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.
"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.
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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.
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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.
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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.