@Elroch just mentioned the word 'inductive'.
When I was taught math - mathematical 'induction' was introduced to me.
Included.
It went (maybe still does) something like this:
(I may not remember precisely. Yes it can be checked.)
And its Rigorous - very strict and very Algebraic ... like math usually is.
First you prove mathematically that an equation is valid for a single constant K.
But one could test that with an actual numerical value of K.
Then you prove it for an algebraic constant K.
Then you prove it - for (K + 1). Again - mathematically. Very strictly.
Algebraically. Not 'extrapolating'.
Rigorously. Airtight. No leaks. No loose ends.
No 'fuzzy stuff' (a no no in math).
And it did not include 'zeroes' at the ends - or division by zero.
Which is something special.
Then you can rewrite (K+1) as a new constant. Call it C.
Then you have the process under way.
Induction (but with very Strict mathematics) -
that the process could be extended indefinitely to ever-increasing values of the 'constant' you are applying to the 'pure mathematics' equation.
But that is not what @tygxc is doing. He's doing something else.
Chess will never be solved, here's why
#2152
About your objectivity and honesty, then, maybe you want to comment this excerpt from the very paper on checkers you cited so much:
"With checkers done, the obvious question is whether chess is solvable. Checkers has roughly the square root of the number of positions in chess (somewhere in the 10⁴⁰ - 10⁵⁰ range). Given the effort required to solve checkers, chess will remain unsolved for a long time, barring the invention of new technology."
That was in 2007. The 10^40 - 10^50 range is no longer valid.
The papers by Tromp (10^44) and Gourion (10^37) are from 2021.
In those 15 years also computers have become faster and chess engines better, now 10^9 nodes/s.
Also progress has been made on the 7-men endgame table bases.
Most of the effort of Schaeffer was related to building his endgame table base.
Schaeffer himself also said:
”The one thing I’ve learned in all of this is to never underestimate the advances in technology”
https://webdocs.cs.ualberta.ca/~jonathan/publications/ai_publications/checksolved.pdf
final line
”The one thing I’ve learned in all of this is to never underestimate the advances in technology”
https://webdocs.cs.ualberta.ca/~jonathan/publications/ai_publications/checksolved.pdf
final line
That's not a retraction and improvements in these 15 years are not a breakthrough. Cloud computing is nothing so special, but you can notify him of these advances, had he missed them. 
#2142
I am the only one providing information on the subject of solving chess and backing it up with facts and figures.
Lie 5. Basically all the others have provided informations on solving chess and have backed them with facts and figures, as you like to say like a mantra, and anyone who cares to read the posts on this thread can verify that by herself. Providing more facts, and more inaccuracies too (to use an euphemism), and link them with analogical more than logical thinking does not make you any better. If you are proven to be the only one about something, is in having such an inflated ego.
Apparently you know no great deal about mathematics. That is fine, no problem, but it is not fine that you accuse me of lying because you do not understand.
I was about to say the same about you, but I prefer to refrain from using arguments like "mine is bigger than yours", as it can be biasing. Apparently, though, none here but you knows a great deal about mathematics, since they reject most of your figures.
About your objectivity and honesty, then, maybe you want to comment this excerpt from the very paper on checkers you cited so much:
"With checkers done, the obvious question is whether chess is solvable. Checkers has roughly the square root of the number of positions in chess (somewhere in the 10⁴⁰ - 10⁵⁰ range). Given the effort required to solve checkers, chess will remain unsolved for a long time, barring the invention of new technology."¹
But surely you know about computer science and mathematics more than Schaeffer and the others, too.
¹ https://www.researchgate.net/publication/231216842_Checkers_Is_Solved page 4 last paragraph.
I find myself agreeing with that post by @haiaku
'Lie 5' means there were four other lies by ... ??
@tygxc claiming he is the 'only one' providing facts and figures ??
Lol !! ..... 
I am referring to posts here. As opposed to being 'personal'.
'Lie 5' means there were four other lies by ... ??
I am numbering them from post #2140, but beware for future reference, because I think post numbers change if someone deletes one or more of them.
#2143
Of course I gave the position as it is, with ply count 0 to start with.
The position as it is has ply count 100. There is no such thing as "the position as it is, with ply count 0". That illustrates exactly what I meant by "a total lack of comprehension of how the rules affect either SF14 or the game results".
There is no point in discussing a position with circumstances close to the 50-moves rule that do not happen.
Do not happen where?
Look at the ply count in the final position.
I still challenge you to show me one grandmaster game or ICCF game where the 50 moves rule was invoked before the 7-men table base was hit.
I bet there is none, but I cannot prove the non existence of such a game.
You won't find any recorded grandmaster or ICCF games played under the rules of the game you are now proposing to solve (current basic rules + two and a Schrödinger's half fold repetition rule) and of course neither will I.
If I could, they would have no relevance to your solution anyway, because your system of takebacks, to be a proof, needs to examine all alternative moves from positions proven to be drawn (not just the four SF14 recommended moves, none of which may be perfect - as in the example under discussion).
If the starting position is really drawn, this will result in positions with eeenormous ply counts under the game you now (as opposed to when the thread started) propose to solve.
Usually - at a moment of confrontation like this -
@tygxc might 'bob and weave'. Post another series of figures perhaps.
I know of another person like this. But much more sophisticated (no not anybody posting here - no not named). Very fancy footwork.
'Lie 5' means there were four other lies by ... ??
I am numbering them from post #2140, but beware for future reference, because I think post numbers change if someone delete one or more of them.
They do indeed - if any post is deleted then renumbering occurs on all subsequent posts.
But this 'five' number is interesting to me.
Deserves more attention in this context.
#2159
"There is no such thing as "the position as it is, with ply count 0"
++ Please present the position right after the last capture or pawn move, i.e. when the count to 50 starts. There is no point in discussing a position that has been botched by near 50 bad moves.
"Anna Ushenina (2491) vs. Olga Girya (2463)"
++ It is an embarrasment she could not checkmate KBN vs. K. The position was an elementary win, one of the 5 basic checkmates. It has no relevance to solving chess.
"You won't find any recorded grandmaster or ICCF games played under the rules of the game you are now proposing to solve and of course neither will I."
++ I still challenge you to show me one grandmaster game or ICCF game under any rules of the game (competition rules, or ICCF rules) where the 50 moves rule was invoked before the 7-men table base was hit. I bet there is none, but I cannot prove the non existence of such a game.
"your system of takebacks, to be a proof, needs to examine all alternative moves from positions proven to be drawn (not just the four SF14 recommended moves, none of which may be perfect - as in the example under discussion)."
++ I presented an argument why the 4 top white moves suffice. If you disagree, then please present a counterexample where the table bases correct move is not within the top 4 moves: a counterexample starting right after a pawn move or a capture, not after the position has been messed up by a series of near 50 bad moves without pawn move or capture.
"From positions that are really drawn, this will result in positions with eeenormous ply counts under the game you now (as opposed to when the thread started) propose to solve."
++ I dispute that. In practice chess games end or reach a table base in under 100 moves. Present me one grandmaster or ICCF game (under competition rules or ICCF rules) where the 50 moves rule was involved before the 7 men table base was hit. I cannot prove the non-existence of such a game. I bet you cannot find one. If the 50 moves rule is not involved before the 7-men table base is hit, then your competition rules (with 50-moves rule and 3-fold repetition rule) are identical to ICCF rules (50-moves rule only before the table base is hit and 3-fold repetition rule).
3-fold repetition or 2-fold repetition or 5-fold repetition is the same in principle. It is just a few repetitions added. If the optimal move is to repeat a position twice, then the optimal move is also to repeat 3 times, and also to repeat 5 times.
#2152
"As a mathematician (well, long ago my two degrees were in maths) I observe that your posts are characterised by taking an unmathematical approach, more akin to someone playing chess than someone proving a mathematical result."
++ Well then maybe you can explain to the non-mathematicians the solution to the problem:
given data points (0, 1), (1, 0.118), (60, 0.021), (oo, 0)
find the data point (60*3600, ?)
The non-mathematicians seem unable to understand my explanations.
#2152
"As a mathematician (well, long ago my two degrees were in maths) I observe that your posts are characterised by taking an unmathematical approach, more akin to someone playing chess than someone proving a mathematical result."
++ Well then maybe you can explain to the non-mathematicians the solution to the problem:
given data points (0, 1), (1, 0.118), (60, 0.021), (oo, 0)
find the data point (60*3600, ?)
The non-mathematicians seem unable to understand my explanations.
@Elroch already told you what he thinks about your reasoning on the matter. Your conceit in believing that none before you, in history, have faced the problem of how many events of a kind occur in a fixed interval of time, or did discover any better formula than yours, speaks volumes about your background in mathematics. And your hubris in inferring people's background from the fact that they consider crap your formulas and calculations is astonishing.
I wonder if @tygxc is going to let anybody in the forum tell him anything at all.
Has there even been one instance of that ?
Nobody has to take that seriously though.
I've seen a certain situation on the site though -
where various people only allow printed matter on another website to tell them something.
Since its printed text that's being read where the author or person who has typed the text - doesn't know who's reading it ...
then the person who reads it and then regurgitates it here because he's being told what he wants to hear ....
doesn't have to feel that somebody told him something !
He or she 'selects' rather than being told.
#2152
"As a mathematician (well, long ago my two degrees were in maths) I observe that your posts are characterised by taking an unmathematical approach, more akin to someone playing chess than someone proving a mathematical result."
++ Well then maybe you can explain to the non-mathematicians the solution to the problem:
given data points (0, 1), (1, 0.118), (60, 0.021), (oo, 0)
find the data point (60*3600, ?)
The non-mathematicians seem unable to understand my explanations.
There are non-mathematicians and non-mathematicians.
You are obviously one of the latter.
Given the unproven assumption that chess is a draw you arrive at the question
given data points (0, 1), (1, 2n+1 x 0.118), (60,2n+1 x 0.021), (∞, 0)
find the data point (60*3600, ?)
The last of the data points being obviously quite meaningless and the first presumably based on the further unproven assumption that all moves from any position are errors.
You then, based on the further unproven assumption that 2n+1=1 for any value of n, decide it actually means
given data points (0, 1), (1, 0.118), (60, 0.021), (∞, 0)
find the data point (60*3600, ?)
Of course, since the last data point is still quite meaningless, the question is still quite meaningless.
If you remove the last data point, there are rather a lot of answers you could get as @llama51's video points out here.
Wolfram gives you a nice little widget for finding the best fit on certain assumptions.
So you can choose an unproven assumption and decide which you like best.
Linear:
Quadratic:
Exponential:
Trignometric.
I would go for exponential if I were you. It's practically zero at zero think time, so you could probably have it all solved on your desktop by next week. Re-lease the supercomputers and make a tidy little profit.
If you still can't understand it all, don't get too downhearted. You could probably do well as a stand up comic. It doesn't need any maths at all.
Regarding mathematical induction apparently the famous French mathematician Pascal was a pioneer of it in the 1600's.
Then there was the Swiss. Bernoulli a bit after Pascal.
Then there was Boole - much later. After whom 'Boolean' is named.
Here's the link to the Wiki article
https://en.wikipedia.org/wiki/Mathematical_induction
there are many web articles about mathematical induction.
But its not like getting 'Made' in the Mafia !
Induction in math has strict mathematical rules.
Point: @tygxc could look up mathematical induction himself -
and try and understand it properly - instead of continuing with invalid 'extrapolations'.
He's not going to let anybody here tell him ... but if its a website he might catch on.
#2166
"There are non-mathematicians and non-mathematicians.
You are obviously one of the latter."
I am pretty sure I know more about mathematics than any of you, including the man with the 2 degrees.
Mathematics has since ancient times been applied to solve all kinds of problems, not to demonstrate that nothing can be concluded.
Induction and deduction are the two main pathways of any science.
Do you really think any of your 4 curves represents the fraction of decisive games versus time?
Coming back to deriving the error rate E from the fraction of decisive games D, it is obvious that E =~D provided D is small enough.
Proof:
At 1 min / move the paper gives D = 0.021.
Under the generally accepted hypothesis that chess is a draw a decisive game contains an odd number of errors.
Thus
D = E + E^3 + E^5 + E^7 + ... = E / (1 - E^2)
Thus
E^2 - 1 + E/D = 0
Thus
E = sqrt ((1 / 2D)^2 + 1) - 1 / 2D
Keying in
D = 0.021
yields
E = 0.020990747
Thus E =~D
quod erat demonstrandum
#2166
"There are non-mathematicians and non-mathematicians.
You are obviously one of the latter."
I am pretty sure I know more about mathematics than any of you, including the man with the 2 degrees.
Mathematics has since ancient times been applied to solve all kinds of problems, not to demonstrate that nothing can be concluded.
Induction and deduction are the two main pathways of any science.
Do you really think any of your 4 curves represents the fraction of decisive games versus time?
Coming back to deriving the error rate E from the fraction of decisive games D, it is obvious that E =~D provided D is small enough.
Proof:
At 1 min / move the paper gives D = 0.021.
Under the generally accepted hypothesis that chess is a draw a decisive game contains an odd number of errors.
Thus
D = E + E^3 + E^5 + E^7 + ... = E / (1 - E^2)
Thus
E^2 - 1 + E/D = 0
Thus
E = sqrt ((1 / 2D)^2 + 1) - 1 / 2D
Keying in
D = 0.021
yields
E = 0.020990747
Thus E =~D
quod erat demonstrandum
We just got this:
"I am pretty sure I know more about mathematics than any of you, including the man with the 2 degrees."
Lol ! 
Does that define that issue - and 'translate' about 200 posts by a particular member here (not I)?
Nothing personal - but is that the 'Rome' of all those posts ?
(saying: 'all roads lead to Rome'. And Rome of course - had an Emperor.)
If that remark (by another member) that I have quoted in italics - was posted to 'get attention' - it should ! It should get attention. Much.
another saying: "the truth will out."
With 'out' acting as a verb there.
In reality - the truth doesn't always emerge - but it often does !
Can take a while though.
Repeat: Somebody (not I) - just posted in a very recent post:
"I am pretty sure I know more about mathematics than any of you, including the man with the 2 degrees."
Here's where I stand. A chess engine may be able to solve chess in the far distant future, but why does it matter? At this point, we have engines capable of playing near-perfect games, millions of times better than any human could dream of achieving. I don't see many major improvements that could be made at this point. As far as I'm concerned, chess may not be absolutely solved, but it is effectively solved.
Here's where I stand. A chess engine may be able to solve chess in the far distant future, but why does it matter? At this point, we have engines capable of playing near-perfect games, millions of times better than any human could dream of achieving. I don't see many major improvements that could be made at this point. As far as I'm concerned, chess may not be absolutely solved, but it is effectively solved.
Good post.
Why does it matter ?
I've got a response ! In the form of a suggestion.
It Doesn't ! It Doesn't Matter.
Its being talked about though.
A lot of things are.
In these public forums - subjects that truly 'matter' and in a very compelling way - well many of those subjects aren't allowed by the management in public forums here - and rightly so.
Its a chess site ?
Yes. But chess isn't just a game - it has a 'community aspect'.
Its a social activity among many other things.
Is all this pingpong regarding responding to @tygxc ...
actually preventing the forum from discussing both strong solving and its difficulties - and alternative chess projects for the supercomputers and engines ?
Maybe - maybe not.
Anyway - he can keep proclaiming week in and week out that he copied figures from somebody else. Accuse others of not doing so - while they use his own figures to challenge and expose the illogics ...
That could be expected.
And that will probably occupy 80% of postings here.