#2978
"to solve a chess problem (e.g. "chekmate in two") we have to check all the opponent's replies to our selected moves, otherwise we cannot be sure we have solved it."
Exactly.
++ Chess is more like "white to play, black draws".
Moves that do not even try to win for white can safely be ignored, like 1 e4 e5 2 Ba6 or 1 a4.
You are talking about playing chess, not solving chess. Your whole mode of thinking is wrong.
@MARattigan
from your post: (which I read in full)
What, in short, do you mean by "position".
'Position' in that particular post of mine there - means arrangement of chess pieces on the board. One piece per square. Or - empty square.
Please note that in that post I'm talking about upper bounds initially.
With a particular idea in mind - in addition to other ideas.
The particular idea is that the actual number of possible legal possible arrangements of chess pieces on the board - must be and always will be and always is Less than whatever upper bound.
If it was not so - then the other number wouldn't be an upper bound.
'Position'. Arrangement of chess pieces. Number of such arrangements.
Without regard to en passant nor castling nor 50 move rule nor repetitions of move nor 'how it got there' and initially - not even whose move it is nor even if its legal or not.
Using things like max of two Kings - at least 32 squares must be empty - maximum of 10 on any of the other ten piece types - maximum of 48 squares for pawns ...
Doing that - I got a 71 digit number (again - 72 digit number) of positions down into a number whose number of digits was in the forties.
And that was over 40 years ago.
Do I have any of the steps recorded ? No.
It took me a few minutes and with no computer.
No 'Tromp'. Just straight math.
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Pertaining to a post by a different person that I chose to glance at:
Regarding 'meaningfulness' of solutions or numbers or results -
this is a leisurely and nonprofessional discussion of a leisure subject on a leisure website.
Suggestion: it is not for anyone here to decide nor declare for anybody else here what is 'meaningful' or not.
People will try - one person in particular.
But such attempts at phony authority are not and will not be 'meaningful'.
Because its always been that way - and there's no reason to think they would be. In other words - by evidence. Not by 'declaration'.
Its a continued irony - those attempts at phony authority by that person that are 'not meaningful'.
A large part of the reason the thread is, as @Optimissed put it, going round and round in circles is that there is not general agreement on what is meant by many of the terms that are in frequent use.
Including, but not necessarily limited to; "chess", "solved", "weakly solved", "strongly solved", "position", "diagram" and "proof".
As far as the term "chess" is concerned, there are many candidates. FIDE define several games; a basic rules game and various flavours of game with competition rules added. There are also games played according to ICCF rules or TCEC rules and versions defined by USCF that many American readers would understand as chess.
With my meaning of "solved" I don't believe any of those versions can be solved, but I'll leave that for a different post.
As regards "position", your meanings are, I believe, different from those of most of the people contributing. Also different from the meaning in any of the documents that have been linked to (including the FIDE laws).
You actually have two different meanings in your above post. In the first definition you specify, "One piece per square" and (subsequently implied) "legal possible arrangements ", but those specifications are omitted in your second definition (the latter specifically).
The difference is that "positions" with your first meaning would not include "positions" with your second meaning that could legitimately occur in a game such as the one below.
Notice I've edited out the White square in the lower right hand corner indicating that it's White's move (compared with the similar image I posted here) to conform with your definition. (Though the "position" in your second sense could legitimately occur in a game only if it's White's move.)
Nor "positions" in your second sense that couldn't legitimately occur in a game such as the following:
Obviously which of the definitions you choose would affect the number of "positions" - finite in the first case, unlimited in the second.
But either of your definitions would fall under what most people here, and some of the linked documents, refer to as diagrams, not positions.
I would say that it is inconvenient for most purposes to have the term "position" refer to anything that doesn't fully define what play is legitimate from the position. With your definitions it is not possible to say exactly what play is legitimate from any "position".