game contains an odd number of errors.
Thus
D = E + E^3 + E^5 + E^7 + ... = E / (1 - E^2)
Thus
E^2 - 1 + E/D = 0
Thus
E = sqrt ((1 / 2D)^2 + 1) - 1 / 2D
Keying in
D = 0.021
yields
E = 0.020990747
Thus E =~D
quod erat demonstrandum

Par for all your "proofs". If you check in a situation where it can be measured as I did here you get:

Fraction of decisive games = 0.1 (under your new game rules with 3-fold repetition - 0.0 under your new game rules with 2-fold repetition. Smaller than in your sample in a game different from whichever you propose to solve.)

Error rate per game = 3.0 (under your new game rules with 3-fold repetition - 2.7 under competition rules - haven't bothered to work it out under your new game rules with 2-fold repetition.)

0.1 is approximately equal to 3.0?

By the way - consider Black's play in this game ...
and it doesn't even take fifteen seconds to consider it ...
g4 e5 f3 Qh4# checkmate.
Something 'imperfect' about black's play there? 

There's even a theory that every chess game would end in a draw if nobody makes a mistake.
That's never been proven and might never be proven ...
(want it Disproven right away?  Lol !  Somebody doesn't make a mistake but they lose on the Clock !   )

so reading a novel and writing & reading forum posts about something are the same. good. people can talk about chess being solvable or unsolvable but this level.. is beyong the necessity. if you know too much this topic why dont you write a program, make a product instead of this. besides no one will read all of this.. thousands of pages will be lost here even if they had useful information. write a book, form a product.. so people can use. whats this?

#2152

About your objectivity and honesty, then, maybe you want to comment this excerpt from the very paper on checkers you cited so much:

"With checkers done, the obvious question is whether chess is solvable. Checkers has roughly the square root of the number of positions in chess (somewhere in the 10⁴⁰ - 10⁵⁰ range). Given the effort required to solve checkers, chess will remain unsolved for a long time, barring the invention of new technology."

That was in 2007. The 10^40 - 10^50 range is no longer valid.

Schaeffer was talking about positions in the absence of the 50 move and triple repetition rules. The removal of these from FIDE's basic rules in 2017 serves only to make the figures correct for the basic game.

Nothing has happened in the meantime to invalidate that range as far as the basic rules game is concerned. Chess has not shrunk.
The papers by Tromp (10^44) and Gourion (10^37) are from 2021.

The figure 3 x 10^37 is for diagrams without excess promotions, and is not in any way relevant. It changes neither Schaeffer's range nor Tromp's estimate (circa 4 x 10^44), which also relates to the basic rules game.

The number of positions in your proposed game of basic rules + two and a Schrödinger's half fold repetition rule would be vastly greater, because then positions must be defined effectively by a pgn from a ply 0 position - different positions for different pgns leading to the same fen.
In those 15 years also computers have become faster and chess engines better, now 10^9 nodes/s.
Also progress has been made on the 7-men endgame table bases.
Most of the effort of Schaeffer was related to building his endgame table base.

Schaeffer himself also said:
”The one thing I’ve learned in all of this is to never underestimate the advances in technology”
https://webdocs.cs.ualberta.ca/~jonathan/publications/ai_publications/checksolved.pdf 
final line

Interesting to note from the paper you quote that checkers has not in fact been weakly solved, nor even fully ultra weakly solved.

@btickler I never talked about time. It was all about the unnecessity of talking about something that much, which is not useful or anything. Too much information is wasted between pages. And why don't you make something useful if you all have that much information on the topic. I said. You are just twisting my words. Like almost anyone who disagrees.

By the way - consider Black's play in this game ...
and it doesn't even take fifteen seconds to consider it ...
g4 e5 f3 Qh4# checkmate.
Something 'imperfect' about black's play there? 

I think you mean that the paper says checkers has not been strongly solved. Strategies for optimal play from the opening position are complete. This only meant about 10^14 calculations (so certainly not the full 10^20 positions). The 10 piece endgame tablebase for the solution has 39 trillion positions, which is between 10^13 and 10^14 positions.

#2218
"Schaeffer’s proof solved checkers for 19 different openings, all of which end in draws. There are 300 total tournament openings"
That is what I say about chess all the time.
Of the 500 ECO codes A00 to E99 only 50 are necessary to weakly solve chess.
If 1 e4 e5 is proven a draw, then it is not necessary to determine if 1 e4 c5 draws as well or not.
If 1 e4 and 1 d4 are proven draws, then it is not necessary to verify that 1 a4 draws as well.
If 1 e4 e5 2 Nf3 is proven a draw, then it is not necessary to look at 1 e4 e5 2 Ba6.

Schaeffer’s proof solved checkers for 19 different openings, all of which end in draws. There are 300 total tournament openings, but many of these were determined to either be mirrors of other positions or altogether irrelevant to the proof because they lead to positions common to other openings.

#2210

"Chess has not shrunk."
++ Chess has not shrunk, but it is smaller than Schaeffer believed in 2007.

No it's not. Tromp's figure is in Schaeffer's range.
The papers by Tromp (10^44) and Gourion (10^37) are from 2021.

Whether a paper is valid doesn't depend on the publication date. Both papers are valid - your use of the second is not.

"It changes neither Schaeffer's range nor Tromp's estimate (circa 4 x 10^44)."
++ Tromp's estimate 10^44 has no relevance to solving chess, as none of his 538 randomly sampled positions found legal can result from the initial position by a game with more than 50% accuracy. All of his 538 positions found legal contain multiple underpromotions to pieces not previously captured.

Firstly you're not proposing to solve chess. As far as I am aware no game referred to as "chess" that excludes the 50 move rule but includes either a 2-fold or 3-fold repetition rule has ever been prevalent.

Secondly, if whatever you propose to solve turns out to be a draw, then, using your method will need to consider all Black responses and also show that its a draw for all alternative White moves at any stage. This will result in a majority of games that look rather different from those you see at your local chess club.

You're good at issuing challenges. I challenge you to prove (or even convincingly demonstrate) just a single one of Tromp's 538 positions cannot result from the initial position by a game with more than 50% accuracy.

But if you could, that wouldn't say anything about the positions you would encounter in your computation.

"The figure 3 x 10^37 is for diagrams without excess promotions"
++ That makes it very relevant. Diagrams = positions, as for any diagram with white to move there is a position with black to move by up/down symmetry.

Diagrams ≠ positions

These are the same diagrams

But in the competition rules game they're not the same position. The first position is winning for White, the second position is a draw.

You can't have the same position with different theoretical results.

In either a variant of competition rules chess that excludes the 50 move rule or a variant of competition rules chess that excludes the 3-fold repetition rule, the second position would also be winning for White. That wouldn't make the positions the same in the former case because the possible forward play in each would be different.

(In your basic rules + 2-fold repetition game both positions are illegal because the game has already terminated; in your basic rules + 3-fold repetition game the second position is a win.)

You seem to have extraordinary difficulty in grasping that the same diagram can belong to different positions in different games or the same games. 

Promotions to pieces not previously captured do happen in less than 1% of games, and mostly to queens, not underpromotions. Underpromotions may happen in less than 0.1% of games.

You should be interested in the positions your proposed procedure needs to consider to complete, not what happens at your local chess club.
If you want you can multiply 10^37 by 10 to include positions with 3 or 4 queens.
That leaves 10^38.

I don't want.

If it were I investigating the feasibility of your approach, I would start off with Tromp's relevant estimate of positions under basic rules and then multiply by different factors depending on the game to be solved. 

The necessary factors are complicated to work out when an n-fold repetition rule is included in the game. That is because a position specification is then a pgn as opposed to a fen.

The tablebase generation procedures neatly bypass the n-fold repetition problem by never producing positions with the same diagram and side to move with different distances to their respective objectives.

Your procedure doesn't detail how it is proposed to get around the problem. SF14 (your proposed vehicle) happily repeats positions up to twice whether it thinks it's winning or not. With your new two and a Schrödinger's half-fold repetition rule half of the SF14 vs. SF14 games here would be drawn under the 2-fold repetition rule when observed. 

An upper bound on the number of positions in you search space would be

2.9 x 10^44 x (n^(2.9 x 10^44)) where n is either 2 or 3 depending on when it is observed. The upper bound is obviously far too high and could easily be reduced - I leave it to you to reduce it.

Even this number is much too large, as a random sample of 10,000 positions without promotions to pieces not previously captured shows the positions cannot result from the initial position by a game with more than 50% accuracy.

As I pointed out that's irrelevant - but I await the result of my challenge with interest.

Tromp conjectured than only 1 in 10^6 might be sensible.

Of his basic rules positions. That has no relevance to a solution along your proposed lines of even a solution to the basic rules game.

That would leave 10^32 sensible positions including those with 3 or 4 queens.

Actually 4 x 10^44 / 10^6 is 4 x 10^38 - I should check your calculator installation.
So the range is rather 10^32 - 10^38 according to knowledge of 2021.

Or not as the case may be.

"The number of positions in your proposed game of basic rules + two and a Schrödinger's half fold repetition rule would be vastly greater, because then positions must be defined effectively by a pgn from a ply 0 position - different positions for different pgns leading to the same fen."
++ This is nonsense. The 50-moves rule is never invoked in practice before the 7-men endgame table base is reached. I challenged you to provide one single grandmaster or ICCF game under any rules where the 50-moves rule was or could be invoked in a position with 8 men or more. I bet no such game exists at all.

I didn't mention the 50 move rule. The relevance of the ply count 0 position is that no positions as defined for the purposes of art. 9.2.1 that occurred previously can occur subsequently.

(Again, what happens at your chess club, whether or not they're playing the same game as you're trying to solve, is of no relevance.)