@10328
"It's too bad there isn't a fifty-move rule for Internet arguments."
Repetitio mater studiorum.
Repetition is the mother of study.
Many here still do not understand that it is not necessary to strongly solve a game to weakly solve it and that it is not necessary to weakly solve a game to ultra-weakly solve it.
"Many here still do not understand that it is not necessary to strongly solve a game to weakly solve it"
Many here do not understand that it is necessary to strongly solve a game to solve it.
Anyway if the pseudo-solving gets those people their funding then that's an approach in 'their context' to 'necessary'.
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As I thought - tygxc wants to get right off that subject of for how many pieces chess has Really been solved for.
Martin seems to have suggested its not 'solved' for anything beyond two Kings.
But I'm saying it is 'solved' for three pieces because its obvious.
@10341
"how many pieces chess has Really been solved for"
++ Chess is strongly solved for all positions of 7 men or less and for some 8-men positions.
Chess is at least in part weakly solved by the 106 ICCF WC Finals Draws.
For all practical purpose Chess is ultra-weakly solved: the initial position is a draw.
"Chess is strongly solved for all positions of 7 men or less and for some 8-men positions."
No it isn't.
Haven't you admitted they couldn't include castling?
If so - shows they're Struggling.
Whatever it is they're doing - they've been hung up between 7 and 8 for quite a while.
Based on what I suggested about 500-multipliers - they might never reach even 11 men.
I repeat - I doubt they've genuinely solved even for six men.
tygxc - suggest you read Martin's recent posts so you know what it is I'm replying to.
But whether you do or not - you're doing OK.
@10343
"they couldn't include castling?" ++ They could, but that is of no use.
"they've been hung up between 7 and 8 for quite a while." ++ Yes
"they might never reach even 11 men" ++ Maybe.
"I doubt they've genuinely solved even for six men" ++ No doubt at all.
"read Martin's recent posts" ++ All besides the question.
@10343
"they couldn't include castling?" ++ They could, but that is of no use.
"they've been hung up between 7 and 8 for quite a while." ++ Yes
"they might never reach even 11 men" ++ Maybe.
"I doubt they've genuinely solved even for six men" ++ No doubt at all.
"read Martin's recent posts" ++ All besides the question.
not if you haven't read his posts.
They've got to include castling for proper solving.
Especially since the more men you add the more relevant castling will be.
We agree on two points tygxc -
two points that are related.
How long did it take for them to proceed through each stage?
What about the 50 move rule?
How long have they been hung up on 8 men?
Its got to be far over a year.
Even with cheating by skipping castling possibilities.
Have they skipped en passant too?
You've got to include all these things tygxc - otherwise its not really solving.
Its 'pseudo'.
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I say again - its solved for three pieces - because however many such positions the computers can probably solve each one so quickly that the whole job is done in under an hour.
And the computer would know the exact number of positions too.
But with four - its beginning to get dubious the computer could do it quickly because there's over 500 times as many positions as with three.
But it seems plausible that if the computers could thoroughly solve all positions with three pieces on board in under one hour - then they could do four pieces in 500 hours.
But for five pieces - you're getting into a factor of 25,000.
There's over 7000 hours in a year.
You're looking at over three years there.
I'd be curious how long it took them to pseudo-solve for five pieces.
@10345
"They've got to include castling for proper solving." ++ It is no problem, but of no use.
"What about the 50 move rule?" ++ The 50-moves rule plays no role. An average ICCF WC Finals game ends in a draw in 38 moves, long before 50. ICCF allows 7-men endgame table base win claims that exceed the 50 moves, but such win claims do not happen, only draw claims.
"otherwise its not really solving" ++ Schaeffer weakly solved Checkers. It is real.
"its solved for three pieces" ++ Chess is strongly solved for 7 men.
"the exact number of positions"
5 men: 26,038,209,193
6 men: 3,787,154,440,416
7 men: 423,836,835,667,331
8 men: 38,176,306,877,748,245
"I'd be curious how long it took them"
6 men: 2005
7 men: 2012
Hello world :stockfish
Those figures don't look right tygxc.
26 billion positions for five men and then only 3.7 trillion for six men?
That's a factor of less than 160.
The true factor is over 500.
Have they used shortcuts for rotations and reflections?
If they have - its still an inaccurate figure.
The correct figure in the trillions was supposed to be well over ten trillion - if the 26 billions figure is correct.
The math isn't hard.
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It took Seven Years to get from six men to seven men even with pseudo-solving?
Seems to prove my points.
Even with the 160 factor in your numbers -
you're looking at over 1100 years to get through 8 men.
If it becomes a lot less then they're doing a lot of more extra-cheating.
Yes I know - they're going to 'improve the algorithm and the computing power'
but Al Gore didn't have much rhythm.
your nodes per second is invalid by the way TY ... because the difficulty of positions varies.
TY TY. (pun not deep)
Legally unreachable would be a subset - is a subset - of 'illegal'.
That one's not tough.
Do we agree on that?
I think so.
...
Yes, because every set is a subset of itself.
Legally unreachable and illegal are exactly the same with the caveat that we understand "legally reachable" as reachable by a series of (made) legal moves and "legally unreachable" as anything else. I believe that is the normal assumption.
From the FIDE laws:
3.10.3 A position is illegal when it cannot have been reached by any series of legal moves.
And that would also correspond with most people's understanding. The aforementioned caveat is generally made when considering printed positions.
To clarify, a board layout such as the following
can legitimately occur in a game, because art. 4 puts no constraint on the path a piece should take when making a move and the White king could simply be moving from e1 to e2 by the scenic route. (The king could also be straddling square boundaries.)
The position at that point is legitimately reachable, but nevertheless illegal because a position with that board layout could not have been reached by any series of (made) legal moves.
While unusual, it would be strictly correct to interpret "legally unreachable" as "not legitimately reachable", because FIDE doesn't specifically define that phrase and that would be the normal reading in English. In that case, "legally unreachable" would be a proper subset of "illegal".
In either case we can agree that legally unreachable would be a subset - is a subset - of 'illegal'.
@10348
"Those figures don't look right tygxc." ++ They are right.
"Have they cheated for rotations and reflections?" ++ Of course they have used symmetry.
"If they have - its still inaccurate." ++ It is accurate.
"It took Seven Years to get from six men to seven men"
++ Yes, and it took even more time to compress the storage so as to fit on a desktop.
"you're looking at over 1100 years to get through 8 men." ++ No, it is in progress.
Well Martin I disagree with a lot of that.
We do agree that legally unreachable is a subset of illegal though.
But not that its 'identical' with 'illegal'.
We're going to continue to disagree on that one ...
but that disagreement won't cause tectonic plate movement - nor a solar flare - nor the planets aligning.
Anyway - you might want to check out my latest post responding to tygxc's latest.
I wonder what his 'out' will be.
Maybe 'Player they weren't working on it the whole Seven Years'.
I did actually agree you can have illegal positions that are not legally unreachable with a strict (but unconventional) reading.
Is that what you had in mind? If not, perhaps you could give an example of a position that is illegal but not legally unreachable with the conventional meaning.
Elroch and MAR, are you guys considering the 50-move rule?
That is not such a big issue, especially for our toy (but maybe intractable!) KRK example. Explicitly including it only multiples the number of positions by 50, ...
100 to nitpick, but it doesn't affect your argument.
@10348
"Those figures don't look right tygxc." ++ They are right.
No they're not. They don't include any positions with castling rights and apply only to the basic rules game. They also don't correspond with positions as understood by chess players because they count positions with possible symmetries as the same, and chess players don't. They're mind bogglingly low estimates compared to the competition rules game - see my comments on "position" in #10309 (they are, albeit, more than the number of positions required to weakly solve competition rules chess by a tablebase approach - not by any approach similar to what you have been suggesting, even one that is, unlike yours, correct in principle).
"Have they cheated for rotations and reflections?" ++ Of course they have used symmetry.
i.e. yes.
"If they have - its still inaccurate." ++ It is accurate.
i.e. it is inaccurate.
"It took Seven Years to get from six men to seven men"
++ Yes, and it took even more time to compress the storage so as to fit on a desktop.
I was under the impression that it took a maximum of one year for the calculations and they still won't fit on the average user's desktop.
"you're looking at over 1100 years to get through 8 men." ++ No, it is in progress.
The two things are not incompatible, but 1100 years is a huge overestimate.
As for whether it's in progress, I think that may depend on whether you're talking about the basic rules game or the competition rules game.
Marc Bourschutsky has produced some 8 man tablebases that can apply to the latter (and some that can't) but this is not part of a project to produce a set of 8 man tablebases for competition rules, because he's working on DTC tablebases.
A set of DTM50 tablebases has been mooted but as far as I'm aware no 8 man tables have been produced so far.
The quickest would be 8 man Syzygy tables. Are you aware of any such 8 man Syzygy tablebases that have been produced?
In any case, I don't think anyone is working on tablebases with castling rights.
Here's another thing that will never be solved by myself:
My existence in this realm knows to humans as the milky-way. It will remain unsolved for quite a while.
@10356
"tygxc's main fault is to engage trolls"
++ Probably. Most are either too lazy to read, or too stupid to understand
Games solved: Now and in the future
@MARattigan
Martin -
...
Try this Martin - as long as Kings aren't adjacent and pawns are on any of their 48 squares - then all positions of three pieces with either side to move are all legal and legally reachable. Can you show an exception to the forum?
...
Very easily, even with the conventional understanding I mentioned in #10349.
Here are a few.
Competition rules only:
That last is only partially described, but applies to any position that fits the description.
Here is one (either game) with two men, courtesy of Andrew Buchanan.
@MARattigan
Martin -
now a more direct reply by me.
You're saying that the tablebases haven't even Rigorously solved for three pieces on the board?
Quote from your post:
"A practical algorithm to completely determine what positions are illegal from either all or particular FRC positions or just from the standard chess starting position is not currently known."
I would think it would be easy for three pieces.
Try this Martin - as long as Kings aren't adjacent and pawns are on any of their 48 squares - then all positions of three pieces with either side to move are all legal and legally reachable. Can you show an exception to the forum?
You don't need to worry about the starting position there.
There's your 'algorithm' right there.
This is easy enough for a human being that I would think that computers could easily handle four - and five with time. Time they've more than had.
But six pieces - that's something else.
The 500 multipliers begin to 'cut in'.
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Plus people thinking 'only legal positions need be considered' are missing the point that to find all legal positions you need to find and 'exclude' all the illegal ones.
Plus if you're doing that anyway in the project there's no reason to exclude the illegal positions from cataloguing.
A position is punched in ...
computer responds: 'Cannot be solved because its illegal.'
Or - 'Is not solved here because its legally unrecheable - see side project for further cataloguing of 'solutions' of unreachable positions that are otherwise legal. ' (maybe no 'funding' for that one)