@5960
Wait......so "follows" means "to result from"? So "chess is a draw" results from the opinions of world champions? What if there were no tournaments and no world champions? Would this mean chess was not a draw? What if chess were just invented and all you had to go on was the rules and none of your 6 points existed? Would this change your belief about chess being a draw?
@5971
"What if chess were just invented and all you had to go on was the rules and none of your 6 points existed?" ++ Then we would not know. In the previous century Rauzer believed 1 e4 wins and Berliner believed 1 d4 wins. Thanks to all the accumulated evidence from humans and computers we now know chess is a draw.
@tygxc "knows" chess is a draw.
Steinitz "knew" he could beat God even if he gave him pawn and move.
"Knowing" is a state of mind, NOT a state of fact.
@5963
About 1b TCEC: of the 50 imposed slightly unbalanced openings:
19 worked as intended: a win and a draw
22 lead to two draws: not unbalanced enough
9 lead to a win and a loss: too unbalanced
If they would not impose unbalanced openings, they would have all draws.
All draws, just like the second batch of games I posted, which start from a theoretically won position.
I suppose you would say the first batch, again from a theoretically won position is unbalanced because only eleven of the twelve were drawn.
Incidentally when are you going to post your calculations to determine the theoretical results of those positions and the number of errors in the games. If you do that we can all talk about sensible things.
@5975
"Knowing is a state of mind, NOT a state of fact."
++ Believing is a state of mind, knowing is objective.
Knowledge = understanding gained by actual experience; range of information;
clear perception of truth; something learned and kept in the mind.
Chess is a draw results inductively from millions of human and engine games and deductively from equal material and position in the initial position and from 1 tempo = 1/3 pawn being unable to queen.
This peer reviewed paper has knowledge in its title:
https://arxiv.org/abs/2111.09259
@5974
I think people underestimate the effect that hundreds of thousands of top class players have imposed, when they analyse the opening position to the best of their ability. I fully believe that their combined efforts is sufficient to fully confirm my belief that it's drawn by best play.
I accept that you "fully believe..." but I do not accept that all these top class players have any effect on the solvability of the game, nor that their opinions do anything other than convince other humans. When chess was invented and the rules were agreed on, at that moment it was either solvable or not. No human knew then whether it was solvable, and despite the strong opinions that exist, we are debating whether any human knows now.
This peer reviewed paper has knowledge in its title:
https://arxiv.org/abs/2111.09259
So does this one.
They have about the same relevance to the topic.
Incidentally when are you going to post your calculations to determine the theoretical results of these positions and the number of errors in the games. If you do that we can all forget about your proposals and talk about sensible things.
@5980
"I do not accept that all these top class players have any effect on the solvability of the game"
++ That is right: the game was created a finite game and thus was solvable on its creation.
That leaves 3 questions:
To answer question 1 we need experience and information. These are millions of human and engine games and also the obseration that the initiative of 1 tempo in the initial position is worth 1/3 pawn and thus not enough to win.
To answer question 2 we must determine the number of relevant positions: 10^17.
To answer question 3 we must determine the number of relevant positions: 10^44.
"distinguishing between overwhelming evidence and proven fact"
proof = evidence compelling the mind to accept a truth or fact
@5982
proof = evidence compelling the mind to accept a truth or fact
Whose mind? There are millions of people who feel there is plenty of evidence to prove there is a God who created the universe, and millions of people who don't. So maybe for some of us, chess is provable and for some, it's not...depending on whether you find the evidence compelling? Well, that would explain the lack of consensus. 
So maybe chess is a matter of faith rather than mathematics?
Whose mind? There are millions of people who feel there is plenty of evidence to prove there is a God who created the universe, and millions of people who don't. So maybe for some of us, chess is provable and for some, it's not...depending on whether you find the evidence compelling? Well, that would explain the lack of consensus.
So maybe chess is a matter of faith rather than mathematics?
It's a matter of faith if one believes a forced draw is proven 
...
@5975
"Knowing is a state of mind, NOT a state of fact."
++ Believing is a state of mind, knowing is objective.
Unquestionably (by unlimited examples), "knowing" defined by "a person claiming they know" indicates a state of mind.
Epistemologically, sometimes the claim is dead wrong, sometimes it is a good bet but not certain, and sometimes it is justified. It is fair to say that in the first two cases the term is being misused by the person concerned.
Your example falls into the middle category.
Incidentally, everyone who has an understanding of how machine learning, reinforcement learning and AlphaZero work also knows that the "knowledge" acquired by AlphaZero and referred to in the paper title is inductive in origin and uncertain in character. Indeed, it is explicitly uncertain, in that AlphaZero expresses its knowledge about positions in the form of an array of probabilities.
@5982
proof = evidence compelling the mind to accept a truth or fact
Whose mind? There are millions of people who feel there is plenty of evidence to prove there is a God who created the universe, and millions of people who don't. So maybe for some of us, chess is provable and for some, it's not...depending on whether you find the evidence compelling? Well, that would explain the lack of consensus.
So maybe chess is a matter of faith rather than mathematics?
Exactly the kind of "knowledge", "belief" and "certainty" that permeates a lot of the arguments here. Human history is replete with examples from every field of inquiry of consensus (or even unanimity) of authoritative "knowledge" that has upon discovery of new facts proved to be hilariously mistaken.
Reliance on the many millions of existing chess games, opinions of world champions, results from the best machines currently existing and the like will never yield a definitive solution. My contention is that only an examination of every possible line of play from the opening position, and every possible reply at every move can lead to an unassailable conclusion.
And saying such an endeavor is forever impossible because we do not presently possess the means to conclude it within a time frame humans can comprehend also relies too greatly on our present understanding being all-encompassing.
@5975
"Knowing is a state of mind, NOT a state of fact."
++ Believing is a state of mind, knowing is objective.
That's incorrect, since we believe that we know things. For our minds, there's no such thing as objectivity. Merely the attempt to be objective.
Of course this is true. To quote the Firesign Theater--"How do we know? How can we ever REALLY know for SURE?" But a certain amount of agreement between people on the nature of "reality" is necessary for there to be any discussion of any subject.
Incidentally, everyone who has an understanding of how machine learning, reinforcement learning and AlphaZero work also knows that the "knowledge" acquired by AlphaZero and referred to in the paper title is inductive in origin and uncertain in character. Indeed, it is explicitly uncertain, in that AlphaZero expresses its knowledge about positions in the form of an array of probabilities.
I'm glad you're admitting that but it does lessen the impact of your previous arguments, made when I was explaining that point to you, regarding certainty!
Not the ones I actually made rather than you misremember! I guarantee you will not be able to find an example and post it here.
I hope everyone realizes that my post 5985 was irony.....making a serious point, but not in a serious way. No, I don't believe chess is a matter of faith!
@5980
"I do not accept that all these top class players have any effect on the solvability of the game"
++ That is right: the game was created a finite game and thus was solvable on its creation.
Chess is about 1500 years old, the 50 move rule was introduced about 550 years ago and an n-fold repetition rule only about 200 years ago, so chess was not created a finite game. It was nevertheless solvable and almost certainly solved on its creation according to any of the definitions of solved you have so frequently posted.
That leaves 3 questions:
To answer question 1 we need experience and information. These are millions of human and engine games and also the obseration that the initiative of 1 tempo in the initial position is worth 1/3 pawn and thus not enough to win.
To correctly answer question 1 we need proof. (You still haven't answered my question whether the 1/3 pawn you refer to is by weight or volume.)
To answer question 2 we must determine the number of relevant positions: 10^17.
Again you use "relevant" without saying to what. Your concept of "position" (a basic rules game state) may or may not be relevant to weakly solving competition rules chess, depending on the method of solution. It may not be necessary to determine even the number of game states. Certainly your concept of "relevant" is irrelevant to any solution (as is 10^17).
To answer question 3 we must determine the number of relevant positions: 10^44.
Again depending on the method of solution. My previous paragraph applies just as well here, mutatis mutandis.
"distinguishing between overwhelming evidence and proven fact"
proof = evidence compelling the mind to accept a truth or fact
Er, what mind?
Incidentally when are you going to post your calculations to determine the theoretical results of these positions and the number of errors in the games. If you do that we can all forget about your proposals and talk about sensible things.
. My contention is that only an examination of every possible line of play from the opening position, and every possible reply at every move can lead to an unassailable conclusion.
That's exactly how I see it.
@5992
"Reliance on the many millions of existing chess games, opinions of world champions, results from the best machines currently existing and the like will never yield a definitive solution."
++ But you cannot discard all that knowledge either and make foolish claims like 1 a4 wins, 1 e4 e5 2 Ba6 wins, 1 d4 loses etc.
"only an examination of every possible line of play from the opening position, and every possible reply at every move can lead to an unassailable conclusion"
++ That would be strongly solving chess.
Literature recognises weakly solving. Checkers, Losing Chess, Connect Four, Nine Men's Morris have all be weakly solved. You cannot impose more stringent criteria on Chess.
Literature also recognises it beneficial to incorporate knowledge in weakly solving a game.
So, cause and effect? Computers drawing 63 out of 100 games causes the result to become a draw?
To be frank, your repetitive nonsense is getting boring.