I am not sure either. But big numbers look big either way. 
I am very sure that you don't distinguish by names of knights, because they do not possess them (eg see FEN).
Chess will never be solved, here's why
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Aug 28, 2024
0
#12563
Elroch wrote:
I am not sure either. But big numbers look big either way.
I am very sure that you don't distinguish by names of knights, because they do not possess them (eg see FEN).
But if you try to square the number of basic rules fp-positions with the Syzygy quoted figures, I think you'll find you have to Christen them.
Aug 28, 2024
0
#12564
RobboThe1st wrote:
It really is an irrelevant thing. Even if a computer can learn to win every game with white there would be so many lines to understand nobody would be able to play them all. The great thing is that the game is that complicated so it can go on being played forever competitively by humans.
As is already demonstrated by the tablebase solutions we have. Humans will generally draw a non trivial KQvKNN position even though in most cases the tablebase contains a win.
Aug 28, 2024
0
#12565
MARattigan wrote:
Elroch wrote:
I am not sure either. But big numbers look big either way.
I am very sure that you don't distinguish by names of knights, because they do not possess them (eg see FEN).
But if you try to square the number of basic rules fp-positions with the Syzygy quoted figures, I think you'll find you have to Christen them.
I can't believe this. They simply are not distinct. Are you suggesting the position count allows for symmetry AND includes a pointless order on each type of piece?
(As an only loosely connected point, I like the observation I read somewhere that LSBs and DSBs are actually two different types of piece for the purpose of analysis. )
Aug 28, 2024
0
#12566
playerafar wrote:
MARattigan wrote:
playerafar wrote:
"A solution that doesn't include castling can perfectly well be a weak or strong solution of a position in either version of chess that includes no castling rights."
One can wade throught that?
...
It was badly phrased. It should have read.
A solution that doesn't include castling can perfectly well be a weak or strong solution of a position that includes no castling rights in either version of chess.
Hopefully you can understand that.
You conceded that your initial attempt was badly phrased.
Good. Progress.
But your 2nd prototype - I don't think its a big improvement.
And I have no red telephone.
You probably won't try this ...
but try to word it without 'weak' or 'strong' because 'version of chess' is already 'weak'.
Just for you.
A solution that doesn't include castling can perfectly well be a solution of a position that includes no castling rights in either version of chess.
Still valid.
As for "version of chess", if you read the FIDE handbook you will see it describes different games depending on which articles apply. A solution (of any kind) of a game depends on the rules of the game (the solution of connect-4 for instance can't be used as a solution of the games in the FIDE handbook precisely because the rules of connect-4 are different from each of those games). By "version of chess" I mean a set of rules governing the game in question. ICCF would be a different version again.
What do you mean by "'version of chess' is already 'weak'" ("Very. Very weak.)?
Very.
Very weak.
But - put in a nice way. Refers to the post. Not the member.
-----------------------
What would actually be 'strong'?
32 piece tablebase including all possible castling situations and en passants and solving all possible ensuing positions including noting all winning positions with 'checkmate in x moves and precisely the value of x in each case'.
Yes, that would be a strong solution, but noting the distances to mate is not a necessary part of that. See the Wikipaedia entry - you could answer your own questions if you read that.
That would be strong. Even if it 'skips' 3fold and the 50 move rules.
Not under competition rules, because then it wouldn't solve most of the ensuing positions.
Why would it be strong? Because it encompasses the moves of the pieces.
But here you're using "strong" in a nonstandard way which seems to envisage encompassing the moves of the pieces but getting some of them wrong, unless you're talking about a solution only under basic rules. The basic problem is when I Google "playerafar strong solution", I don't get any entries, so if you want people to understand you, you're best using standard definitions. It's also more likely to be what the question is about.
------------------------------------------------
Are there ways it could be even stronger?
Yes - and not just those two extra rules.
A stronger solution would also indicate if there's a forced stalemate and minimum number of moves to that.
Stalemate tablebases have been produced, including minimum number of moves, but never referred to as strong solutions of the positions addressed.
Minimum number of moves to a forced draw because of insufficient material.
There could even be embellishments:
Like - minimum number of moves to mate if helpmates are factored in too.
And helpdraws.
----------------------------
Note that if there's a forced checkmate in a minimum number of moves - that minimum could be lower if there's 'help'. Happens constantly in games.
Tablebases take a lot of resources to produce, so though many embellishments are possible, some, such as your "Minimum number of moves to a forced draw because of insufficient material" are unlikely to be produced unless you do it yourself. Even then people are unlikely to agree to call it a strong solution of any of the positions addressed in any version of chess.
Aug 28, 2024
0
#12567
Elroch wrote:
MARattigan wrote:
Elroch wrote:
I am not sure either. But big numbers look big either way.
I am very sure that you don't distinguish by names of knights, because they do not possess them (eg see FEN).
But if you try to square the number of basic rules fp-positions with the Syzygy quoted figures, I think you'll find you have to Christen them.
I can't believe this. They simply are not distinct. Are you suggesting the position count allows for symmetry AND includes a pointless order on each type of piece?
(As an only loosely connected point, I like the observation I read somewhere that LSBs and DSBs are actually two different types of piece for the purpose of analysis. )
Yes that's what I'm suggesting.
Wilhelm/Nalimov figure for KNNNvK (which has always matched basic rules fp-positions when I've hand checked) is 242065096.
Syzygy reported is 181551378.
242065096/181551378=1.333314...=8/6 to the nearest damn it. (Difference, I think, is symmetric positions not accountable for from Sysygy figures.)
That appears to be 8 for the board symmetries and 6=3! for Lightfoot, Prancer and Charger. If there are pawns the 8 turns into 2 but the factorials remain. At least that's the best fit I've found so far for various endgames. I think there are further complications with bishops.
As for LSBs and DSBs being different pieces, I agree they should be. No moves in common. Shame they haven't usually been treated that way in tablebase construction, but Marc Bourschutsky is constructing his 8 piece DTC tablebases that way.
Aug 28, 2024
0
#12568
MARattigan wrote:
Nobody appears to have corrected this so far, so I'll give you a clue.
remember they said non-integers, yours solves exclusively for natural numbers
i remember doing that problem proposed by thee when i was in HS.
SilverThylacine wrote:
nerd aahs
brainrot aah
Aug 28, 2024
0
#12571
MEGACHE3SE wrote:
MARattigan wrote:
Nobody appears to have corrected this so far, so I'll give you a clue.
remember they said non-integers, yours solves exclusively for natural numbers
i remember doing that problem proposed by thee when i was in HS.
The phrase was actually "nor non-integers", which makes a difference. Admittedly Lola didn't say "nor negative numbers", but that was obviously intended judging from her own reply.
The solution in integers follows directly from the solution in natural numbers. The extra solutions are x=y<0 and -2^-4=-4^-2.
Aug 28, 2024
0
#12572
A few perfect games have already been calculated, but they all lead to draws
Aug 28, 2024
0
#12573
MARattigan wrote:
playerafar wrote:
MARattigan wrote:
playerafar wrote:
"A solution that doesn't include castling can perfectly well be a weak or strong solution of a position in either version of chess that includes no castling rights."
One can wade throught that?
...
It was badly phrased. It should have read.
A solution that doesn't include castling can perfectly well be a weak or strong solution of a position that includes no castling rights in either version of chess.
Hopefully you can understand that.
You conceded that your initial attempt was badly phrased.
Good. Progress.
But your 2nd prototype - I don't think its a big improvement.
And I have no red telephone.
You probably won't try this ...
but try to word it without 'weak' or 'strong' because 'version of chess' is already 'weak'.
Just for you.
A solution that doesn't include castling can perfectly well be a solution of a position that includes no castling rights in either version of chess.
Still valid.
I would call that one a huge improvement.
And it starts to look valid instead of invalid.
As for "version of chess", if you read the FIDE handbook you will see it describes different games depending on which articles apply. A solution (of any kind) of a game depends on the rules of the game (the solution of connect-4 for instance can't be used as a solution of the games in the FIDE handbook precisely because the rules of connect-4 are different from each of those games). By "version of chess" I mean a set of rules governing the game in question. ICCF would be a different version again.
What do you mean by "'version of chess' is already 'weak'" ("Very. Very weak.)?
Very.
Very weak.
But - put in a nice way. Refers to the post. Not the member.
-----------------------
What would actually be 'strong'?
32 piece tablebase including all possible castling situations and en passants and solving all possible ensuing positions including noting all winning positions with 'checkmate in x moves and precisely the value of x in each case'.
Yes, that would be a strong solution, but noting the distances to mate is not a necessary part of that.
But you've agreed it would be a strong solution.
Common ground. Is progress.See the Wikipaedia entry - you could answer your own questions if you read that.
We're discussing this. It isn't about Wikipedia.
That would be strong. Even if it 'skips' 3fold and the 50 move rules.
Not under competition rules, because then it wouldn't solve most of the ensuing positions.
I say it would be. We disagree.
Why would it be strong? Because it encompasses the moves of the pieces.
But here you're using "strong" in a nonstandard way which seems to envisage encompassing the moves of the pieces but getting some of them wrong, unless you're talking about a solution only under basic rules. The basic problem is when I Google "playerafar strong solution", I don't get any entries, so if you want people to understand you, you're best using standard definitions. It's also more likely to be what the question is about.
------------------------------------------------
Are there ways it could be even stronger?
Yes - and not just those two extra rules.
A stronger solution would also indicate if there's a forced stalemate and minimum number of moves to that.
Stalemate tablebases have been produced, including minimum number of moves, but never referred to as strong solutions of the positions addressed.
Maybe because they leave out other things.
Minimum number of moves to a forced draw because of insufficient material.
There could even be embellishments:
Like - minimum number of moves to mate if helpmates are factored in too.
And helpdraws.
----------------------------
Note that if there's a forced checkmate in a minimum number of moves - that minimum could be lower if there's 'help'. Happens constantly in games.
Tablebases take a lot of resources to produce, so though many embellishments are possible, some, such as your "Minimum number of moves to a forced draw because of insufficient material" are unlikely to be produced unless you do it yourself. Even then people are unlikely to agree to call it a strong solution of any of the positions addressed in any version of chess.
I think you've missed the point about minimum number of moves to a material-based draw.If the engine found such sequences during its search for a win then why would that 'drain resources' to include it in its stated solution?By the way - minimum number of moves to material draw could take several forms. Have several meanings.
I've replied to your points in orange with my six replies in green.
I usually don't do the 'nested quotes' 'internal replies' thing because it gets harder for people in the forum to read and follow.
So usually I look for one point that looks most salient whether valid or invalid and address that instead.
But this time I made an exception Martin.
Just for you.
Why?
Because you took the time and care to read through my post and respond.
Idea (not suggestion): If we're continuing these lines of discussion -
start over with a brand new post addressing the points instead of continuing with quoting.
Why? Easier to read for everyone in the forum.
A few perfect games have already been calculated, but they all lead to draws
really not they say...but plz post those u have found 2b pefect (or near to ?)
En passant should be included in most tablebases as it is a fundamental part of multi-pawn endgames, castling is almost never an option by the time there are 6-8 pieces left or was already done so it's not as important.
on pissants a stoopit rule lol !
Aug 28, 2024
0
#12577
Castling matters because the further you go back the more likely it figures.
And besides - just waving something off arbitrarily at an arbitrary point is neither mathematical nor scientific.
Either you're considering legal moves of the pieces or you're not.
You might as well say: 'Lets skip all positions with three or more promotions too'
Like skipping castling - its not only weak - its invalid too.
I agree all possible legal moves should be included, but if let's say they only had the processing power to include either en passant or castling but not both, en passant takes priority in the endgame.
Aug 28, 2024
0
#12579
Regarding recent dicussion - I saw a nice idea mentioned earlier.
For 'shorcut solutions'.
An idea that I brought up a long time ago but somebody nixed it because 'computers can't think that way'
which is probably a valid point. But can be validly circumvented.
------------------------------------------------
It goes something like this. For example.
Somebody's up a massive amount of material against a lone King.
Say a Queen and two knights and a bishop.
That King's on move. He's not stalemated.
There is no forced route to stalemate for him.
Now why should the computer be obliged to find 'mate in x' there?
---------------------------------------------
It can just state in all such situations - with disclaimer:
Strong solution - this is a win. Disclaimer: 3 fold repetition not considered. 50 move rule not considered.Want to make it stronger?
'only a draw if 3 fold repetition or 50 move rule draw is forceable or happens' Tablebase addresses the diagram and legal moves available.Is not a 'gametree' analysis.'It can include that with every single positon arbitrarily.
Zero 'drain on resources'. Its a text statement. Printed 'in parallel'.
I repeat - 'strong solution of each such position' based on knowledge and logic of the game.
Point: 'computer can't think that way' but the computer doesn't have to be exclusive of knowledge of the game and known logic of the game.
Concerning exactness, I have to report that I accidentally posted the number of positions in the (as yet incomplete) 8 piece Syzygy tablebase. The number in the 7 piece Syzygy tablebase is 423,836,835,667,331.
On that front you have to be extra careful about what you mean by "position".
The figure you quote according to the Syzygy site is the number of "unique legal positions" contained in it's tablebases as defined by Kirill Kryukov, which don't correspond with most peoples understanding of position. E.g. entries with these basic rules fp-positions are counted as the same.
Also in the counts for individual endames this would appear to represent 2!x3! times as many entries as you might expect depending on which of the horses is Prancer, Charger or Lightfoot and which tower is the Tower of London and which the Leaning Tower of Pisa.
I don't know if that carries through to the quoted total.