Chess will never be solved, here's why

- The word "beach" is loosely defined and impossible to delineate for purposes of counting grains of sand.

- The word "sand" is also loosely defined.

- Sand particles are constantly being added to the world and making their way into beaches via erosion et al.

- Sand particles are constantly being removed from beaches in many ways.

Interesting conversation.

No, It's just because so many people here have disagreed with me over things I find obvious and clear, and when I challenge them there is usually no attempt to answer. People just sidestep. I know the chances of anyone having my IQ are vanishingly small and to you, conveniently, it's a delusion. The point is I know I'm clever and when Elroch or you fail to get the point of whatever it is, forever and forever, I'm obliged to put it down to that. I really am used to it. You, in your strange world of delusion, edit out uncomfortable facts but I have to admit that I am arguing here with a series of has-beens and never-wases because even at my age I'm still learning. You win a prize for guessing what I'm using it to learn.

It was good to see MAR finally getting the bit between his teeth. I think I commented a couple of months ago that I thought he was the only one here who has a good intellect. I'm not counting myself .... in a way I'm not here. That is, not accepted because I don't make the right grunts. Noises. MAR is finally taking on Elroch. I won my argument with E about game theory a dozen times and Elroch wasn't capable of even understanding that, let alone admitting it. So let's see how MAR does.

@MARattigan, the notion of solving chess is an abstract one, about the game as a mathematical object, an example of a combinatorial game. The precise drawing rule needs to be specified, but nothing that is not part of chess as a combinatorial game. There is no need for resignation or agreement of draws. While they could be added as optional actions they are superfluous to a solution.

The entire literature on solving combinatorial games deals with combinatorial games in the same way. (Eg that on the solution of checkers and a few modern popular games).

https://www.gamesver.com/is-connect-4-a-solved-game-what-does-that-even-mean/

Apparently Reversi/Othello remain unsolved, while 4x4 and 6x6 versions have been solved.

@Elroch. Agreed I don't think I said any thing to contradict that.

Except that if resignations and agreed draws are added they need to be prioritised with other game terminations or you don't have a zero sum game. Also you can't make the objective checkmate because that is never achievable against all opposition; if your opponent resigns you're stuffed.

The drawing rules for FIDE basic rules, FIDE competition rules, ICCF and TCEC are all different and would need different abstract games (TCEC could be very interesting). I'm not in any way convinced the solutions will be the same. They're all aiming toward different endpoints.

See, that's the only way your narrative holds up, if you are a 1 in a billion level genius, and everybody who disagrees with you are has-beens or never-have-beens.  Now apply Occam's Razor and let the truth in...

What is it that makes you something more again?  I'm not talking about IQ test scores or the psychic musings of long ago girlfriends...

You see, I don't really care if you want to have an opinion on everything and be stubborn about it.  The problem is that you can't seem to do this without disparaging everyone around you.  If you were one of those posters that ended with "well, I disagree, so I guess we're at an impasse", then I would not have much to say to you over time.  I can only speak for myself, but I am guessing others feel similarly.  I'm also guessing whatever you might have said that you deemed complimentary to Maratiggan might not have been taken as such.  You have said similar things in the past about how felt about others... myself, Elroch, Tygxc, even CooloutAC, and how you "complimented" others' intelligence...by squarely placing it well below your own supposed but completely unproven level .

You keep saying "you see". I noticed it twice at the beginning of paragraphs. I also noticed that you don't really care. I haven't read the rest because it's so predictable. No point ... you aren't interesting. I gave my age specifically to see what you would do with it and sure enough, back came "old and bitter". A stereotype and it wouldn't be a very kind one if it were true. But I have a beautiful wife who looks 20 years younger than she is AND she's younger than me by 8 years, most things I need, my son is successful and a good person and I'm happy. I keep fit, do long walks, keep busy, have lots of interests. What do you do? Find people to try to upset. That's about what you seem to enjoy. I don't need to prove anything to you. Ability speaks for itself but only for people who know the language. 

@Elroch

Apologies.

On further reflection I have to retract the last point if you discount TCEC. I think you're right about the common weak solution to (versions of chess suitably abstracted from) all three.

Obviously the Sysygy construction if continued to 32 men would give such a solution.

The results could be different for different versions, but the moves would produce the correct results in each case.

But the child's pamphlet usually still contains a resignation rule and an agreed draw rule without any prioritisation of concurrent termination results that involve them, so it's still not a zero sum game. To solve you need to either drop them in your abstract game or prioritise concurrent terminations. I've not seen any suitable rules that do.

Lol.  No, I didn't say a word about your age, or call you bitter, until after seeing you wax eloquent for years on end.  I don't judge you or your life...*until* you judge others around you.  Then I hold up the mirror.  That's the ultimate issue.  The things I know about you, by the way, are all things you have used in the past in attempts to show yourself as "better than" or to try and support dubious claims about others.  Hoist with your own petard.

Speaking of ability, if you had the ability to exist here without having to put down everyone around you when you don't get your way, then the forums would be better off, and you would be far better off.  Your life would be measurably better if you never talked about IQ or basically anything that implies nobody on whatever thread you happen to be infecting can hold a candle to you intellectually.

...and someone with an actual 160 IQ would have theoretically figured this out by the age of 70 , if IQ actually meant what you'd like it to mean.

your definitions arent correct, can chess be solved, I dont know, havent done the mah myself, but Im pretty sure you can, no one will waste his time doing it because the partial solution we have is more than enough and we get faster methods to get to solving chess every now and then, so starting a 10 years process right now doesnt make sense if you cansider that maybe if you start nex year it will only take 8 years, but im pretty sure they already know its posible and how much it would take them.

@5352

"you can't use Stockfish in solving anyway, because it is incapable of evaluating perfect play"
++ You can use Stockfish. As calculated before: if you let the cloud engine run for 17 s (or a desktop for 17000 s = 4.7 h) in a legal position of between 32 and 7 men, then the table base perfect move will be among the top 4 engine moves except for 1 position in 10^20.
That is good enough as there are only 10^17 relevant positions.

"If you want to solve it going forwards, you have to handle repetitions/circular positions"
++ Yes, 3-fold repetition is a major drawing mechanism e.g. 16% of ICCF WC games.

"I wouldn't consider chess fully solved if the 50 move rule is applied"
++ The solution will not invoke the 50-moves rule as in the perfect ICCF WC games we have.
On the other hand if chess is solved without the 50-moves rule, then that same solution also applies to the case with the 50-moves rule. The 50-moves rule is a red herring.

@5397

"you can't use Stockfish in solving anyway, because it is incapable of evaluating perfect play"
++ Yes we can use Stockfish. As calculated before: if the cloud engine runs for 17 s (or a desktop for 17000 s = 4.7 h) in a legal position of between 32 and 7 men, then the table base perfect move will be among the top 4 engine moves except for 1 position in 10^20.
Unproven outside of endgames."
++ Proof: calculated by extrapolation from the AlphaZero autoplay paper.
https://arxiv.org/pdf/2009.04374.pdf Figure 2.
1 s / move: 11.8% decisive, 88.2% draws
1 min / move: 2.1% decisive, 97.9% draws
Extrapolating:
1 h / move: 2.1% * 2.1 / 11.8% = 0.37% decisive, 99.63% draws
60 h / move: 0.37% * 2.1% / 11.8% = 0.07% decisive, 99.93% draws
60 h / move on the engine of the paper corresponds to 17 s / move on a 10^9 nodes/s cloud engine
0.07% decisive means 0.0007 errors / game means 10^-5 errors / position
Thus for 4 candidate moves: (10^-5)^4 = 10^-20 errors / position.
Thus in 1 position out of 10^20 the table base correct move is not among the engine top 4 with the cloud engine running for 17 s at 10^9 positions / s, or a desktop running for 4.7 h.

This is verifyable. Take a 7 men position KRPP vs. KRP. Let a desktop run for 4.7 h.
The table base correct move is among the top 4 engine moves.

"That is good enough as there are only 10^17 relevant positions.
Also unproven."
++ Proven in 2 ways.
1) top down: from the Tromp count 10^44 legal positions proven none can result from optimal play and the Gourion count 10^37 positions then applying analogy to the weak solution of Checkers 10^14 and Losing Chess 10^9: a weak solution requires less positions than a strong solution. That leaves 10^17 relevant positions. 1 e4 e5 2 Ba6? or 1 a4 are not relevant: no optimal play by both sides.
2) bottom up: forward calculation with width w = 4 (from the above argument) and depth d = 39 (average length of ICCF WC games, > 99% sure to be optimal play from Poisson distribution fit) .

An upper bound assuming no transpositions:
1 + w + w² + w³ + ... + w^d = (w^(d+1) - 1) / (w - 1) = (4^40 - 1) / (4 - 1) = 10^23
A lower bound assuming permutations of all white moves :
1 + w/1! + w²/2! + w³/3! + ... = e^w = e^4 = 55 regardless of depth d
Geometric mean of lower and upper bounds: 
sqrt (55 * 10^23) = 10^12
Thus 10^17 is plausible.

"you've been through this before with so many other people...everyone on this thread"
++ So far nobody has come up with any argument leading to another figure than 10^17.
If somebody has a valid argument why it should be 10^18 or 10^16 I am all ear.

"myself" ++ You keep erroneously using the number 10^44 needed for strongly solving chess

"Elroch" ++ Keeps insisting that 1 e4 e5 2 Ba6? or 1 a4 win for white, that 1 d4 loses for white, refuses to accept that an endgame with opposite colored bishops is a draw
Keeps refusing to incorporate knowledge into the game solving, though Connect Four has been solved with knowledge: 9 rules.

"Maratiggan" ++ Keeps trolling with the 50-moves rule and other artificial constructs

"Mpaetz" ++ Has not stated anything on that matter as far as I remember

"Optimiseed" ++ Just expresses his liking for a magical evaluation algorithm instead of calculation and then divinely jumps to 5 million years out of nowhere

"Pfren, BlueEmu" ++ Have not stated anything on that matter as far as I remember,
only some emotional opinion no it cannot be done,
presumably out of dislike of the possible solution of the beloved game.
It is like "Never shall I be beaten by a machine!", Kasparov 1989

I am the only one who presents facts and figures,
and I back these up with peer-reviewed literature.

No, you don't.  Your top down and bottom up proofs have no such backup.  Your Alpha Zero paper is addressing a completely different topic:

Assessing Game Balance with AlphaZero:  Exploring Alternative Rule Sets in Chess

...and you are cherry picking something you need for your pet theory from it, which is not its intended purpose, and ergo there is no particular rigor in those results..  This is a paper mostly for pushing for Kramnik's pet idea of removing castling from chess .

@5399
"which is not its intended purpose"
++ That is right, it is not its intended purpose.
However, I am free to use any available data for any other purpose than intended.
The other paper https://arxiv.org/abs/2111.09259 is not intended to select the 4 best moves 1 e4, 1 d4, 1 c4, 1 Nf3 and dismiss the worse 16 in weakly solving chess.
The Tromp and Gourion papers are not intended to provide starting points 10^44, 10^37 to estimate the number of relevant positions to weakly solve chess.
The solutions of Checkers, Losing Chess, Connect Four are not intended to derive conclusions about weakly solving Chess.
ICCF (grand)masters do not play a World Championship to provide data on optimal play.
The only paper with such intent is
https://www.sciencedirect.com/science/article/pii/S0004370201001527 

Someone is oblivious to the difference between DEDUCTION and EXTRAPOLATION.

@5401

"Someone is oblivious to the difference between DEDUCTION and EXTRAPOLATION."
++ I can use deduction, induction, extrapolation or whatever to logically arive at the estimate that the table base exact move in a 32 to 7 men position is within the top 4 engine moves with the 10^9 nodes / s engine running for 17 s with an error of 1 in 10^20 positions.
You can verify: run a desktop for 4.7 h on a KRPP vs. KRP endgame and see for yourself.

You can use whatever method you like. Tea leaves, Tarot cards, Astrology, whatever. It's a free Internet

However, most people know that extrapolation does not provide certainty and NEVER provides proof. Indeed, it is not only not 100% reliable, it is typically LESS reliable than other methods of APPROXIMATE statistical inference.

Why extrapolation is unreliable

@5403

"You can use whatever method you like. Tea leaves, Tarot cards, Astrology, whatever."
++ Ramanujan said the Goddess Namagiri Thayar revealed him mathematical theorems.

"extrapolation does not provide certainty" ++ It does not need to be exact.
1 error in 10^20 positions or 10^19 or 10^21 does not matter. Approximate is enough.

"NEVER provides proof"
++ Proof is evidence that compels the mind to accept a fact or truth.
To my mind it compels to accept that 4 candidate moves are good.
Carlsen said he considers 3 candidate moves.

"it is typically LESS reliable than other methods of APPROXIMATE statistical inference."
++ Instead of taking data published in a peer-reviewed journal by scientific authors,
I could have ran some autoplay games myself on a desktop and then reported the results.
That would be LESS reliable in my opinion.