
Chess will never be solved, here's why
In Elroch's commentary - perhaps the person in charge of the algorithm funding inhales too much car and smokestack exhaust and terminates that funding.
@11068
"the implementation of solutions are specific to each game"
++ Yes, like for Chess prune 1 e4 e5 2 Ba6? right away.
Rather, like the implementation of solutions (remotely resembling your non solution) is specific to FIDE basic rules chess, FIDE competitio rules chess, ICCF chess etc.
Allis' weak solution of Connect Four, the weak solution of Losing Chess, and even Checkers all used game knowledge. For Chess that is necessary even more.
All using proven knowledge to verify (as opposed to expedite) the solution, no mention of a big red telephone anywhere.
"elimination of 27 orders of magnitude is larger than all of checkers by 10 million times"
++ Larger game, larger reduction.
Don't think you quite grasped what he said.
Besides from 10^38 to 10^17 is 21 orders of magnitude.
I think he was basing it on 4.8x10^44 which is appropriate for basic rules chess. With 10^38 you've already started your silly reductions. You already conceded 4.8x10^46 (still a vast underestimate) for FIDE competition rules chess at the start of the thread before immediately forgetting about it, so you should accept 29½ orders of magnitude at least for that and ICCF chess (though it's out itself by many orders of magnitude).
You gave no reasoning why you could ignore the triple repetition rule for versions other than FIDE basic rules, You failed to put any upper limit even on the number of positions in KRK under FIDE competition rules. We don't currently have even an ultra weak solution of all positions in that endgame, nor any proposal for producing one.
Isn't the musing about the repetition rule a red herring for solving chess (as opposed to playing an imperfect opponent)?
The reason is quite simple: if there is a forced win, there is a forced win without repetition. So consider a repetition of position to be a loss if you like (handily pruning forward analysis - there being no problem with the tablebase end) and seek a winning strategy. If there is none you can be 100% sure there is no winning strategy.
Having verified this for both sides, you can do the same but counting a repetition as a win. You are likely to find both sides will be able to achieve this, making the result a draw.
The problem, of course, is that this solution remains computationally intractable on account of its size.
No comment there from Elroch about the ridiculousness of taking the square root - not a gigantic reduction when you're talking about small numbers to start with ...
but with big numbers like 10 to the 34th to start with it gets more and more ridiculous. Its like tygxc wants to 'extract' one position from each 100 million trillion positions and then go by that one.
that root is tygxc's 'magic carpet' to Nirvana-claims about 10 to the 17th.
He will get much attention.
Another 5000 posts thus coming up ...
But O likely to be the only jealous one. Foolishly jealous. As always.
@optimissed. Whats you argument agains cantor?
Answer came there none, but I would guess the real answer is that he has zero chance of understanding anything Cantor said.
the bit that tygxc misses is that he doesnt get to choose black's response.
by definition, the strategy steal must encompass ALL possible black responses.
The key is that you can run all positions past @tygxc himself, and he judges whether they are 100% winning. He can see this in a way that others can't (including conventional engines rated over 3500, which evaluate then as a material advantage much less than that where there is a forced mate, or similar strength top AIs which ascribe them a probability of winning less than 1.0) - he also has the unique capability to detect that when two players have had a run of draws, the next game between them will also be a draw, refuting common sense and quantitative assessments.
I am not sure how he achieves this supernatural insight, but he is psychologically certain of it despite all objective reasons not to be, so it must be ok.
i mean his logic does depend on such evaluations
No comment there from Elroch about the ridiculousness of taking the square root - not a gigantic reduction when you're talking about small numbers to start with ...
but with big numbers like 10 to the 34th to start with it gets more and more ridiculous. Its like he wants to 'extract' one position from each 100 million trillion positions and then go by that one.
that root is tygxc's 'magic carpet' to Nirvana-claims about 10 to the 17th.
He will get much attention.
Another 5000 posts thus coming up ...
But O likely to be the only jealous one. Foolishly jealous. As always.
@tygxc says that while the square root approximation was woefully over-optimistic with checkers (a game where all the play is irreversible until promotion occurs) it it enormously pessimistic with chess (a game where most moves are reversible from the outset to the end). Exactly the opposite of what the differences would suggest (with complete reversibility being the ideal case for reducing the complexity).
Of course, he relies on the fact that chess is so simple compared to checkers that an imperfect player can ignore 90% of the moves as irrelevant without a valid reason and be 100% sure nothing has been missed.
All wrong, but seems to make sense to someone who doesn't know the difference between playing chess and solving chess.
@11068
"the implementation of solutions are specific to each game"
++ Yes, like for Chess prune 1 e4 e5 2 Ba6? right away.
Rather, like the implementation of solutions (remotely resembling your non solution) is specific to FIDE basic rules chess, FIDE competitio rules chess, ICCF chess etc.
Allis' weak solution of Connect Four, the weak solution of Losing Chess, and even Checkers all used game knowledge. For Chess that is necessary even more.
All using proven knowledge to verify (as opposed to expedite) the solution, no mention of a big red telephone anywhere.
"elimination of 27 orders of magnitude is larger than all of checkers by 10 million times"
++ Larger game, larger reduction.
Don't think you quite grasped what he said.
Besides from 10^38 to 10^17 is 21 orders of magnitude.
I think he was basing it on 4.8x10^44 which is appropriate for basic rules chess. With 10^38 you've already started your silly reductions. You already conceded 4.8x10^46 (still a vast underestimate) for FIDE competition rules chess at the start of the thread before immediately forgetting about it, so you should accept 29½ orders of magnitude at least for that and ICCF chess (though it's out itself by many orders of magnitude).
You gave no reasoning why you could ignore the triple repetition rule for versions other than FIDE basic rules, You failed to put any upper limit even on the number of positions in KRK under FIDE competition rules. We don't currently have even an ultra weak solution of all positions in that endgame, nor any proposal for producing one.
Isn't the musing about the repetition rule a red herring for solving chess (as opposed to playing an imperfect opponent)?
The reason is quite simple: if there is a forced win, there is a forced win without repetition. So consider a repetition of position to be a loss if you like (handily pruning forward analysis - there being no problem with the tablebase end) and seek a winning strategy. If there is none you can be 100% sure there is no winning strategy.
Having verified this for both sides, you can do the same but counting a repetition as a win. You are likely to find both sides will be able to achieve this, making the result a draw.
The problem, of course, is that this solution remains computationally intractable on account of its size.
That depends entirely on the method used.
If it's a tablebase construction 4.8x10^44 collections of position attributes is perfectly adequate for a weak solution of competition rules chess because they can be built by a method that excludes repetitions and sequences exceeding 50 moves (Syzygy actually considers wins frustrated by the 50 move rule, but that's not necessary).
But if you're using Stockfish (or ICCF contestants who take the moves from Stockfish) it doesn't prune the search in the manner you suggest. This is SF playing White.
the square root 'trick' by tygxc actually holds some value, unfortunately tygxc illogically twists what that value is. you all probably are already aware of this, but the solution set of the weak solution is the square root of possible relevant positions.
however, tygxc keeps claiming the solution set as the calculations needed to reach the solution set, which is objectively false.
the square root 'trick' by tygxc actually holds some value, unfortunately tygxc illogically twists what that value is. you all probably are already aware of this, but the solution set of the weak solution is the square root of possible relevant positions.
however, tygxc keeps claiming the solution set as the calculations needed to reach the solution set, which is objectively false.
MEGA
I entirely disagree with the square root idea.
Here's one of the reasons - the more positions there are to square root - the more the ratio of reduction drastically increases.
The argument that the large number of positions contains a lot of silly promotions and underpromotions - that's going to justify a reduction to one hundred thousand trillionth of the previous number?
If you've got a proof that such a thing would be the slightest bit valid I hope you post it here.
But no obligation. Not from me anyway.
I'm not one of the 'links please' people.
the square root 'trick' by tygxc actually holds some value, unfortunately tygxc illogically twists what that value is. you all probably are already aware of this, but the solution set of the weak solution is the square root of possible relevant positions.
however, tygxc keeps claiming the solution set as the calculations needed to reach the solution set, which is objectively false.
If there is a forced mate the solution set could be very much smaller (e.g around 1.5x10^19 if there's a forced mate in 12 from the starting position). Rather less likely, but also true if there are forced draws (single repetition, stalemate, recognised dead position as the leaves).
But, as you say, the solution set is a rather small subset of set of positions that must be evaluated in a forward search.
Who came up with the square root idea?
I mean who was is the scientist/mathematician?
Does he have universal peer support of same?
Why not the cube root so the whole thing could be 'weakly solved' by next week?
tygxc has been pushing 'five years'.
Note the danger of saying 'one year'.
Its already two years since his initial claim of 'five years'.
(I'll anticipate the reply tactic: 'funding')![]()
the square root 'trick' by tygxc actually holds some value, unfortunately tygxc illogically twists what that value is. you all probably are already aware of this, but the solution set of the weak solution is the square root of possible relevant positions.
however, tygxc keeps claiming the solution set as the calculations needed to reach the solution set, which is objectively false.
MEGA
I entirely disagree with the square root idea.
Here's one of the reasons - the more positions there are to square root - the more the ratio of reduction drastically increases.
The argument that the large number of positions contains a lot of silly promotions and underpromotions - that's going to justify a reduction to one hundred thousand trillionth of the previous number?
If you've got a proof that such a thing would be the slightest bit valid I hope you post it here.
But no obligation. Not from me anyway.
I'm not one of the 'links please' people.
I am the sort of person who doesnt make claims unless I can back them up with that level of proof.
here's a "proof" of sorts.
at every line of white and black, you must consider the X possible white moves and then hthe X possible black moves to each white move. X*X = X^2 complexity added at each point.
the "weak solution" is knowing the SINGULAR white move to make in each position to guarantee the mate/draw (assuming its not a black win)
so we consider 1*X positions instead of X^2 positions at each point from the previous line.
by definition this isnt a proof, just a demonstration of an heuristic.
As my previous post explained, this implicitly assumes the tree of games is the same as the tree of positions. Because there are reversible moves in chess, the number of positions is way smaller than the number of games. 5 x 10^44 versus ~10^120
This means that positions dodged by only looking at one white move often reappear later.
MEGA
that's interesting - and I also have to respond to Elroch's post just now.
your
'by definition this isnt a proof, just a demonstration of an heuristic.'
It sounds like you're making a big division at each move (two ply) that would impose a divider usually ranging from about 10 to 60.
If we were to try an average number of white move options at 30 and an average game length of 40 moves -
then you'd get a total divider of 30 to the 40th power.
Which would be even greater than the humungous reduction that the square root imposes.
In fact there aren't even that many chess positions at all.
No comment there from Elroch about the ridiculousness of taking the square root - not a gigantic reduction when you're talking about small numbers to start with ...
but with big numbers like 10 to the 34th to start with it gets more and more ridiculous. Its like he wants to 'extract' one position from each 100 million trillion positions and then go by that one.
that root is tygxc's 'magic carpet' to Nirvana-claims about 10 to the 17th.
He will get much attention.
Another 5000 posts thus coming up ...
But O likely to be the only jealous one. Foolishly jealous. As always.
@tygxc says that while the square root approximation was woefully over-optimistic with checkers (a game where all the play is irreversible until promotion occurs) it it enormously pessimistic with chess (a game where most moves are reversible from the outset to the end). Exactly the opposite of what the differences would suggest (with complete reversibility being the ideal case for reducing the complexity).
Of course, he relies on the fact that chess is so simple compared to checkers that an imperfect player can ignore 90% of the moves as irrelevant without a valid reason and be 100% sure nothing has been missed.
All wrong, but seems to make sense to someone who doesn't know the difference between playing chess and solving chess.
@Elroch I agree with your 'All wrong' there.![]()
MEGA
that's interesting - and I also have to respond to Elroch's post just now.
your
'by definition this isnt a proof, just a demonstration of an heuristic.'
It sounds like you're making a big division at each move (two ply) that would impose a divider usually ranging from about 10 to 60.
If we were to try an average number of white move options at 30 and an average game length of 40 moves -
then you'd get a total divider of 30 to the 40th power.
Which would be even greater than the humungous reduction that the square root imposes.
In fact there aren't even that many chess positions at all.
the gist of the "proof" is that if (and this is a decently big if) each move by a player multiplies the complexity by "X", if we only consider every other move to increase the complexity, then the new end comlpexity is a square root of the original end complexity.
of course, the multiplicative increase in complexity isnt a constant.
This from tygxc just in the last few posts

"That leaves 10^34 positions, of which the square root i.e. 10^17 are relevant to weakly solve Chess."
Not only does tygxc's post prove what I was saying about his ridiculous square root claim - that he so claims - but again there's that 'weakly solve' assertion there - disproving Elroch's claim of 'irrelevancy'.
And O has no counter to being exposed. O is @Optimissed.
He just yells 'alt' and similiar - pathetically.
Earlier he tried to lie that he can physically take on three men - so many lies he tells. Does he expect anybody to believe them?
------------------------------------------------
And BC can't shut up anybody here and good thing.
He'll try though. Foolishly.
Am I 'insulted'? 'Annoyed'?
Such foollishnesses are to be expected from O and BC.
There's big differences between 'annoyed' and 'don't care' and 'not passive'.
There's hope for BC - he's probably very young with young male adult issues like TP and Silver and EE all appear to have. Not quite the same though.
If BC is in fact middle-aged - well then it does look kind of hopeless.