Not really a paradox. Just often not so in such circumstances!
A paradox in what it means as far as the ongoing discussion is concerned - as opposed to a paradox intrinsically.
That almost makes sense. Bravo. However, the paradox exists in your thoughts and it's due to your own expectations.
@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 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.
/////////////////////////////////////////
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'. 
Not really a paradox. Just often not so in such circumstances!
A paradox in what it means as far as the ongoing discussion is concerned - as opposed to a paradox intrinsically.
Stands. And is proven by what has happened.
As for arguments over the word 'paradox' - those in turn could be paradoxical and could go on forever.
People might try to assert authority as to usage - they will.
But the statement stands.
@tygxc makes his posts civilly. Its been paradoxical and continues to be paradoxical in its effects on the conversation and therefore in what it means to the ongoing discussion.
'Paradox' is a somewhat general term. It is not mathematical.
But perhaps some will overlook that.
Whether in attempts to be semantically correct -
or in attempts to grab at imaginary authority.
I just got a postcard from Fermat (got delayed in the post). Apparently he's solved chess but his quill had run out of ink so he couldn't include the proof.
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'.
Neither is it for anyone to insist on sanity, as a prerequisite for conversation here. The fact that at least one person is completely without it is a happy coincidence with the pleasure taken in occasional and general amusement.
(It's just a shame that the same cannot be said for the lack of intelligence in that person.)
Now, the problem with Sveshnikov's idea is that present evaluation functions aren't accurate. That can be seen by the horizon effect, where an engine evaluation changes as it moves forward and yet, quite often, it wouldn't go in the right direction of its own accord. They are just too weak, because the techniques the evaluation functions use are too primitive, as yet. There's no doubt about it. I think everyone here would agree on that.
Agree. That's why to falsify, if possible, a statement like e.g. "Black can draw from the initial position, here's how", the moves Black plays must be tested against all the possible opponent's moves. It's inelegant, but humans have not been able to conceive something both cheaper and equally accurate, so far.
"the moves Black plays must be tested against all the possible opponent's moves. "
that sounds like 'strong' solving.
Another thing that is apparently not yet well established in the discussion is that Strong solving and 'weakly' solving are not exclusive of each other.
Strong mathematics - (in other words real math not pseudo-math) can be used to cut down the number of positions to be considered.
'Solving' can be and is - a multi-phased operation.
Strong and weak are not in 'separate boxes' except for those who want to internally insist to themselves that they are.
So - various approaches to 'weakly' solving can be surrounded by 'strength' - and on multiple sides - rather than 'ends.'
The 7 piece tablebases on one side.
Mathematical cutdowns of illegal positions on another.
The more obvious cutdowns that is.
Only two Kings allowed. Of two colors. Only one piece per square.
Minimum 32 squares always empty.
And yes the math for that is 'there'.
And there's a finite number of positions.
'Very' finite because its upper bound and improved (lesser) upper bounds not only exist - but are known too.
On another side - for 'weakly' solving ... are positions that theoretically could be won - but can be regarded as 'solved'.
For example - most K+R versus K+R positions.
In most of them - there's no forced win available.
But a win could become available if one opponent 'helps'.
Downside: KR vs KR already 'solved' in the tablebases.
Point: Solving projects could get another big beneficial cutdown of positions to be considered - if some positions can be 'arbitrated' away.
It would begin with 8 piece positions with precisely equal material and material types.
Example: two bishops and two knights each.
If there's no immediate win available - many players would agree to a draw.
There's something called 'losing chances'.
Does the discussion link up with 'regular chess' ?
Sure it does.
In tournaments where there's a dispute and one player wants the director to rule a draw - a standard is sometimes used.
Like this: Paraphrased:
'If in the tournament director's opinion a master level player could not swindle a C player into losing the position then the director can rule a draw'.
This pertains directly to 'weakly solving'.
So do the dynamics of most chess games.
Players try to pressure other players into mistakes. Happens constantly.
Could an algorithm be developed concerning 'insufficient losing chances' ?
It already has been developed I'd say.
But not developed enough to make big progress in 'solving chess'.
The tablebases will declare a draw if there's K+N versus K+N except if its mate or stalemate already there or immediately available.
Point: there's a 'helpmate' available with K/N versus K/N
Checkmate ! But black's knight didn't have to go to g8.
So whether his knight was at f6 or h6 - or anywhere else on the board
the tablebase would 'solve' it as a draw.
Is that 'strongly' or 'weakly' solving ?
Could it be both?
Point: Insufficient losing chances.
Unless black just happens to have blundered into Ng8 -
most players would agree to a draw.
Connects up with regular chess in other words.
Shorter version:
An opponent opens 1) a4 ...
so black asks for the tournament director to come over and declare a draw ...
Tournament Director Reply:
"No. Both of you have Sufficient losing chances !"
But then he adds - 'have either of you offered a draw though? Is there agreement?'
That's different.
#2946
"There isn't even a lot of evidence on the move 1. a4."
++ See figure 5 of this paper with 'knowledge' in its title.
https://arxiv.org/pdf/2111.09259.pdf
#2950
"the so-called strong solution is irrelevant to this conversation"
++ A strong solution i.e. a 32-men table base is unfeasible with present technology.
#2950
"the so-called strong solution is irrelevant to this conversation"
++ A strong solution i.e. a 32-men table base is unfeasible with present technology.
Not the point, because it's logically irrelevant. I gave reasons why that is so. That idiotte is posting more and more of his rubbish and seems to want to take over the entire thing and get everyone reading endless drivel. Without having to search for where you may have answered, are you in agreement with the content of my last post? It's basic stuff and, if not, there's no point in continuing and you had better go back to talking among yourselves.
Now, the problem with Sveshnikov's idea is that present evaluation functions aren't accurate. That can be seen by the horizon effect, where an engine evaluation changes as it moves forward and yet, quite often, it wouldn't go in the right direction of its own accord. They are just too weak, because the techniques the evaluation functions use are too primitive, as yet. There's no doubt about it. I think everyone here would agree on that.
Agree. That's why to falsify, if possible, a statement like e.g. "Black can draw from the initial position, here's how", the moves Black plays must be tested against all the possible opponent's moves. It's inelegant, but humans have not been able to conceive something both cheaper and equally accurate, so far.
But how can they be tested, without devising more reliable assessment algorithms? And how may they be devised, without a breakthrough in the general way that positions can be understood to evolve during games? There are two main processes: destabilisation and crystalisation.
And how can any of this be discussed, in an environment where at least one person doesn't even understand that "solving chess" can only be achieved by finding a way to generate meaningful moves, which are moves which, from an "objective" point of view, are attempts to play the strongest game possible for each side? There's bound to be some latitude and it's necessary to assess a variety of good replies. However, if tygxc is right in one thing, it's that by far the greatest majority of possible moves are irrelevant to anything approaching a solution of chess, just as they would be irrelevant to a strong player, who knows by experience that they are not moves that will improve their game.
#2952
"what "solve" means, in the context of chess."
++ ultra-weakly solved means that the game-theoretic value of the initial position has been determined,
weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition,
and strongly solved is being used for a game for which such a strategy has been determined for all legal positions.
"We're only interested in meaningful positions: that is, positions reached in the context of at least a strong attempt to play the best moves on either side." ++ That is weakly solving chess, which is feasible and only requires legal, sensible, reachable, and relevant positions far less than the number of 10^44 legal positions.
"how are the best moves to be played or identified, without an evaluation function?"
++ Ultimately by the 7-men endgame table base.
"Such an evaluation function must be heuristic."
++ All evaluation functions are flawed. Deep calculation and pruning by heuristics is the way.
"it can only be achieved via successive approximations, using evaluation functions."
++ No, all evaluation functions are flawed.
"They are just too weak, because the techniques the evaluation functions use are too primitive, as yet." ++ No: Stockfish calculating deeper with a primitive evaluation function beat LC0 with a more elaborate evaluation function and shallow calculation.
https://chessify.me/blog/nps-what-are-the-nodes-per-second-in-chess-engine-analysis#:~:text=Nodes%20per%20second%20(NPS)%20is,thousand%20or%20one%20million%20respectively.
"There's no doubt about it. I think everyone here would agree on that."
++ There is doubt. Not everyone here agrees.
Strong solution is very relevant.
Those who try to use personalization as an argument are consistently failing in such attempts.
But don't seem to be learning from that experience.
I'm using the term 'those' losely. Its hardly plural.
Extremely concerned he is - that anybody might 'take over' whatever from whoever else. Much or most if not all of that simply imaginary.
On the other hand @tygxc - who is Not that person - while recognizing that forming a database of every possible chess position with an accurate determination of whether each such position is a win/winning or drawing/drawn position - isn't feasible at present and might not be for a very large number of years -
has made many energetic posts concerning alternatives to such thorough solving.
Those 'weak' alternatives are neither exclusive nor inclusive of strong solving - nor is such strong solving irrelevant to 'weak' solutions.
The 'weak' alternatives have been the main subject and it can be noted that the forum topic title doesn't qualify as to weak nor strong 'solved'.
Since 'weak' could have a very big range of meaning (regardless of how much ven den Herik's definition could be invoked or interpreted or misinterpreted) - then @tygxc 's arguments always might have that 'unbrella protection' of the word 'weakly'.
As @Elroch conveniently said earlier, the search for a weak solution resembles what we do to solve a problem of chess. We pick up a candidate move, according to an heuristic, and see if it can reach the goal no matter what the opponent does. At every depth in our search we repeat this process. The better the heuristic, the less we have to check all our candidate moves, but to claim we have solved the problem we have to pick in turn all the possible opponent's replies. For a strong solution, instead, we should pick in turn all our and the opponent's moves at every turn and see what happens. This is more demanding and not necessary required. Of course, a strong solution includes a weak one.
Strong solution is very relevant.
No, it's completely meaningless, because it consists of all possible lines, which are very nearly all nonsense, in chess terms, so that there wouldn't even be any point in trying to evaluate them. The so-called strong solution isn't a "solution" in any meaningful way at all. It certainly isn't "strong", in the way that "strong" is usually meant ... i.e. "useful". It's just an encyclopaedic array of all possible move permutations.
If you think you can prove it's relevant, then try. You should also realise that talking in general terms about the quality of different people's arguments is very foolish. All it achieves is to demonstrate your complete cognitive ineptitude and lack of ability. Stick to poetry.
Its obviously relevant. Whoever who thinks its so important to authoritate - can try to prove its irrelevant.
In other words follow his own suggestions that he never does.
And shorter:
The fact that strong solving isn't feasible at present (although possible - and a solution does exist because the number of possible positions is very finite)
doesn't mean that that unfeasibility is necessarily ongoing for centuries.
Hardware is improving. So is software. So are algorithms for chess.
Even in as little as ten years from now - perhaps the situation could be considerably changed.
Unlikely such improvements are going to shave a lot of digits off those daunting upper bound numbers though. Quite an Occam's razor needed for that Shave !
But improvements could change the situation regarding the 'weak' solving moreso.
Issue: Sufficient losing chances. Quite central.
Not really a paradox. Just often not so in such circumstances!
A paradox in what it means as far as the ongoing discussion is concerned - as opposed to a paradox intrinsically.