Chess will never be solved, here's why

Both (for the first, I mean specifically that errors may depend on the position), and of course I agree with you, but @tygxc must agree with himself . As for A0 and SF, I think he thinks that his concept can be extended virtually to any top engine.

Hi alex.   Biggest mistake in chess - failing to distinguish observation (looking) from calculation (comparing carefully considered sequences of moves)  (leads to deficiency in observation - which is a Trainwreck)
but there are lots of other mistakes ...
including not studying mistakes.
One wins by not making mistakes.
You won't beat your opponent if he doesn't make a big enough mistake ...
is an 'operating basis'.  But he won't beat you either - if you don't.
Its even discussed in this forum - a position that the game ends in a draw if nobody makes a mistake in the game.  (the "pure" version of it)
In actual games - more realistic is that a game ends in a draw if nobody makes a big enough mistake.

the first 'pure' one has never been proven -  but appears to be a good practical approach for developing players ...

And regarding the fundamental errors that seem to be recurring in @tygxc 's post for months now ...
at least three other posters besides myself - or more like four others ...  seemed to have also noticed the misuse and invalid premises within the extrapolations being asserted by @tygxc ...
and they're articulating it well.  Technically as well as generically.

'But @tygxc 'must agree with himself' '...  Lol hahhahahahahahah
'must agree with himself' ...
perhaps a good plain-english way of referring to something called ...
'cognition bias'?

If I flip a coin once - and it lands perfectly heads ...
does that mean I know to within one billion trillionth of accuracy as to what happened when four coins were flipped many Deca-Drillions of times - how many stayed on their edge?
How does he get a 'heads up' on this ?

Difficult to tell whether you're being funny intentionally or not.

Of course extrapolating from known values for 3, 4, 5, 6 and 7 men that lie on a straight line to 32 men (over 3 times the range covered by the known values) is very unreliable.

Haworth himself doesn't venture a prediction beyond 10 men.

How does that make calculating from two values on an undetermined curve to something 1800 times beyond the range covered reliable? (Especially when the two values turn out to be wrong if you actually measure and the resulting prediction obviously wrong if you try sampling.)

#2624

"Two of them depend on whether the 50 move rule is in effect."
++ That is why those 2 positions are not relevant.

"How can you say the positions don't depend on whether the 50 move rule is in effect and then in the same sentence say you're not prepared to consider them because they're close to triggering the 50 move rule?"
++ Because we are discussing solving chess i.e. from the initial position and not from an artificially constructed position devised to trigger the 50-moves rule.

"If you're not doing a takeback you have to consider all possible opponent responses."
++ I can prune to reasonable responses. I do not have to consider 1 e4 e5 2 Ba6.

"The result is your process will spend most of its time shuffling with bad moves."
++ No, on the contrary, by limiting to top 4 white moves I prune bad moves and save time.

"How do you justify your assertion that the positions your process will actually reach are irrelevant?" ++ No, on the contrary: I intend my process to reach relevant positions only.

"What happens in practice is not relevant."
++ Per my calculation 99% of ICCF draws are ideal games with optimal play.
What happens in those games is most relevant, as these are part of the weak solution of chess.

"Practical players cannot usually prosecute mates of depth 50 or more unless their opponent is weaker or the mates have been analysed to that depth and they are conversant with the analysis."
++ ICCF grandmasters with their engines can.
Even unaided humans can reach depth 20-30 in a few hours. I gave 2 examples.

"This is already the case with five men on the board. It applies more as the number of men increases."
++ 5 men is not relevant: the process has looked it up before in the table base when it was 7 men. 7-8 men is relevant as it is the boundary between the 7 (or partial 8)-men table base and the region 26-8 men of interest.

"Some people don't believe such positions exist with 8 or more men on the board even when they're shown examples."
++ They do exist, but are not reachable from the initial position by a game with > 50% accuracy. For example the long checkmate in the position with 2 dark square bishops cannot be reached with > 50% accuracy.

"but reserves the right to change the ply count in any such positions posted"
++ Yes, that is right: let us discuss positions right after a capture or a pawn move,
so that the 50-moves counter and the 3-fold repetition counter are reset to 0.

"I.e. ambivalent about whether the 50 move rule will be included in the rules of the game he attempts to solve."
++ No, not ambivalent. The rule is not invoked in ICCF WC draws, so it can be ignored.

"Your procedure won't be playing ICCF games; not even the same rules unless you've got another variation in your proposed game."
++ It does not matter: ICCF rules or standard rules. ICCF rules are more decisive as they allow 7-men table base win claims, but such claims do not happen, so it is the same as if such claims were not allowed.

"I already gave you two in different endgames." ++ No, none is relevant.

"You can definitely assume your computation won't spend all its time in KRPP v KRP."
++ Most of the time it will reach KRPP vs. KRP. Some other endgames like queen endings, minor piece endings, pawn endings are more decisive and thus unlikely to occur. Opposite colored bishop endings are likely to occur, but drawish and of less interest. Endings with more than 1 pawn imbalance are unlikely to occur.

"But if you're trying to prove a solution the question of SF14's top 4 moves is irrelevant."
++ If the 4 best moves cannot win, then the bad moves cannot win either: the bad moves are irrelevant.

"There need not be more than one good move"
++ Yes, that is right. As long as the one good move is within the top 4 all is right.

"none of the good moves need be in SF14's list"
++ My extrapolation from AlphaZero autoplay shows that at 60 h/move of AlphaZero the good move will not be among the top 4 moves in 1 position out of 10^20.
So far no counterexample has been found where the table base exact move in a 7- or 8-men position does not correspond to even the desktop top move at minutes/move.
The rule of top 4 also coincides with what Carlsen said in an interview: that he looks at 3 candidate moves.
The rule of top 4 also coincides with accumulated opening knowledge by humans and AlphaZero, e.g. that 1 e4, 1 d4, 1 c4, and 1 Nf3 are the top moves, that 1 e4 e5, 1 e4 c5, 1 e4 e6, 1 e4 c6 are the 4 top moves etc.

"So when Black looks up 1.a4 in your solution what will he see?"
++ Black sees nothing. But on request and following the same procedure as for 1 e4, 1 d4, 1 c4, 1 Nf3 the same solution can be generated on demand and the outcome is clear before it is done.

I can reach depth 20-30 in less than a minute. One crappy but legal line ticks the box.

Perhaps you don't know that sample lines don't provide reliable analysis - this seems highly likely since you refer to "unaided humans", never mind engines that only investigate a larger sample.

#2625

"https://arxiv.org/pdf/1712.01815.pdf , page 5 second paragraph. There, they say 80000  positions per second vs. 7 × 10⁷, in another paper 60000 vs. 6 × 10⁷, but the ratio is nonetheless roughly 1/1000, as for Lc0 compared to SF on the same hardware."
++ I still do not know the nodes/s of AlphaZero in the paper I used figure 2 of to extrapolate the time for the top 4 moves. If we assume it was 80000 nodes/s just the same, and if we convert this from the thick nodes of AlphaZero to the thin nodes of Stockfish, then that would yiels 80 * 10^6 nodes/s on Stockfish. That means on a 10^9 nodes/s cloud engine instead of 60 h/move only 17 s/move would be enough to guarantee that the optimal move is within the top 4.

"You used also time * 60 = 5.6 times less decisive games, and time * 60 = error / 5.6"
++ I use = as shorthand for means, or yields, or signifies.
I probably should not do that and apologise for any confusion this may have caused.

"given 60 times more time, the error rate is reduced by a factor 5.6"
++ Yes, that is the correct formulation

"From two points you can obtain its parameters"
++ It is even 4 points: with unlimited time all legal positions can be exhaused, chess strongly solved and the error rate is 0.
With zero time, no correct move can be produced and thus the error rate is 100%.
So an exponential decay of error over time is the only mathematics model that makes sense and the 2 points are enough to estimate its 2 parameters.

"you should prove that errors are really statistically independent"
++ If the error rate is low enough, errors do not occur in multiples and thus are statistically independent

#2627
"As for A0 and SF, I think he thinks that his concept can be extended virtually to any top engine."
Yes in principle any top engine will do. However, as the aim is not to play strongly in short time, but to calculate all the way to the endgame table base, an engine with thin nodes and more nodes/s like Stockfish is preferable.

All of your analysis is how to probably play good chess, not how to SOLVE chess.

#2634
"All of your analysis is how to probably play good chess, not how to SOLVE chess."
To solve chess is to play very, very good chess such that none, present or future, plays better.

If you literally mean it hasn't got time to produce a move, then it cannot produce an error, so the error rate is 0% (cough).

If, on the other hand, you mean it hasn't got time to evaluate a move before making it then the error rate should be well under 50%. The great majority of positions have a large material difference and in such positions it is usually impossible for either side to make an error.

How would either side to move make an error from this random board layout for example?

But where have you used this value anyway? 

You seem to have added it solely to disguise the fact that you're extrapolating from two figures to a point 1800 times removed from the range that includes the figures.

#2632

"I can reach depth 20-30 in less than a minute."

I repost:

unaided human GM A. Kotov over the board 2.5 h / 40 moves: 21 moves deep
https://www.chessgames.com/perl/chessgame?gid=1084375

unaided human second B. S. Vainstein during overnight analysis of adjourned game KRPP vs. KRP 41 moves deep
https://www.chessgames.com/perl/chessgame?gid=1033779

This makes it plausible that 10^9 nodes/s cloud engines can indeed in 5 years calculate the whole of chess 39 moves deep.

Check my post here

Maybe, but an exponential decay over time would have this form (using your symbols, but t for time)

error = a e⁻ᵇᵗ

If. But in your assumptions a draw occurs if an even number of errors occur and (always in your assumptions) the total probability that an even number of error occurs is (using mostly your notation)

E₀ + E² + E⁴ + ...

Where with E₀ I'm representing the probability to have 0 errors. The probabilities have those expressions because you suppose the errors statistically independent (check the end of your previous post here). You used an expression like that to deduce that the error rate is low, thus your argument is circular.

No, it isn't.

It is to PROVABLY be able to do so. Not just be confident. Confidence is very cheap in chess.

#2638

"Check my post here" ++ Yes, but that still does not say the nodes/s in the paper I used as reference. Anyway, the previous 60 h/move AlphaZero can be shortened to around 17 s/move on an 10^9 nodes/s cloud engine Stockfish.

"Maybe, but an exponential decay over time would have this form (using your symbols, but t for time)

error = a e⁻ᵇᵗ"

++ That is mathematically equivalent. It is all the same.
Anyway in plain English: 60 times more time gives 5.6 times less error.

"the total probability that an even number of error occurs is (using mostly your notation)

E₀ + E² + E⁴ + ...

Where with E₀ I'm representing the probability to have 0 errors." ++ Yes, that is correct.

"The probabilities have those expressions because you suppose the errors statistically independent (check the end of your previous post here), hence your argument is circular."

++ No, the argument is not circular if the error rate is low.
For a high error rate you could argue that multiples are dependent.
Applied to the ICCF WC I find the decisive games contain 1 error only and the draws contain 0 errors in 99% of cases and 2 errors in 1% of cases.

Applied to the Zürich 1953 candidates with its higher error rate you could argue that there might be some dependence so that the calculation is not completely exact in that case with the higher error rate.

In human play unlike engine or ICCF there are also psychological factors. E.g. I hang a piece, but you may not believe I hang any piece and thus miss the opportunity to win the piece.

#2639
"It is to PROVABLY be able to do so."
++ You seem a bit of a purist regarding proof.
I claim 1 e4 e5 2 Ba6 loses for white.
Do you believe that?
How can I prove it to you?
Do I have to provide all possible variations up to checkmate?
I cannot reasonably do that.
Do you consider it unproven or even false that 1 e4 e5 2 Ba6 loses for white?

#2642

"Unproven certainly. Can't say if it's false until it's proven one way or the other."
++ Purists of all countries, unite!
Will the Sun rise tomorrow? Unproven certainly. Can't say if it's false until it's proven one way or the other. The Sun might get swallowed by a wormhole tonight.
How many humans are there? Unproven certainly. Can't say if it's false until it's proven one way or the other. We cannot count them all and some die and some are born while counting.
Is 1 + 1 = 2? Unproven certainly. Can't say if it's false until it's proven one way or the other. Depends on axioms.
Is the circumference of a circle with radius r equal to 2 pi r? Unproven certainly. Can't say if it's false until it's proven one way or the other. Depends on axioms.

When you offer to solve chess, it means you are offering to produce a proof.

You don't need 3 supercomputers and seven maids to just voice an opinion. 

Sponsors wouldn't be too happy if they played Black and after 1 e4 e5 2 Ba6 your solution said, "don't know, but I can tell you if the Sun will rise tomorrow".

I can help you out here by pointing out that propositions are ALWAYS proved CONDITIONAL on axioms.  For chess, you need to assume which moves are legal, for example as part of your axiom scheme.  Good luck trying without using those assumptions.

Of course with this productive viewpoint, 1 + 1 = 2 is proven and the  circumference of a circle is known to be 2πr, contrary to your (frankly) worthless views above.

@tygxc You say we "gang up", but I cannot but quote @MARattigan and @Elroch. Probably all our knowledge is based on axioms, so whithout digging into epistemology, you have a definition you accepted as a starting point: either you follow that definition, or any theory you may provide about solving chess is about another "solution".