Chess will never be solved, here's why

No it's not 10^44.5, in the game that @tygxc is now proposing to solve, if you don't have a procedure for solving that eliminates the problem of repetitions. (His game includes the 3-fold repetition rule.)

Each way of reaching a position gives you a different set of positions with the same material that, if you're to mate,  you must thread a way through to avoid a draw by repetition. Different mates for different ways of reaching the position. Some ways eliminate the mate altogether.

The correct description of a position is a PGN, not a FEN. Even the PGN is slightly deficient, but, apart from the slight deficiency, a PGN from the last ply count 0 position is sufficient.

With @tygxc's currently defined game and procedure the number is HUGELY greater than 10^44.5.  

That's one of the reasons the Syzygy tablebases provide only a weak solution of chess under competition rules. You can't start playing an endgame and expect Syzygy to bail you out if you get into difficulties and haven't followed his advice from ply count 0.

If it weren't for the fact that @tygxc has dropped the idea of including the 50 move rule, the number would be a hundred times HUGELY greater than 10^44.5. Winning positions with a ply count of 99 under the 50 move rule are actually very rare (but get less rare for positions with the same diagrams but smaller ply counts).

Tromp's figures apply to the basic rules game ONLY.

@Elroch

The same would seem to apply to the "competition rules" version of checkers, which is another reason that makes me uncomfortable about the reported solution, in the absence of further info, given that Chinook seems designed to play the "competition rules" version. 

The numbers describing the state space don't seem to be correct for a forward search - but I still have to work out whether the Kishimoto - Müller algorithm in Chinook completely solves the problem. A description of that, at least, is available.

Can you stop quoting that please?

It's Shannon's approximation of the number of 40 move games with an average of 30 moves per ply, Nothing at all to do with the number of legal games.

It's misinterpreted all over the internet (and obvious b*llocks).

Bad enough with @tygxc trying to swamp the internet with the fact that there are 10^2 legal chess positions.

Yes, good point that hadn't sprung to my mind.

The number of legal games (say until mate, statemate or some repetition rule) is absurdly large with any ruleset, most ridiculously with basic rules. In that scenario with nothing like the 50 move rule, consider where you are in one of the equivalence classes of positions defined by the existence of a legal path in either direction between them. It is legal to traverse the entire set of positions before moving on to a new equivalence class, only restricted by some sort of automatic drawing repetition rule (unlike the ones where the draw needs to be claimed, when the number of game is clearly infinite). There can be a ridiculous number of positions in an equivlance class. Eg with some pawn configuration and a set of other pieces, the pieces can reshuffle themselves into any legal configuration they can reach. A game typically consists of passing through up to a hundred or two equivalence classes (pawn moves and all captures always move between equivalence classes).

Though this is of purely abstract interest, the exact drawing repetition rule might affect whether it was possible to visit every position in an equivalence class (a bit like a multipiece version of the knight's tour problem.  An equivalence class of positions has a directed graph whose directed edges are legal moves leading between two nodes which are legal positions.  It is not necessarily possible to navigate such a directed graph without visiting the same node 2 or more times (the exact possibilities that can occur in chess would require some investigation).

For example for the equivalence class with just two kings there are somewhat less than 8000 legal positions (determined by the locations of the kings and which player is to move). The number of edges from a node is the number of legal moves, and the number of edges to a node is the number of legal moves leading to the positions (or the number of legal reverse moves).

I hypothesise there is a legal sequence visiting every legal position (with just two kings) once (like in the even simpler knight's tour problem). [Exercise for reader: prove this hypothesis ]

Anyhow, the number of legal chess games even if you use a 50 move rule is absurdly large. Way more than 10^N where N is the longest legal game.

Depends, I think , how abstract "abstract" is.

Here is the first game I played against the version of Rybka I downloaded to replace the version with an "e" on the end that, unlike current SFs, could handle 50 move deep KNNKP endings without a tablebase (on 20 year old kit).

(A bit disappointed I was - even GNU chess could do those on 20 year old kit.)

But if you look closer, it actually forces me to take its bishop on move 49, which is obviously an effect of the 50 move rule.

If you look a bit closer still it seems to be avoiding even single repetitions, so it's interesting to speculate what would have happened under current basic rules if the 50 move rule handling had been disabled in Rybka.

My guess is that after exhausting almost all its variations in the h8 corner its repetition avoidence algorithm would force it to eject me from the corner, probably towards a8 and it would then mate me about 20 moves later.

But there is also the possibility that it would paint itself into a corner (and me into the h8 corner) and draw under the triple repetition rule.

Both possibilities very similar to possible attempts at the knight tour.

I've met similar situations with SF8 in KNNKP.

It has been solved before bozo 🤡🚬

I continue to maintain that the repetition rule and the 50 move rule are sidelines compared with issues like whether forced checkmate is available in a game. 
And very analagous to whatever time controls are used in a game ...
as example:  somebody might assert (we see it periodically here) that the game is a draw with best play by both sides -
but that can be Instantly Disproven ...  somebody's flag falls on their clock and its called and even though 'mistakes' are not found in the move selection by either side - 
the game is in fact Not a draw. 
Somebody has won and somebody has lost.  Yes - insufficient material could be called too - for draw - but that exception does not invalidate the fact that best play does Not always lead to a draw.
Far from it.

When you have a position in front of you for solving or tablebase purposes - is it necessary to make it 100 positions according to how many ply of the 50 moves are left to win within that rule?
Or should it be regarded as one position ?
I've commented on that before.
But there's new ways to comment about that.

Attention does have to be given as to whose move it is - whether en passant is available - and whether castling rights are still there.
Note - isn't it kind of strange to ignore castling rights issues - or arbitrate castling as illegal while attaching importance to the 50 move rule?
Looks quite arbitrary.

But anyway - I've got better ways to resolve that 50 move stuff -
not stated yet.  

Is it necessary to consider a position as potentially two positions because of whether there has been no - or one repetition of position already?
Arguing that the theory of play must be different since a player might  then draw by looking to force another repetition?
Or should that be regarded as just one position?
Again - there's ways to put that in perspective.

And I've said before that @MARattigan makes the best posts here.
I believe that continues to be true.
But there's perhaps only one person here (not I) who as usual will then in his deluded way assert that that implies some kind of 'superiority' or 'deference'.  He's obsessed with his imagery about same.

Regarding the idea that the number of moves elapsed in the 50 move rule or repetition rule - might affect strategy and therefore solution of a position ...  isn't invalid.
Perhaps progress will be made if and when its established that nobody has an argument to prove to the contrary.  
But there are still arguments to indicate that those considerations are sidelines.
For example:  if you've got a 50 move count going - doesn't that mean that the position to kick off the 50 at the beginning of the count - is Known?  Or should be? 
Couldn't that mean that the main issue is to solve that position?
This connects up with the definition of solving as to whether its binary A or B or not - as in several outcomes of 'solving' instead.
I suggest the 'several outcomes' is more valid.
Meaning that solving a position means making a report on its issues.
Not just whether checkmate is available or not.

Similiar with repetition of position.
What position is being repeated ?
Could/should the computer report on every single position in chess
that "well we could have had this position before - so therefore we have to regard every position as two positions - on that."
See how ridiculous that gets ?
How about a position with only black's knight at c6 as off its original square ?
Is that legal?  Sure it is !
1) Nf3 Nc6 2) Ng1.  And there you are.
So now black plays Nb8.   !!!
The computer must now regard the opening position as 'two positions' because there might already have been two-fold repetition ??

#2296
"I accept your premise that this position is not the solution to chess."
++ It goes further than that.
All proof games of all 538 positions Tromp found legal have an accuracy near 0%. That means that the vast majority of Tromp's 10^44 legal positions form no part of the solution of chess.

The real number of sensible and legal positions lies between 10^38 and 10^32.
That would be the number needed to investigate for strongly solving chess.
For weakly solving chess a far smaller number of relevant, reachable, sensible and legal positions need investigating.

#2291

"(i) If you add moves and/or change the move order some people might say that changes something by definition." ++ But the accuracy stays near 0%.

"(ii) You don't prove the accuracy is near 0." ++ I leave that for you to verify.

(iii) You don't prove if you add some moves and/or change the move order, the accuracy stays near 0%. ++ Just try and see for yourself.

"I'm sure as the World's strongest grandmaster it won't take you long."
++ I am no grandmaster, I never said that.

"For weakly solving chess a far smaller number of relevant, reachable, sensible and legal positions need investigating."
But arbitrary capricious invalid ways of dismissing positions are met with disagreement.
And self-convictions of 'knowing more' without any quality of knowledge are not going to 'vindicate Sveshnikov' except in the imagination.
And - is that even the real goal ?

There was a very great scientist - Sigmund Freud - who argued for the existence of 'the unconcious mind'.
A mind in which we don't always know - what is going on.
And never know - completely what is going on in it.
A mind that often controls - determines - decides.
But many deny this.  
And many might misinterpret the greatness of scientists like Freud and Einstein - feeling that they're 'personally greater'.  'Superior'.
Hitler felt he was 'superior'.  Didn't work out so well.
There's a school of thought that says no person is 'greater' than another - unless one chooses to have it that way.

I doubt very much that the 'real agenda' is to vindicate Sveshnikov.
Something very different going on here.   
Perhaps - whoever should instead concentrate on his feelings of 'knowing more'.

Paradox in chess (abounds) and in 'solving' chess (also abounds).
I've suggested that the 50 move rule and repetition rule are sidelines compared to the issue of whether forced checkmate is available or not.
I went into that a few posts ago.
But that in turn does not mean that that higher issue of whether forced checkmate is available or not - is a binary A or B be-all or end-all of the business of 'solving' chess.
Or thee end-all of same.  It might appear to be.  But it isn't.
There's too many significantly different outcomes to positions.
Especially when the limitations of today's computers are factored in.

#2289

"Both those numbers (10⁹ and 10⁷) were referred to the proof size, not the number of nodes searched and I think you know it well now as before."
++ No, I did not know. From the first paper I interpreted 10^9 of 10^18 searched i.e. exactly the square root. The second, later paper says 10^7 nodes in the proof tree and each node needing 10^7 positions.

"And is it impossible that's not enough to make it understandable, not only to the less gifted?"
++ I patiently try, but some seem unable or unwilling to understand.
I explained x times why there are less relevant, reachable, sensible, and legal positions than legal positions, but the erroneous 10^44 keeps turning up.
I explained x times why weakly solving chess needs less positions than strongly solving chess, but people keep sticking to millions of years based on strongly solving chess.

"You stil put many things together, as if they were questionable the same."
++ I have been called crackpot, autist, narcissist, liar... I have been said to understand nothing about mathematics, nothing about computers, to have zero credibility... People put forward utter nonsense and call that refuting or debunking...

"You simply do not accept that basically all the others may have the same opinion about your theories" ++ I am outnumbered, that does not make me wrong.

"you exclude the possibility that your reasoning may be impossible to understand for anyone."
++ I may be not that good at making myself understood.

"I have been outplayed at chess by people who had far less scientific education"
++ I believe that. At a certain point our national champion was a butcher.

"You really think you "beat" all the others here at science, which is about objectivity"
++ I know about my own scientific background and as for the others I infer it from what they write.

"And for sure I do not see this thread as a contest; you do"
++ No, I do not at all. I find it a fascinating subject and I like to think and write about it. Some others make it a contest and even boast they are top debaters. I certainly am not.

"you behave like an unscrupulous lawyer: first the win, then the truth."
++ No, not at all. I do not sling insults. I do not troll. I do not accuse. I do not gang up "well said XYZ"

"you think you can use your supposedly better than ours evaluation function, to understand how much of the search space can be cut down"
++ No, I do not have any better evaluation function, I do not believe in evaluation functions, only in deep calculation. I do however advocate common sense and heuristics.

"preventing any further search in that excluded part, in order to speed up the process."
++ Yes: no need to investigate 1 a4, or 1 e4 e5 2 Ba6, or 1 e4 c5 after 1 e4 e5 is already proven to draw.

"AFAIK no one out there (not only in this thread) supports your approach, because it is fallacious by faulty generalization." ++ It is schocking that people see a need to investigate 1 a4, or 1 e4 e5 2 Ba6, or 1 e4 c5 after 1 e4 e5 is already proven to draw. Are you one of those?

#2293

"Apparently you don't understand how computers work."
++ It has been a long time since I have programmed any computer. In 1978 I wrote a chess program in Fortran 4 with Hollerith punch cards and ran it on a Siemens 4004 mainframe.

"If you give the system a set of rules to apply to "eliminate" non-sensible positions, the act of evaluating each position and checking the criteria you have set is a significant portion of the effort you think that you are avoiding."
++ No, I do not give any rule to eliminate non-sensible positions. The illegal, non-sensible, non reachable, non relevant positions just do not turn up during weakly soving chess.   

"Whether you pre-parse all this and de-couple it from the actual evaluation of the sensible positions make little difference"
++ No, I do not pre-parse or parse I do not even evaluate, I only calculate from the 26-men tabiya towards the 7-men endgame table base.

"10^44.5 unique positions"
++ 10^44 legal positions, far less sensible (10^38 - 10^32), far less reachable (10^18), 10x less relevant (10^17)

"you are left evaluating unique positions, not valid game paths"
++ No, I follow relatively few valid game paths and visit unique positions all automatically legal, sensible, reachable, and relevant and retrieve the absolute evaluation draw / win / loss from the table base. I do not visit positions because they are legal, sensible, reachable and relevant, on the contrary: they are legal, sensible, reachable, and relevant because they are visited during weakly solving. The few game paths are just lines from the 26-men tabiya towards the 7-men endgame table base that connect the visited nodes.

I am not really concerned if you don't like the Shannon Number.  Unlike, say, Kasparov's purported 180+ IQ, the Shannon Number was the accepted estimate for decades.  So listing the progression from 10^120 to 10^44.5 followed by the bogus cuts to 10^36 and 10^17 holds up well, because that's exactly how this has progressed historically .

That's not weakly solving chess.  That's just GIGO.

Lots of claims - while avoiding the issues of computer speeds -
sidestepping with 'nodes per second' - still not grasping about the subjectivity of 'reasonableness of moves' while mathematics demands objectivity plus quality of reasoning - not 'know more'.
The two of them could talk to each other - in theory.
But about 'feelings of superiority' as subject.  Identify with each other.
Get in touch with 'the inner self'.  Use what they have in common.

woah cant believe this is still on

Hi !  Welcome to the forum !
Do you have a theory as to what the 'finale' might look like ?
Scenarios ?   
As to what the 'end of discussion' would look like in the forum?
The subject of 'solving' chess connects up with regular chess much more than people might think.
There's over 50,000 tactics puzzles on the website.
That's right.  50,,000 plus.  Each with its own discussion forum.  Yes !
Millions of members.  Trying to 'solve'.
Many millions (hundreds of millions - probably billions now) of attempts on the puzzles - each player trying to 'solve'.  'Solving' and 'how to solve' being central issues.
There's a lot of 'solve' in chess.  Its like - a commodity.  Or privilege.

uh no i just came in as i still follow this thread but i am not going to be involved

Quoting for posterity.