Chess will never be solved, here's why

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Avatar of Optimissed

^ gibberish.

Avatar of DiogenesDue
MARattigan wrote:

I think you're still missing a point.

If the game to be solved is basic rules chess then the following algorithm secures a draw for White from the position shown and it's easy to prove  that each the draw is secured whatever moves Black plays. This wouldn't however be regarded as a solution by most people involved in the thread.

White's algorithm: Move the rook to whichever of g8 or h8 is not occupied.

 

An ideal game under your definition could be

2n-1. Rh8 Kd2

2n.    Rg8 Kd3

but in this particular position, if White follows the algorithm any game would necessarily be ideal game under your definition. It's easy to prove (I'll provide a proof if you insist) that each move in the above game is optimal for the player making it.

I would say the aim is rather to produce a game in which play by both sides is perfect as I defined it in #147 here https://www.chess.com/forum/view/general/chess-will-never-be-solved-heres-why?page=8 with proof that each move is optimal for the player making it.

Under competition rules your definition would be OK, but I think most people would understand OP's statement to be about the basic game.

I didn't actually say anything about repetition at all, but yes, it doesn't take proverbial rocket science to understand that any "solution" for a given chess position must discard repetitions after some set of criteria are met, or the analysis cannot proceed and runs forever.

Any entry level programmer that can hold down a job would understand this.

Avatar of DiogenesDue
Optimissed wrote:
MARattigan wrote:

@Elroch

Yes, I should have said basic rules with the starting position in art 2.2 and the starting material in 2.1 amended to the position shown. It was just to illustrate @btickler's definition of "solved" was incomplete. 

I wanted to do it from the starting position, but I'm still waiting for @tygxc to finish his project.

Obviously his definition of almost anything will be incomplete. For Heaven's sake, you're trying to do some vaguely cutting edge thinking here, so how does that square with referring to a definition that's put forward by, well, maybe you should insert the relevant words and see where it leads

You're both wrong wink.png.

It's not my definition at all.  It's *the* definition of weakly solving *any* game.  I would have the thought the link and the italics would make this blindingly obvious.  

P.S. It's always amusing when Opti bumbles into a mistake while disparaging others' intelligence..

Avatar of playerafar

For some - any assertion of independent thought - or disagreement  from somebody else...  is seen as an 'impertinence' or 'inflated assertion'.  
Or in some cases - is Resented intensely ...    happy.png

Avatar of MARattigan

@btickler

Yes it was blindingly obvious. I would have thought my response to @Optimissed in post #481 would have made that blindingly obvious.

I would say it's the definition of weakly solving a finite game, which basic rules chess is not.

Would you say my example in #467 weakly solves that position under basic rules? It is precisely what is asked for in your definition.

Avatar of playerafar

'The' definition of 'weakly' could be amended to 'a' definition.
Even if its arguably a 'superior' definition. 
There might be quite a range of possible such definitions. 

Avatar of MARattigan

@btickler

"P.S. It's always amusing when Opti bumbles into a mistake while disparaging others' intelligence.."

I never take any notice. Hardly going to be worried by the opinion of a man who, on the strength of scraping a third in philosophy from Royston Vasey polytechnik, feels qualified to denigrate the mental powers of various fellows of the Royal Society, Isaac Newton, Albert Einstein et al. An honour to join their company really.

 

Avatar of DiogenesDue
MARattigan wrote:

@btickler

Yes it was blindingly obvious. I would have thought my response to @Optimissed in post #481 would have made that blindingly obvious.

I would say it's the definition of weakly solving a finite game game, which basic rules chess is not.

Would you say my example in #467 weakly solves that position under basic rules? It is precisely what is asked for in your definition.

Yes, you need a (I won't say "the" because there's more than one way to skin that cat) set of repetition rules to make chess into a finite game in order to solve a position going forward.

Much in the same way that Rock-Paper-Scissors has the "1-2-3" motion...if it didn't, one player could just never make his move and a game that is not really able to be "drawn" would have no outcome.

The overall definition of a weakly solved game would not lay out such things for chess specifically, but the parameters of the definition are still good.

In terms of a forced win and the building of tablebases, instances of infinite repetition will obviously not show up when working backwards from any mate.  That part of chess *is* solved wink.png ...if moves are repeated endlessly, the game is essentially drawn as mate cannot result.

The "blindingly obvious" comment was less directed your way than the other, FWIW.

 

Avatar of Optimissed
btickler wrote:
Optimissed wrote:
MARattigan wrote:

@Elroch

Yes, I should have said basic rules with the starting position in art 2.2 and the starting material in 2.1 amended to the position shown. It was just to illustrate @btickler's definition of "solved" was incomplete. 

I wanted to do it from the starting position, but I'm still waiting for @tygxc to finish his project.

Obviously his definition of almost anything will be incomplete. For Heaven's sake, you're trying to do some vaguely cutting edge thinking here, so how does that square with referring to a definition that's put forward by, well, maybe you should insert the relevant words and see where it leads

You're both wrong .

It's not my definition at all.  It's *the* definition of weakly solving *any* game.  I would have the thought the link and the italics would make this blindingly obvious.  

P.S. It's always amusing when Opti bumbles into a mistake while disparaging others' intelligence..

That's lack of comprehension. I did not say "btickler made that definition". Nowhere did I say that. If Elroch did, he may have been implying that you quoted it. All I did was suggest that any definition made or forwarded by you should be suspect and therefore, if you made that definition, it should be treated carefully. You aren't very intelligent and you constantly make that very clear to very many but not to all.

Avatar of Optimissed

You talk also of "weakly or strongly solved" and yet you seem oblivious to the fact that an assumption that chess is drawn with best play may be considered to be a viable, weak solution. It's weak because there isn't a deductive proof but it's my contention that a deductive proof will never be available and therefore, we have to make the best out of the evidence we do have. If we're troubled by indecision, regarding how strong a solution we can obtain, I don't believe there is ever going to be an end to that torment.

Personally, I think that no-one will ever prove that chess isn't a draw with best play. That's whatever the arguments happen to be and may be forwarded by others, because by now, it seems clear that there are no potentially good arguments available to the effect that chess is going to be "solved", any more than we've solved it already. I fully agree with the spirit of the Original Post in this thread and was trying to help the slower intellects among you catch up. But you can worry all you like about what the lack of deductive proof implies and whether you ought or ought not to think that chess is a draw or may not be a draw. It isn't important what you or I or anybody thinks.
tongue.pngnervous.pnghappy.png

Avatar of MARattigan
Optimissed wrote:

You talk also of "weakly or strongly solved" and yet you seem oblivious to the fact that an assumption that chess is drawn with best play may be considered to be a viable, weak solution.

That, at any rate, was clearly included in his definition (and mine).

It's weak because there isn't a deductive proof ...

No, it's weak because it only guarantees the correct result from the starting position. Try understanding some of what is posted before replying to it.

If you can't understand, you can ask, and hopefully someone will attempt to make it clearer to you.

...

 

Avatar of DiogenesDue
Optimissed wrote:

You talk also of "weakly or strongly solved" and yet you seem oblivious to the fact that an assumption that chess is drawn with best play may be considered to be a viable, weak solution. It's weak because there isn't a deductive proof but it's my contention that a deductive proof will never be available and therefore, we have to make the best out of the evidence we do have. If we're troubled by indecision, regarding how strong a solution we can obtain, I don't believe there is ever going to be an end to that torment.

Personally, I think that no-one will ever prove that chess isn't a draw with best play. That's whatever the arguments happen to be and may be forwarded by others, because by now, it seems clear that there are no potentially good arguments available to the effect that chess is going to be "solved", any more than we've solved it already. I fully agree with the spirit of the Original Post in this thread and was trying to help the slower intellects among you catch up. But you can worry all you like about what the lack of deductive proof implies and whether you ought or ought not to think that chess is a draw or may not be a draw. It isn't important what you or I or anybody thinks.

"Weakly solved" in the context of games is not open to your interpretation.  It's already defined...and not nearly as fuzzily and vaguely as your notion of it.

You may have personally decided to dispense with the entire field of Thermodynamics wink.png...but you can't really dispense with the definition of weakly solved games on anyone else's behalf.

Avatar of DiogenesDue
Optimissed wrote:

That's lack of comprehension. I did not say "btickler made that definition". Nowhere did I say that. If Elroch did, he may have been implying that you quoted it. All I did was suggest that any definition made or forwarded by you should be suspect and therefore, if you made that definition, it should be treated carefully. You aren't very intelligent and you constantly make that very clear to very many but not to all.

As I have said in the past..."show, don't tell".  Saying that you consider me "not very intelligent" doesn't really have any meaning as a standalone observation, does it?  I could say the same of you, but what would it mean?  It would probably mean that I have no other way to try and hold my own in an argument I am losing.

P.S. Your excuse would fly better if you had said "the definition he linked" or something to that effect, rather than "his definition", which implies...well, exactly that...that it's my own definition.

Avatar of playerafar

'Somebody' here needs to be constantly intensely personal here because of some factor or factors at his end that probably have little or nothing to do with the other members here.
But he can be posted around - among other things.

Avatar of playerafar

Regarding 'having a repetition rule' and '50 rule' and including them in the solving - or not ...  is actually somewhat muddled if its to be just A or B.
But there's also just C.  
In other words disallow repetitions.  Have none in the solving at all.
There's repetitions as a toggle of two moves but only tablebase a position if its unique on the board is my suggestion.  
But for 50 moves - discard that and instead - count all unique positions - its necessary because they can lead to other unique positions among other things.  

Point - anytime a position isn't immediately 'totally solved' in an extremely short time it just gets referred instantly to another computer.
The number of positions handled increases - until all possible positions have been accounted for.  With some unsolved for the time being.
Do what's easy first - is the idea suggested.  
This approach can also be used with castling and en passant possible.  If its very quickly 'solved' with all legal continuations factored - then some might go in the completed pile whether with whatever castling or en passant possible or not and some to the other computer.  

Previous 'game' possibilities are not taken into account by the first computer - including 'could you have gotten there legally?'  That's something that's handled by maybe a third computer.  It works on the number of positions that are legal but 'couldn't have got there'.   
By the way - sometimes illegal moves are made.  But if they're not called right away and past legality restored - the game goes on !   I mean that !  

Another point:
All positions can't even be accounted for - let alone 'solved' - until the actual number of unique positions has been determined.  
Upper bounds aren't satisfactory. 
But they can be measured against - to chart progress.

And - the thread topic is actually invalidly put - but that's okay. 
More accurate would be 'Nobody knows' if chess will ever be solved.  
(Including if society will even be around that long.) 
This is an expression of the upper bound on possible chess positions - with no addition nor subtraction in it ...
updated:  64 x 60 x (62!/32!) x (11 to the 30th power)
(accounts for 64 squares)
Its been stated here there's been 'work' done to cut that down substantially - and how but apparently not with the expressions thoroughly set out here.  Just a power of 10 'result'.  

Avatar of tygxc

#508
It is 3.8521 * 10^37
https://arxiv.org/pdf/2112.09386.pdf 

Avatar of playerafar
tygxc wrote:

#508
It is 3.8521 * 10^37
https://arxiv.org/pdf/2112.09386.pdf 

@ ty
'It' is not that ...
At the very outset of your document- 'promotion' is rejected.
And is it saying that 'captures' are rejected too?
If so - then its not much use as an upper bound because the true number of possible positions is of so many orders of magnitude Higher ...

"The number of legal chess diagrams without promotion is bounded from above by 2×1040.
This number is obtained by restricting both bishops and pawns position and

by a precise bound when no chessman has been captured."

Its got two illegitimate restrictions regarding promotions and captures.

A true mathematical upper bound would have 31 terms in it - with '1' at each end.  (all pieces captured and at the other end - no moves made) ...
One computer could work from the left (simple endgame 'tablebases') and the other from the right (itemizing all legal continuations - but having much more difficulty 'solving' - in fact it wouldn't solve unless that can be done in nanoseconds) - it would refer legal unsolved to a third computer - legal instantly 'solved' (like 'checkmate' for example) to a fourth computer - illegals to a fifth   ... they could refer 'difficults' to a sixth and seventh computer.
In theory - would computers 1 and 2 'link up' ?
Why not? 
The proof is that its been happening since the game was developed.  happy.png
In practice - some of that 'linkage' already has been going on even without computers ...  opening positions leading to minimal material 'solved' endgames.  Even in the opening post it seems to be alluded to.

Avatar of playerafar

So:
 64 x 60 x (62!/32!) x (11 to the 30th power)  (new and improved)
now stands as 'upper bound' of possible chess positions until a properly presented lesser upper bound is posted.
Regarding the expression in blue -
its predecessor is simply 13 to the 64th power. 
13 possible states of each square.

Yes - obviously the blue expression can be reduced by bishops restricted to 32 squares and pawns restricted to 48 squares ... and pawns restricted to 16 max and to 8 and 8 by color.  
that 16-max pawn restriction is going to be simpler than the other two pawn restrictions I believe - it could possibly be done while keeping the general expression 'pure' for now with no addition and subtraction ? 
Not sure.  Yet.  
But maybe the 16-max for pawns can be factored in like the 64 x 60 for the two Kings.

Avatar of tygxc

Excess promotions are excluded in the count 3.8521*10^37 indeed.

An earlier estimate was higher, but the vast majority of those positions contains multiple excess promotions, often even underpromotions, multiple same color bishops on one side and other nonsense.

Some positions with 4 queens make sense.
However the upper bound 3.8521*10^37 contains many non sensible positions too, with quadradrupled pawns etc.

So 3.8521*10^37 is a good estimate for the legal positions even with like 4 queens.

Avatar of playerafar
tygxc
 
 
 0 
#512

Excess promotions are excluded in the count 3.8521*10^37 indeed.


but so are captures right?  Neither exclusion is legitimate.
'Subjective solving' isn't good enough.
If this is to be done - better its done right.