Chess will never be solved, here's why

I'll try to explain it. You're a statistician and therefore accustomed to dealing with sets of events in the "macro". Considering a unique event, you will tend to see its outcome "a" or outcome "b" probabalistically, since as a unique event but still an event which is viewed in the context of the set, superficially outcomes a or b follow probability patterns. Within the context of the set, viewing all the events as a whole, each unique event is simply part of this or that subset as part of a statistical pattern. That tells us nothing about the event itself.

Bayesian probability is about the state of belief in a proposition that is uncertain (cannot be deduced by Boolean logic from the known information). It is well-known to be fully suited to dealing with samples of one, using all the inductive power available and no more.

An outcome on the chess board may be considered to have a definite result with best play: but it is one that may be unknown.

Correct. That is a situation where one wishes to quantify belief, and the only consistent way to quantify belief is Bayesian probability.

All probabilities that are assigned to it are therefore the result of guesswork based on inductive reasoning.

This is an inconsistent sentence.

The prior is the only thing that could be described as "guesswork" (though you would not use this word if you were familiar with the work in the subject, which often gives an answer to "what is the appropriate prior?".  And of course, inductive reasoning has no element of guesswork. Fundamentally it is the correct application of Bayes rule (difficult as this may be to formalise in a specific example).

That is effectively equivalent to basing them on error limits.

This is an incorrect comparison to something you are familiar with from frequentist statistics.
Anyway, that's my thinking. 

"information on the strength of the two players"
++ No, that is not relevant. I take a sufficiently large tournament with a sufficient number of players of sufficient quality and then apply statistics to that. The last ICCF WC is suitable as well as Zürich 1953. From the statistics follows that only chess is a draw is consistent with the observed data and follows the number of games with no errors: 127 for the ICCF WC and 74 for Zürich 1953.

It is relevant because it is available information that definitely affects the rate of errors. Weaker players make more errors. Players playing against stronger players make more errors (because stronger players are so because they provide more opportunities for the opponent to make errors). The only question is how relevant it is. Undoubtedly, like most things, you would be keen to make an absolute proclamation about this without any quantitative reasoning.

Although we may not have quite hit it off immediately, because you don't like my terrible ego, nevertheless I'm glad that you are enjoying these interesting things. I've had a difficult day, including a business trip, by car, with a person who was driving and shouting at all the traffic for 150 miles. It wasn't easy and so thankyou for your calmness and friendliness.

@4502

"why you think that ICCF games can be proven to be of sufficient quality"
++ A World Championship Finals, 17 ICCF (grand)masters with engines, 50 days / 10 moves.

"why ICCF games have reached some "quality" threshold that is absolute"
++ There is no such threshold.
Take the 1953 Zürich Candidates' Tournament:
210 games = 118 draws + 49 white wins + 43 black wins
Assume chess a draw.
Fit a Poisson distribution so the probability of an odd number of errors is (49 + 43) / 210.
Result: mean value = 1.044 error / game.
Games with 0 errors: 74
Games with 1 error:  77
Games with 2 errors: 40
Games with 3 errors: 14
Games with 4 errors:  4
Games with 5 errors:  1

Now assume chess is a white or black win.
Fit a Poisson distribution so the probability of an odd number of errors is 118 / 210. 
Result: impossible fit

Conclusion: chess is a draw with best play from both sides.

Thank you. You know, egos are well shared on this page. It’s normal and it doesn’t bother me at all. The important thing is to turn the pages and that, like you, I also know quite well how to do it.

A false positive result, sadly.  You'll find that out eventually if you disagree on other occasions.

You know, you can’t just look at the negative:
If I disagree I simply express it. But, as in chess, everyone can be mistaken. And in the next game, we fix to improve.
This is what interests me in Life, as in chess.
Yours truly

me just wondering what will fools arguing on the thread getting by posting lakhs of passages to someone who will not listen?

The fact that it's inconsistent with your own thoughts on the matter is no proper argument against.

@4523

"you cannot determine what is actually an "error" with certainty."
++ An error (?) is a move that changes the game state from draw to loss, or from win to draw.
A blunder or double error (??) changes the game state from won to lost.

"You are using engine evaluations of errors to evaluate the absolute accuracy of engines."
++ No, I am not using engine evaluations at all. I am using statistics and probability on a sufficiently large tournament of sufficient level. Is this so hard to understand?

@4524
"It is relevant because it is available information that definitely affects the rate of errors.
Weaker players make more errors. Players playing against stronger players make more errors (because stronger players are so because they provide more opportunities for the opponent to make errors). The only question is how relevant it is."
++ All of that is true, but not relevant.
At Zürich 1953 they played at 1 error per game, Smyslov less and Stahlberg more.
In the 30th ICCF WC Final Kochemasov played 16 error-free games, and Stephan made 3 errors.
Relevant is that only chess being a draw is consistent with the observed data and
that in Zürich 1953 74 error-free games were played and in the 30th ICCF WC Final 127.

"an absolute proclamation about this without any quantitative reasoning."
++ I am the only one here to present quantitative reasoning.
Others make absolute proclamations without any reasoning, quantitative or qualitative, at all.

@4534
"you cannot claim that something changes the "game state" when you are trying to prove said game state evaluation is correct in the first place"
++ You still do not understand.
I need no game state evaluation.
If chess were a white or a black win,
then every draw would contain an odd number of errors that change the game state.
If chess is a draw,
then every decisive game contains an odd number of errors that change the game state.
With only that I apply statistics to a sufficiently large tournament of sufficient level.

@4535
"You don't know how many errors were in any of those games."
++ Yes, I know that from statistics and probability.

I know with > 99% certainty that Kochemasov made no error in the 30th ICCF WC Finals.
I know with > 99% certainty that all 9 decisive games contain exactly 1 error.
I cannot tell which move was the error, though it usually is the last move.

I know there were 74 games with no errors, 77 with 1 error, 40 with 2 errors, 14 with 3 errors, 4 with 4 errors and 1 with 5 errors in Zürich 1953, but I cannot tell which moves in which games.
I know they made on average 1 error / game, Smyslov less and Stahlberg more.

"You only know that various moves have been evaluated as suboptimal play, by suboptimal evaluations." ++ No, I use statistics and probability only, no evaluations.