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')
Chess will never be solved, here's why
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Jun 1, 2024
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#8322
Jun 1, 2024
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#8323
playerafar wrote:
MEGACHE3SE wrote:
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.
Jun 1, 2024
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#8324
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.
Jun 1, 2024
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#8325
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.
Jun 1, 2024
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#8326
Elroch wrote:
playerafar wrote:
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.
Jun 1, 2024
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#8328
playerafar wrote:
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.
Jun 1, 2024
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#8329
I recall one claim that more pieces may not provide longer mates. There is as yet no 8 piece mate longer than the longest 7 piece mate.
Jun 1, 2024
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#8330
playerafar wrote:
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?
The square root idea is intuitively trivial. If a typical position has M moves and every sequence of moves gives a unique position, the number of positions after N full moves is like M^(2N). If instead you only consider one move for the proponent of a strategy, this is reduced to M^(N), the square root of the first number.
This calculation is actually for the number of distinct games, not positions, and assumes the two are similar (which is true when the positions are all distinct).
Real chess has both transpositions (reducing the number of positions) and reversibility (increasing the fraction of positions reached by a strategy), so the idea is very loose indeed.
It is a better model for some other games to chess.
Jun 1, 2024
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#8331
I have an interesting update on the longest mate topic. For a long while the longest mate was a 7 piece ending that took 549 moves. But the new longest mate (reported last year) is an 8 piece pawn ending that takes 584 moves.
The claim about longest mates getting shorter with larger tablebases appears to be restricted to those with no pawns.
Jun 1, 2024
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#8332
Elroch wrote:
I recall one claim that more pieces may not provide longer mates. There is as yet no 8 piece mate longer than the longest 7 piece mate.
Really not surprising, only a tiny percentage of 8 piece tablebases have been produced, almost all pawnless. They're all DTC databases so the length of the mates is unknown and it's unlikely that the longest mates will occur in pawnless endgames.
I'm still expecting mates around 1200 moves when the 8 man DTM tablebases finally arrive.
Jun 1, 2024
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#8333
MEGACHE3SE wrote:
playerafar wrote:
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.
Of course it isn't a constant.
And taking an average wouldn't be exact but we could consider plausible averages.
And the reduction would be far more than 'the square root'.
That 'square root' doesn't seem to follow either.
yes it looks good ...
If you take a series of terms that multiply together and square root each one - and then multiply them together do you get a result equal to if you had just square-rooted the whole thing?
That's plausible except for one gigantic problem.
The reduction you get in the number of possible positions is just too large.
Even if it really is the square root - the reduction much too large to be plausible for anything but Non-solving.
And considering just one move for white each time - isn't just 'weakly solving' - its also Non-solving.
//////////////////////////////////////////
The computer does an 'Algo' each time for 'best move for white' and then eliminates all the others?
Too much of the time - multiple moves are comparable.
Too comparable. And the more depth and time that is applied the more the computer changes its mind.
And different software gets different results.
And updated software gets different results.
/////////////////////////////////////////////////////////
But just the size of the reduction you get - instantly discredits the square root idea.
//////////////////////////////////////////
The square root idea has another 'glitch-looking thing' in it.
It implies that the longer the game goes - the more its valid to reduce the positions even more exponentially.
Try an idea of the reverse being true.
The longer the game - the less you can cut it down.
Including by ratio.
/////////////////////////////////
Not satisfied?
How about this next one ...
the longer the game - the higher the total incidence of 'no best move' options for white.
And there again - the more invalid the square root becomes.
///////////////////////////////////
'Only one best move at each point' is valid in specially selected or constructed tactics puzzles.
But in the total game of chess?
Hardly.
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MEGA - maybe we're going to disagree on this.
Or 'it'll be in disagreement'.
But that's okay. Because for one thing - you're not O and I'm not O.
We do better.
We always will. Almost everybody does. And will.
Jun 1, 2024
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#8334
Elroch wrote:
I have an interesting update on the longest mate topic. For a long while the longest mate was a 7 piece ending that took 549 moves. But the new longest mate (reported last year) is an 8 piece pawn ending that takes 584 moves.
The claim about longest mates getting shorter with larger tablebases appears to be restricted to those with no pawns.
Actually @moremover claims 595 already, but the tablebases are far better at that kind of thing.
@11110
"true if there are forced draws (single repetition, stalemate, recognised dead position as the leaves)"
++ Stalemate or dead position do not occur, but 3-fold repetition is a major drawing mechanism:
in 30 of the 106 ICCF WC Finals draws.
@11111
"Why not the cube root"
For strongly solving: N white moves * N black replies = N² positions
For weakly solving: N white moves * 1 black reply = N positions = Sqrt (N²) positions
@11112
"Its already two years since his initial claim of 'five years'."
++ We are now about there: 106 draws out of 106 games in the ICCF WC Finals.
Besides, it was not my claim, but that of GM Sveshnikov.
Jun 1, 2024
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#8339
tygxc wrote:
@11111
"Why not the cube root"
For strongly solving: N white moves * N black replies = N² positions
For weakly solving: N white moves * 1 black reply = N positions = Sqrt (N²) positions
My comment about cube root was a joke.
But the square root idea looks like its a joke too.
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?