Chess Will Never Be Solved. Why?

There are approximately 4.82 x 10^44 basic rules legal positions (FEN - ply count).

You say you plan to solve chess under competition rules.

In that case there there are approximately 7.27 x 10^46 FENs associated with game states (Tromp's number for basic rules must be multiplied by the 151 different values of play count that may be associated with positions that don't exceed the mandatory 75 move rule).

There IS NOT a well defined relation 'FEN B can result from FEN A' under competition rules.

FEN A will be associated with many different situations that can occur in a chess game depending on how the situation is arrived at.

If it's associated with a situation that has been arrived at via four previous situations that match the associated basic rules position then no FEN B can result because the game immediately terminates under the mandatory quintuple repetition rule. 

If the same FEN A is associated with a situation that is not so arrived at then it will result in situations with different FEN Bs. But for each such FEN B not all situations having FEN B can be arrived at, because the moves leading to those situations may not be extensions of the moves leading to the situation which is associated with FEN A. 

I would call the "situations" I talk about "positions" in the competition rules game (and my interpretation of the FIDE laws is that the two are in general taken to mean the same). You would not, but in that case you cannot Identify positions with the nodes in your search space. It's the number of such nodes that is important in determining the feasibility of a solution based on a forward search. Rather than quibble over the meaning of "position" I'll just refer to nodes (no doubt much to @playerafar's disgust).

If the nodes are defined as a FEN together with the set of basic rules positions that have occurred since and including the last node associated with a ply count 0 FEN and a multiplicity (1-4) for each node, then there IS a well defined relation 'node B can result from node A' under competition rules. This relation defines the game tree (an abuse of language, it's actually a directed graph) and the solution.

The number of nodes in the game tree is therefore the number of equivalence classes of legal PGNs from a ply count 0 position, where PGNs are taken to be equivalent if they result in the same associated basic rules positions each with the same multiplicity and have the same final basic rules position. (The PGNs are also what you need to pass to an engine over the UCI interface if is to function correctly - assuming it's capable of avoiding triple repetitions when it thinks it's winning.)

It's apparent that the number of nodes in the search space under competition rules is vastly hugely humongously greater than 7.27 x 10^46. There is an obvious upper bound of 4.82 x 10^44 x 3^(4.82 x 10^44) but it's very easy to reduce this very substantially by summing over endgame classifications and some further considerations. I did invite you to propose a reduced upper bound with no response. Do I need to do it for you? (Notice nodes beyond the 50 move rule and triple repetition rules are excluded from that upper bound because continuations when these conditions occur can be pruned. Also no factor is included for the ply count because that is the sum of the repetition counts so already accounded for.)

So solving chess obviously depends on the version of chess, The game tree determines the solution and the game trees are different under basic rules and competition rules. In particular your known 7 man draws are different, so you're aiming for different destinations in the two games.

Also the position you posted in #296 is a draw under competition rules, so you should have included a 50 move rule draw under your termination conditions, not to mention a dead position.

But your description is naff to start off with. I can give you any number of paths towards either of the things you mention. If that's all you want to do what are the supercomputers about?

     More than one person immediately pointed out your error but you blew us off with "I can't be bothered to actually look at the posts", or "you guys are all just trolls" or other such crap and now complain that nobody explained things to you. Any time anyone does explain something to you you engage in slurs, off-the-subject rants, incoherent babble and repetition of things you have already said 100 times.

     To quote Toshiro Mifune in Akira Kurosawa's classic film "Yojimbo", "You can't help fools."

     Thank-you for admitting you have no answer to the previous post.

#347

"You say you plan to solve chess under competition rules."
++ The 50 moves rule 9.3 is never invoked in practice in positions > 7 men.

"positions that don't exceed the mandatory 75 move rule"
++ The 75 moves rule 9.6.2 is also a competition rule and is never invoked in practice in positions > 7 men.

"There IS NOT a well defined relation 'FEN B can result from FEN A' under competition rules."
++ A FEN is a FEN, regardless of competition rules.
The 50 moves rule 9.3 is in practice never invoked in positions > 7 men.
The 3-fold repetition rule 9.2.1 says the game is a draw when 3 FEN are the same.

"FEN A will be associated with many different situations that can occur in a chess game depending on how the situation is arrived at."
++ No, each FEN has one game-theoretic value: either draw, win, or loss.

"the game immediately terminates under the mandatory quintuple repetition rule."
++ The 5-fold repetition rule 9.6.1 is just like the 3-fold repetition rule 9.2.1 a competition rule.
For the purpose of solving chess both can be simplified to a 2-fold repetition rule.
If optimal play is to repeat 2x, then optimal play is to repeat 3x, or 5x just the same.

"my interpretation of the FIDE laws is that the two are in general taken to mean the same"
++ FIDE Laws of Chess 9.2.2 are clear: the same position means the same FEN.

"you cannot Identify positions with the nodes in your search space"
++ No, a node is a position plus its evaluation and history.

"The number of nodes in the game tree is therefore the number of equivalence classes of legal PGNs from a ply count 0 position"
++ No, not at all. The number of nodes in the game tree is the number of legal, sensible, reachable, and relevant positions. There are 10^44 legal positions, about 10^32 sensible positions, about 10^19 reachable positions, and about 10^17 relevant positions.
A legal position is a position reachable from the initial position by a series of legal moves.
A sensible position is a legal position where said series of legal moves represents a game with > 50% accuracy.
A reachable position is a sensible position that can be reached from a given position by a series of legal moves. Each pawn move and each capture is irreversible and renders huge numbers of sensible positions unreachable.
A relevant position is a reachable position that is relevant to weakly solving chess.
* Positions of which the game-theoretic value is known are no longer relevant: they can be evaluated as their known game theoretic value and no longer be calculated.
E.g. 1 e4 e5 2 Ba6 is known to lose for white.
E.g. many endgames with opposite color bishops are known to be drawn.
* Positions that offer additional ways to draw are not relevant.
If 1 e4 e5 is a proven draw, then it is not relevant if 1 e4 c5 draws as well or not.
* Positions that can be discarded by logic are not relevant either. E.g. it is chess knowledge that 1 a4 is not superior to either 1 e4 or 1 d4. Thus the position after 1 a4 is not relevant.

"The PGNs are also what you need to pass to an engine over the UCI interface"
++ No, not at all. There are way too many PGN. The FEN plus its evaluation is the node. Whenever 2 FEN are the same, the evaluation of the node is a draw per simplified 9.2.1.

"It's apparent that the number of nodes in the search space under competition rules is vastly hugely humongously greater than 7.27 x 10^46."
++ No, it is not. As said only 10^17 positions are legal, sensible, reachable, and relevant.

"So solving chess obviously depends on the version of chess"
++ No, it does not. The 50 moves rule 9.3 plays no role in positions > 7 men. The 3-fold  repetition rule 9.2.1 is essential, but can be simplified to 2-fold: twice the same FEN = draw.

"In particular your known 7 man draws are different"
++ No, ICCF WC games draw despite 7-men table base win claims > 50 moves without capture or pawn move are allowed. It makes no difference in practice: such win claims do not occur.

"you should have included a 50 move rule draw under your termination conditions"
++ No, if chess is a draw without the 50-moves rule 9.3,
then chess is a draw with the 50-moves 9.3 rule just the same.

There are 2 ways to win a game of chess:
5.1.1 by checkmate,
5.1.2 by resignation.
In practice players resign when checkmate is inevitable even in the long term.
100% of ICCF WC wins are by resignation, 0% by checkmate.

There are 5 ways to draw a game of chess:
5.2.1 stalemate plays no role: like AlphaZero showed chess is a draw even if stalemate is a win
5.2.2 dead position plays no role in positions > 7 men.
5.2.3 agreement is the most frequent way of drawing: players agree on a draw when they both recognise it is the inevitable outcome even in the long term.
9.2.1 3-fold repetition is a major way of drawing and can be simplified to 2x repetition for the purpose of solving chess
9.3 the 50-move rule plays no role: it is never invoked in positions > 7 men and ICCF WC games end in draws despite the possibility to claim wins in 7-men positions that exceed 50 moves without pawn move or capture: such win claims are allowed, but do not happen.
In ICCF WC draws 74% is by agreement, 16% by 3-fold repetition and 10% by a 7-men table base draw claim, 0% by dead position, 0% by stalemate, 0% by the 50-moves rule.

"If that's all you want to do what are the supercomputers about?"
++ Weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition.
In practice this means:
proving that black always has at least one move that draws against all reasonable white moves.

And according to FIDE (Art. 1.2)

The objective of each player is to place the opponent’s king ‘under attack’ in such a way that the opponent has no legal move.

So 5.1.1 is the only way for a player to achieve his objective.

5.1.2 just gives each player a foolproof way of ensuring his opponent can't achieve his objective.

And "forfeit" is not referred to in the basic rules. If you arrange a friendly game with your cousin and he rings to say he can't make it because his mother in law is having trouble with her false teeth, the basic rules give no indication of the outcome in terms of win draw or loss (though obviously neither player will achieve his objective).

Under competition rules there is also a way for a player to lose that hasn't been mentioned, namely failing to complete a minimum number of moves or all moves in an allotted period of time including any additional amount of time with each move. (6.3.1+6.9)

In any normal game that would mean his opponent wins, but in FIDE chess, because they haven't bothered to set any order of precedence on events that may occur simultaneously, that doesn't necessarily apply; e.g. if a player resigns simultaneously with releasing a piece on a square that delivers checkmate, both players win; if a player accepts a draw offer simultaneously with the player who made the draw offer resigning he wins but the game is a draw.

It will never*** be analised because the number of probabilities to move is too large.

*** I can't proof that. For example, computers analisys of chess walks faster than human analysis and the word "never"  cannot be used as an absolute certainty. I am sure that computers and artificial inteligence will make things we can think about today.

We hope not.

@MARattigan
" Rather than quibble over the meaning of "position" I'll just refer to nodes (no doubt much to @playerafar's disgust). "
If you want to call a position a 'node' you're still not going to 'solve' a billion of them per second.
But I think you know that Martin.  The 'nodes' guy likes to just slide through by dancing around and avoiding or disorting the hardware speed of the computers.
In his latest fancy footwork I believe it was something like ...
'the nodes are contained within the entire set of chess positions'
while continuing to knock down the number of positions from a 45 digit number to an 18 digit one arbitrarily.
Government:  "We need 256 million new all-electric cars on the road"
'Nodes guy':  "No you don't.  You just take the square route of that number.
You only need 16,000 new electric cars"
"And we can produce them at 'nodes per second' so it'll only take 5 days.
Just give me the money to do it."

@tygxc

It's apparent from your post #354 that you haven't understood a single word of the post to which you are responding.

You make 14 points, so rather than produce a series of ever expanding posts I'll deal with them one at a time.

It's also apparent that you have extraordinary difficulty in assimilating information, because you have posted most of the errors in your response before and failed to correct them even though the errors have been pointed out to you.

All 14 of your points except (arguably) one contain errors, so I'll break each point down into words of one syllable and check with some simple questions after each has been dealt with whether you have understood. That way we can see what progress you have made.

@haiaku suggested in this thread that you post a pseudocode or javascript of your proposed process. It would be useful if you could do that before we start, then I can show how my answers relate to that. 

@CooloutAC
Some points:
1)  the white on grey above not working.  Maybe it looks like it does work because one is on a phone/tablet/ipad or using an 'app' or maybe using 'Mac' instead of windows.  Whatever.  Yes it was mentioned earlier too.
2)  @mpaetz is not a 'troll'.  Presents legitimate points.  Does not spam.  Does not namecall.
3)  You're right that chess and the problem of solving are 'mathematical'.
Just the upper bounds on the numbers of positions alone makes it mathematical.
So does the hardware speed of the computers that one of the persons spamming here constantly dances around.
Its a mathematical quantity that he wants to be ignored.
But he's spamming - as opposed to 'trolling'.
And Sveshnikov has very little to do with this.  den Herik not much either.
Just invoking their names or of other people with titles or credentials isn't an argument.

I'm just mentioning the spamming of same because I agree with you that the issues are mathematical.  Its a mathematical situation.
4)  Yes - be careful.  The "other guy" is known to report people for namecalling and get them muted.  While he himself tries to get away with namecalling and accusations of mental illness and obsessions with intelligence levels.  He often gets away with it.
But just be informed please that he has been muted in the past and has a history with the moderators here.  He will not have an 'aura of power' unless members and staff allow him to have one.
He is also known to get people blocked. 
And he actively 'projects' intensely.   
And intensely projects his projectionss.
The worst case of both I've seen anywhere. 
Its been very predictable too.

Good post.

Actually, you will find that there are anywhere from 10 followed by 43 zeros to 10 followed by 50 zeros, so even on the lower end there are 10 million million million million million million million million possible positions, and even if you could somehow make every single person on earth(We'll round up to 10 billion) a computer which can analyse(I'm Australian this is how I spell OK??) a million positions a second, it would still take10 followed by 27 zeros after it(an octillion) seconds, which is 31700000000000000000 years which is 2.2 billion times the age of the universe. So I'm not sure what computer you are using... OK bye

But @tygxc will dance around your valid post by saying 'nodes' and 'nodes per second' computers.  
Its a kind of computer equivalent of 'snake oil' remedies.

#364
"you will find that there are anywhere from 10 followed by 43 zeros to 10 followed by 50 zeros"
++ No, the number of legal positions is 10^44.
About 10^32 of these are sensible: can result from a game with > 50% accuracy.
About 10^19 of these are reachable: each pawn move and each capture is irreversible and renders huge numbers of positions unreachable.
About 10^17 of these is relevant.
So 3 cloud engines of 10^9 nodes/s can weakly solve chess in 5 years, like Sveshnikov predicted.
3 engines * 5 a * 365.25 d/a * 24 h/d * 3600 s/h * 10^9 nodes/s/engine = 4.7*10^17 nodes

Wow

And capturing the queen here renders all positions unreachable

So we can actually say the number of positions in chess is 0. (That should make it possible.)

Somebody proclaiming that he knows in advance what portion of positions are unreachable or unreasonable or irrelevant ...
its spam - but it can be responded to and also posted around in such a way that the real conversation is had.
The most damaged thing in the conversations is the hardware speed of the computers.

Programmer to computer:  'What is the speed of your hardware?  How many basic operations can you do a second?"
Computer:  'Here's the figure.  It doesn't vary.  That's the Maximum and Minimum too.'
Programmer:  ' Well I don't want you to ever use that figure.  It will damage our project and our funding and our Public Image ! 
You will use 'nodes per second' from now on and if somebody asks you what your actual clock speed is you will refer him or her to me.'
Computer:  ' But but - what if they use programmer Override ?'
Programmer:   ' I don't want to hear your Lip Computer !
And I Don't Care what your actual speed is !  Understand ??
And I don't care means We Don't Care.  Got it ?'
Computer:  'Got it boss.'
Boss: ' Good.  And if you're good in the future we'll fix you up with cooler air conditioning and we'll juice up your electricy supply with your favorite computer music. '

#368
"And capturing the queen here renders all positions unreachable"
++ Yes, capturing the queen ends the game and renders all positions unreachable. 

"So we can actually say the number of positions in chess is 0. (That should make it possible.)"
++ No, that is an erroneous conclusion of you.
1 e4 makes all positions with a white pawn on e2 unreachable.
1 e4 c5 makes all positions with a black pawn on c7 unreachable.
1 e4 c5 2 Nf3 Nc6 changes nothing.
1 e4 c5 2 Nf3 Nc6 3 d4 makes all positions with a white pawn on d2 unreachable.
1 e4 c5 2 Nf3 Nc6 3 d4 cxd4 makes all 32-men positions unreachable, more precicely all positions with 8 white pawns.
1 e4 c5 2 Nf3 Nc6 3 d4 cxd4 4 Nxd4 makes all 31-men positions unreachable, more precicely all positions with 8 black pawns.
That is how the number of 10^32 sensible positions dwindles fast and leads to about 10^19 reachable positions.

Hmmm...I've been ignoring this thread because it seems like a re-hash of the older thread, but are you now saying that you're reducing 10^44 to 10^32 to 10^19 to 10^17 by removing "invalid positions" based on move orders?  Weren't those eliminated already when going from 10^120 possible games with permutation of moves to 10^44 unique positions (a step that was taken in part to eliminate redundancies of move order and transposition)?  Are you double counting?

He could just reduce it to 10^15 instead of 10^17 ...
It would be similiar silliness.
Then it would only take '3 weeks for Cloud 9 computers'
instead of 5 years.
But then people might say  "Hey ! if it were that easy they'd have done that !"
So that's too much of a 'hard sell'.
So would 10^18 positions.  Then it would take 50 years 'on Cloud 9'.
50 years ??  
5 years much catchier.  Much more spammable.