Chess will never be solved, here's why

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mpaetz

     Accepted wisdom has been proved to be incorrect too often for it to be relied on to be foolproof. A strong solution is more thorough than a weak solution. I have made no "foolish claims" such as you posit. I just insist that claims made on a less substantial basis are more open to question.

     That's my opinion on this topic. My belief is that chess is very probably inherently a draw, but my opinion (or yours, or any other contributor here, or Kasparov's, or Capablanca's, or a team of GMs with a lot of computer aid, or even Steinitz--who claimed a greater knowledge of chess than God himself) cannot be taken as ultimate truth.

 

tygxc

@5999

"A strong solution is more thorough than a weak solution."
++ Yes, a strong solution is stronger than a weak solution, hence its name.
However, a strong solution of Chess must consider all 10^44 legal positions,
and thus prohibitively takes 10^44 nanoseconds of time and 10^44 bits of storage.

Checkers, Losing Chess, Connect Four, and Nine Men's Morris have been weakly solved only.
Thus when we talk of solving Chess the only meaningful is weakly solving.
That requires only the 10^17 relevant positions and can be done in 5 years.

MARattigan
mpaetz wrote:

     ... I have made no "foolish claims" such as you posit. I just insist that claims made on a less substantial basis are more open to question.

...

I've been following the thread closely and I don't recall anyone making such claims.

Mike_Kalish

@5998

"But you cannot discard all that knowledge either"

 

I don't think anyone wants to discard that knowledge. We're just saying it falls short of a mathematical solution. I find it quite compelling and I believe it, but to me, it's not a proof. 

tygxc

@6002
"I don't think anyone wants to discard that knowledge."
++ There are people here who doubt that 1 a4, 1 Nh3, 1 g4? 1 e4 e5 2 Ba6? cannot win.
They thus discard the accumulated knowledge.

"We're just saying it falls short of a mathematical solution."
++ In solving games it is beneficial to incorporate knowledge.
Allis solved Connect Four with 9 knowledge rules. That is accepted mathematical proof.
http://www.informatik.uni-trier.de/~fernau/DSL0607/Masterthesis-Viergewinnt.pdf 

Mike_Kalish

@6003

"I don't think anyone wants to discard that knowledge."
++ There are people here who doubt that 1 a4, 1 Nh3, 1 g4? 1 e4 e5 2 Ba6? cannot win.

 

I should have just spoken for myself. 

tygxc

@6004
++ But then a weak solution that dismisses 1 a4, 1 Nh3, 1 g4? 1 e4 e5 2 Ba6? based on knowledge instead of calculating those to a draw or loss is valid proof.

Elroch

I found a stone tablet with "Solving chess requires only 10^17 relevant positions and can be done in 5 years." written on it, so you can be sure we have a reliable basis for that.

Unfortunately, I dropped it, but take my word for it.

tygxc

@5997
The word of GM Sveshnikov is good enough.

Elroch
tygxc wrote:

@5997
The word of GM Sveshnikov is good enough.

Absurd.

CrusaderKing1

Even if you did find a way to "figure" chess out, the Fischer chess 960 would eventually take its place.

However, I think there is simply too much to remember in chess, and only a handful of people would ever be "able to figure it out", even if it was possible. 

6000 posts. Nice.

tygxc

@6000
"I think there is simply too much to remember in chess"
++ Yes, but Kramnik used to study 10,000 games per month.
A player who has memorized 10,000 perfect games with optimal play by both sides from the weak solution of chess has an advantage. 

Elroch

He'll still get crushed by Stockfish. Chess is too big for humans to get it right.

tygxc

@6002
"He'll still get crushed by Stockfish."
++ If Stockfish deviates from the memorized games without making an earlier error.

Mike_Kalish
Elroch wrote:
tygxc wrote:

@5997
The word of GM Sveshnikov is good enough.

Absurd.

So after all this, it seems come down to what we mean my "solve". One "definition" (Elroch) involves considering every possible legal move in every possible legal position, so 0% chance of error. The other definition (tygxc) is more of a "for all practical purposes" definition that says "Sure, there's a .0000000000000000000001 chance we're wrong, but we can all just agree that's close enough, and a valid proof."  

Everyone else seems to line up with one of these two. I clearly line up with Elroch, assuming I understand what he's saying.

Am I characterizing this correctly?

 

tygxc

@6004

"So after all this, it seems come down to what we mean by solve"
++ The definition is clear:
'Weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition.
The game-theoretic value of a game is the outcome when all participants play optimally.'
https://www.sciencedirect.com/science/article/pii/S0004370201001527 

"considering every possible legal move in every possible legal position"
++ No, that would be strongly solving chess to a 32-men table base with 10^44 legal positions.

"Am I characterizing this correctly?" ++ No, the definitions are clear.

There are 2 differences.
1) I interpret any opposition and all participants playing optimally such that white must resist against the draw and thus that white moves that clearly do not resist or clearly resist less and thus clearly are not optimal can be discarded. E.g. 1 e4 e5 2 Ba6?

2) I also take from the above peer-reviewed paper:
'Next to brute-force methods it is often beneficial to incorporate knowledge-based
methods in game-solving programs.'
I also note this MSc. dissertation: A Knowledge-based Approach of
Connect-Four The Game is Solved: White Wins.
http://www.informatik.uni-trier.de/~fernau/DSL0607/Masterthesis-Viergewinnt.pdf
I also note this peer-reviewed paper
Acquisition of Chess Knowledge in AlphaZero
https://arxiv.org/abs/2111.09259 
That ranks 1 e4, 1 d4, 1 c4, 1 Nf3 as more optimal than the other 16.
So as knowledge is allowed and beneficial in solving a game, I use the knowledge acquired by AlphaZero with no other input but the Laws of Chess to restrict the weak solution to the 4 most optimal moves 1 e4, 1 d4, 1 c4, 1 Nf3 that oppose most to the draw and to discard the other 16 moves. If the 4 best moves only draw, then the 16 worst moves cannot win either.
I also note that Checkers has been weakly solved with only 19 relevant openings of the 300 imposed openings, thus that it is OK in solving chess to only consider relevant openings only.

Mike_Kalish

@6005

Thanks.....both for taking the time to explain all this and for not ridiculing what was probably an over simplification on my part. I'm trying to see both sides of this, but most of this is very new to me. Interesting nonetheless. 

Elroch
mikekalish wrote:
Elroch wrote:
tygxc wrote:

@5997
The word of GM Sveshnikov is good enough.

Absurd.

So after all this, it seems come down to what we mean my "solve". One "definition" (Elroch) involves considering every possible legal move in every possible legal position,

so 0% chance of error.

That is close to the standard definition of a strong solution.  While I have referred to it, I have mostly addressed the ntion of weak solution (a complete optimal strategy for each side). This is much smaller computationally, rather like if you always play the same opening lines you don't need to know the entire opening encyclopedia, just a small fraction of it (less than 1% in fact!).  As you say, the key point is that you have to deal with every legal move the opponent can make, exactly like solving a mate in 2 problem.

The famous and challenging solution of checkers was a weak solution that required years of computation. @tygxc advocates a sort of sloppy version (where large parts of the solution are ignored, for reasons that would not be viewed as adequate by anyone working in this area, and then he still gets the complexity wrong (because each side often has many moves that can't be even sloppily rejected and games can be long).

The other definition (tygxc) is more of a "for all practical purposes" definition that says "Sure, there's a .0000000000000000000001 chance we're wrong, but we can all just agree that's close enough, and a valid proof."  

Something like that. This is not satisfactory in a rigorous subject, which is why it took years to solve checkers, rather than a sloppy version being knocked off over  weekend.

Everyone else seems to line up with one of these two. I clearly line up with Elroch, assuming I understand what he's saying.

Am I characterizing this correctly?

You are mostly right: I advocate strict rigour - the same as the peer-reviewed literature on solving other games.

 

 

JonathanBoykin

It looks interesting as usual. Thank you so much for sharing with us.

TheGrandJoker

You guys are forgetting a bigger aspect to playing chess. Which is manipulate your opponent. Non-manipulative chess can be solved, or if you are not studying to beat a certain opponent faster because of a weakness in his gameplay. Computers can figure out the best moves better than humans, but to beat certain people you need to know more about the individual.