that's Instantly Wrong.
Underpromotion can be done to knight check to get a critical tempo -
either to save one's own skin or to get checkmate or even both.
It can also be done to win material.
'Knowing' about something - having 'facts' - 'peer review articles' ...
without understanding basics of logic and math - with such basics flying right by ... totally missed ... where most people (including pre-teenagers) do grasp or partially grasp. And grasp while remaining unskilled and admitting to themselves and others they're unskilled or without much aptitude or inclination.
Or even admitting they don't get the basics - that they don't understand.
Or - becoming skilled because they tried to grasp the basics - successfully - or did so without effort.
But this is a Very special situation ...
somebody claiming he 'knows more' - while not grasping basics.
There's a saying: "the more he learns the less he knows."
Often happens.
But on this scale?
Chess will never be solved, here's why
#2216
"Pick a random sample of say 10^8 positions with imperfect players and make inference about 10^46 positions."
++ There are only 10^44 legal positions
I acknowledge this typo.
Thus your sample involves uncertain conclusions based on a sample comprising about 1 of each 10^36 positions. It is virtually worthless for drawing conclusions.
and the vast majority of these cannot be reached in a reasonable game with > 50% accuracy.
You know you are guessing wildly. So do we all.
Some of ICCF or even human games may already be ideal games with optimal moves.
So what? Why would you even think this is relevant?
Try to understand post #2205, which explains why a sizeable fraction (probably > 0.1%) of positions with multiple underpromotions probably occur in (game-theoretic) optimal play If you don't understand it, ask. The empirical based intuition should suit your style. You might like to investigate the statistics of the number of legal moves that lead to a given position with drawish evaluation from another with drawish evaluation (Stockfish evaluations near zero are being used as an empirical proxy for the inaccessible tablebase drawing criterion).
#2212
"the 50 move rule cannot be ignored"
The 50 moves rule can be ignored for all positions with 8 men or more.
You obviously missed these positions the first time I posted them for you. Each has 8 men and is mate for White under basic rules but a draw with the 50 move rule in effect.
I've posted them for you again, but if you just carry on repeating, " The 50 moves rule can be ignored for all positions with 8 men or more", I shan't try again - I'll just have to assume stem death.
It never gets invoked in grandmaster or ICCF games before the table base is reached.
It is just a practical rule to ensure that games and tournaments finish in a reasonable time,
even if some player does not know her 5 basic checkmates.
Whoever disagrees, please do present one grandmaster or ICCF game where the 50 moves rule was or could be invoked before the 7-men endgame table base was reached.
GMs are quite often out of their depth with only five men on the board and sometimes less. ICCF players invariably give up playing long before the 7 man tablebase. We can agree that the rule is almost irrelevant in practical chess if there are 8 or more pieces.
We can also agree that it's not relevant to your solution, since you have now dropped it from the game you want to solve. It would have been before you dropped it, because you don't show any method of restricting the positions arising in your computation to those known to have occurred during games in your chess club.
I think you mean that the paper says checkers has not been strongly solved. Strategies for optimal play from the opening position are complete. This only meant about 10^14 calculations (so certainly not the full 10^20 positions). The 10 piece endgame tablebase for the solution has 39 trillion positions, which is between 10^13 and 10^14 positions.
I was referring to the comments:
(a)
The fact that the game wasn’t solved for every possible position and then tucked away in a database doesn’t seem to bother him. ”Well, the checkers players would love it, because [then] you’ve got this oracle that can tell them everything—answer every single unanswered question in the game of checkers,” he says. ”But first of all, I don’t have the patience to do it. And second of all, I don’t have the technology to do it.” Even with the best data-compression techniques, Schaeffer says, the amount of storage required to solve all possible positions of checkers would exceed even the capacity of the world’s biggest supercomputers with tens of petabytes (1015) of storage by an order of magnitude. That puts it—at the earliest—at least a decade away.
This refers to a strong solution - "all possible positions".
and
(b)
Schaeffer’s proof solved checkers for 19 different openings, all of which end in draws. There are 300 total tournament openings, but many of these were determined to either be mirrors of other positions or altogether irrelevant to the proof because they lead to positions common to other openings.
Both mirrors and transpositions are fine - they are dealt with.
or from https://www.researchgate.net/publication/231216842_Checkers_Is_Solved
The checkers proof consisted of solving 19 three-move openings, leading to a determination of the starting position’s value: a draw. Although there are roughly 300 three-move openings, over 100 are duplicates (move transpositions). The rest can be proven [not have been proven] to be irrelevant by an Alpha Beta search.
So that's it: a complete opening strategy leading to the the tablebase - i.e. a weak solution.
Yes. Optimissed seems not be clear that "weak solution" is an established label for a precisely defined entity. Referring to a "very weak solution" as he does is unhelpful, as this is an undefined term.
An entity that can't possibly exist, without first there being a semi-strong solution.
Did you miss the bit about that NOT BEING DEFINED?
Where do I mention a very weak solution, anyway?
To be precise it was "strategy ... very weak"
The point is that if the definition doesn't exist, a term is meaningless.
Emphasis seems necessary.
I think you mean that the paper says checkers has not been strongly solved. Strategies for optimal play from the opening position are complete. This only meant about 10^14 calculations (so certainly not the full 10^20 positions). The 10 piece endgame tablebase for the solution has 39 trillion positions, which is between 10^13 and 10^14 positions.
I was referring to the comments:
(a)
The fact that the game wasn’t solved for every possible position and then tucked away in a database doesn’t seem to bother him. ”Well, the checkers players would love it, because [then] you’ve got this oracle that can tell them everything—answer every single unanswered question in the game of checkers,” he says. ”But first of all, I don’t have the patience to do it. And second of all, I don’t have the technology to do it.” Even with the best data-compression techniques, Schaeffer says, the amount of storage required to solve all possible positions of checkers would exceed even the capacity of the world’s biggest supercomputers with tens of petabytes (1015) of storage by an order of magnitude. That puts it—at the earliest—at least a decade away.
This refers to a strong solution - "all possible positions".
Yes it does.
The question remains - is there a database for the weak solution of the positions he analysed or did he bin the actual moves for that?
He seems to have been interested mainly in an ultra weak solution witness:
Even if an error has crept into the calculations, it likely does not change the final result. Assume a position that is 40 ply away from the start is incorrect. The probability that this erroneous result can propagate up 40 ply and change the value for the game of checkers is vanishingly small
from https://www.researchgate.net/publication/231216842_Checkers_Is_Solved
If he doesn't count an error as changing the solution unless it changes the value of the game, that implies the intention is an ultra weak solution.
The paper also says:
The computer proof is online at www.cs.ualberta.ca/~chinook
so I could try that, but what I get is first:
then when I click on "checkers solution"
Not designed to inspire confidence. Can you locate said database or details of the proof?
So for me the question remains open. There are a fair number of things I would want to clarify.
The first would be what game exactly do they claim to have solved?
When I look up "checkers rules" online, I get two flavours corresponding to the basic rules game of chess and the competition rules game of chess. The first is unlimited; the second has a 40 move rule and a 3-fold repetition rule.
There is no mention of which version is solved in either the above link or the link https://webdocs.cs.ualberta.ca/~jonathan/publications/ai_publications/checksolved.pdf posted by @tygxc earlier.
and
(b)
Schaeffer’s proof solved checkers for 19 different openings, all of which end in draws. There are 300 total tournament openings, but many of these were determined to either be mirrors of other positions or altogether irrelevant to the proof because they lead to positions common to other openings.
Both mirrors and transpositions are fine - they are dealt with.
or from https://www.researchgate.net/publication/231216842_Checkers_Is_Solved
The checkers proof consisted of solving 19 three-move openings, leading to a determination of the starting position’s value: a draw. Although there are roughly 300 three-move openings, over 100 are duplicates (move transpositions). The rest can be proven [not have been proven] to be irrelevant by an Alpha Beta search.
So that's it: a complete opening strategy leading to the the tablebase - i.e. a weak solution.
That would be it if any of his 19 3-move openings had turned out to be a win, but they didn't.
Therefore he has to consider all the rest of the 300.
I have no problem with discounting mirrors and transpositions but:
The quotes:
Although there are roughly 300 three-move openings, over 100 are duplicates (move transpositions). The rest can be proven to be irrelevant by an Alpha-Beta search. (https://www.researchgate.net/publication/231216842_Checkers_Is_Solved)
and
Schaeffer’s proof solved checkers for 19 different openings, all of which end in draws. There are 300 total tournament openings, but many of these were determined to either be mirrors of other positions or altogether irrelevant to the proof because they lead to positions common to other openings. (https://webdocs.cs.ualberta.ca/~jonathan/publications/ai_publications/checksolved.pdf)
suggest that 180 openings have yet to be analysed. Note the phrase, " can be proven", rather than, "have been proven" in the first quote - and no mention of how an Alpha-Beta search would lead to a proof (the process is not normally reliable).
For the moment I remain unconvinced.
@Elroch is usually correct. On occasion when somebody makes an accurate statement - he asserts about a somewhat different matter.
But that doesn't mean he's always off target.
Unfortunately - this could lead to situations where he rightly calls out a big error - but whoever isn't listening.
Which can happen anyway.
In math - whether the so-called 'pure' math or 'applied' math or statistical math ... whatever type of math it is - there are basics.
Foundations of mathematical processes.
Including about definitions and mathematical induction and logical assertions connected with mathematics.
One doesn't need two degrees or even one mathematics degree to both know about and grasp those basics.
But that doesn't mean the degrees Hurt. 
Point: those who don't catch on to the basics in math early on about the strictness and objectivity ...
well then everything they 'learn' afterwards or 'think they grasp' that is heavily mathematics-dependent may be distorted or continually eclipsed by the failure to catch on to the basics early.
Such situations are often insidious.
It would be like studying electricity having failed to catch on years previously to what amps and volts and watts are.
Something 'on the hard drive'.
The irony is that somebody with far less knowledge and experience may actually understand better.
They haven't made the mistakes yet and might never do so.
So they therefore cannot 'build on those mistakes'.
Optimissed labels, so that weak and strong are not considered on a spectrum 
...
Weak solution = solved for one starting point
Strong solution = solved from any starting point
1) Inferences from weak solutions ... bad idea mathematically.
2) Depending - relying - premising ... on 'weak' solutions - also 'getting worse'.
3) Poorly-defined weak solutions - or total failure of definition -
further compounding the errors of 1) and 2).
But does this all mean 'weak solution' is always useless and irrelevant ?
No.
Plus - comparing 'weak solution' with what players actually do to make progress in the game - one might find more connections there than with 'strong solution'.
Players 'strongly solve' K+Q against K and K+R against K.
Some take some time to 'strongly solve' most K+P versus K.
Mostly done early in their chess development.
But for the most part - chess development and activity is 'weakly solve'.
Or only 'strongly solve' within short sequences or 'islands' within each 'ocean' of the game or type of position concerned.
"You may imagine Elroch tends to be right. That may be but it doesn't apply to things he doesn't understand."
But so often or most of the time - the converse.
Its that 'other' that doesn't understand - but thinks he does.
@Elroch often calls out some big mistakes. But whoever doesn't listen.
Its 'unfortunate'. But goes with the territory of forums like this.
Its similiar with @MARattigan and @btickler and @haiaku .
They're almost always right.
But that doesn't mean whoever is paying attention properly.
"Somebody" has been complaining for almost the entire forum that its 'getting nowhere'.
But almost always - instead mistakes are being exposed.
Whether mistakes within the subject matter or other kinds of mistakes.
Those mistakes are not to be blamed on @Elroch but rather - on whoever fails to take responsibility for his mistakes with or without blaming them on others. Apparently there are only two persons consistently doing so.
... Since the authorities who seem to be omniscient fail to mention a semi-strong process, they are in error. ...
And since the self appointed authority who does mention it doesn't define it, he's talking gibberish.
[snip]
The checkers proof consisted of solving 19 three-move openings, leading to a determination of the starting position’s value: a draw. Although there are roughly 300 three-move openings, over 100 are duplicates (move transpositions). The rest can be proven [not have been proven] to be irrelevant by an Alpha Beta search.
[snip]
This point may have been missed earlier. I continue to assert there is a genuine weak solution of checkers. It permits (game-theoretic) optimal play as black or white.
IMHO, there is only one possible interpretation of "can be proven" there - that they have been proven. It's just a matter of showing that the knowledge that arises about positions for the 19 openings imply the results for the others by showing there is always a transposition to some position dealt with in the 19 openings available. (So you never actually need the tablebase to solve all the other openings).
If the proofs were not available, such a claim would be outrageous - believing that there is a proof would have no more substance than guessing that checkers is a draw.
Gradually circling around back to 'cabal'. Accusing the forum.
Have seen the cycle before. 'shouldn't forget' something that is invalid in the first place. Pattern of unfounded premises.
Which can get even worse in things mathematical.
Usually - it means I don't read those posts.
But occasionally make an exception.
The point is that if the definition doesn't exist, a term is meaningless.
Emphasis seems necessary.
Correct. Especially in math - but in other contexts too.
But at least two people aren't catching on.
They probably won't.
But we'll continue to hear to the effect of 'better than all of you' from both of them.
I mentioned that you're the most able but that doesn't mean I think I could learn much from you. You're just as unfocussed as the rest, because you shouldn't need me to define it *again*. Indeed, if you could think for yourself, you wouldn't need it to be defined at all, because you'd be able to work it out. There's a reason it's a clique.
I don't see how there's any notion of a clique between people that don't interact outside of public thread posts, really.
That would imply a pre-existing relationship, but the common focal points for this theoretical clique historically would seem to be Tygxc and yourself, or more accurately, the ummm...steadfast and closely-held ideas you both post month in and month out. Maybe you have something in common...but I wouldn't call you two a partnership .
[snip]
The checkers proof consisted of solving 19 three-move openings, leading to a determination of the starting position’s value: a draw. Although there are roughly 300 three-move openings, over 100 are duplicates (move transpositions). The rest can be proven [not have been proven] to be irrelevant by an Alpha Beta search.
[snip]
This point may have been missed earlier. I continue to assert there is a genuine weak solution of checkers. It permits (game-theoretic) optimal play as black or white.
You could be right. Do you know which version of checkers has been weakly solved?
IMHO, there is only one possible interpretation of "can be proven" there - that they have been proven. It's just a matter of showing that the knowledge that arises about positions for the 19 openings imply the results for the others by showing there is always a transposition to some position dealt with in the 19 openings available. (So you never actually need the tablebase to solve all the other openings).
OK, but my point was that the first quote seems to suggest that applied to only about 100 of 300 openings.
If the proofs were not available, such a claim would be outrageous - believing that there is a proof would have no more substance than guessing that checkers is a draw.
I believe that in matches one of the 19 openings is preset. If so, an algorithm for drawing from each of those positions would be a weak solution of that game. It comes back to which game of checkers has been solved.
But having spent about a quarter of my working life debugging system problems I probably have a somewhat jaundiced view of the probability of a decades long computerised project involving vast amounts of data producing exact results at the end anyway.
Some op is sure to drop a crate of beer onto one of your tape cartridges at some point and sweep it silently into the bin.
With tablebases, for a given objective, it is, in principle, possible to produce completely independent versions - different people, languages, systems and check for a complete match at the end. With a weak solution two totally independent solutions may match nowhere at all, even if they're both correct, so verification would be a major problem.
For me to be convinced, I'd really like to see more details of the steps taken to eliminate errors than just "This site can't be reached".
#2216
"Pick a random sample of say 10^8 positions with imperfect players and make inference about 10^46 positions."
++ There are only 10^44 legal positions and the vast majority of these cannot be reached in a reasonable game with > 50% accuracy.
Some of ICCF or even human games may already be ideal games with optimal moves.
The rules of the games are such, that they compel moving pawns or trading pieces to avoid losing. The dynamics stem from the rules. Pawns 'want' to move forward, because the closer to promotion to a queen the more powerful they get. Pieces on central squares are more powerful than pieces on the edge. So 32 pieces fight for 4 central squares. That inevitably leads to trades.
"To me, the most likely candidates would be imbalanced pawnless positions. Eg one side has 3 rooks, the other 5 minor pieces"
++ Such positions cannot happen in a reasonable game with > 50% accuracy.
Nobody promotes a pawn to a 3rd rook or to a 5th minor piece without compelling reason and the only compelling reason is to avoid stalemate.
Both sides needing to avoid stalemate makes no sense at all.