...
I've never seen +100 or higher. Can't recall +80 or higher.
...
That used to give an evaluation of around 128. (Only gives 100 now, but Wilhelm gives it 184.)
You shouldn't take SF evaluations as indications of either the theoretical evaluation or the likely result if it plays itself.
The position is drawn if Black plays correctly.
(I think it may be illegal though.)
mmm
Что за приложение?
@MARattigan
"The position is drawn if Black plays correctly.
(I think it may be illegal though.)"
Of course its illegal. 
There's more than 16 white pieces there.
But of course you knew that !
Regarding Stockfish - I usually trust its numerical evaluations and especially its 'mate in whatever' number of moves.
But here's a point which many might miss -
they might regard a position with 'mate in' as solved - and from there try to suggest all other positions that do not have a 'mate in' from there as 'dismissable'.
That's an invalid idea. If other moves are made - then we have new positions - which could have arisen from the position with the 'mate in' - or from some other source.
Those other positions so generated still remain to be analyzed.
They cannot be dismissed.
So attempts to 'cut down' that way aren't legitimate.
I think the method of reverse analysis from minimal material situations offers more possiblity of progress.
Add pieces by reversing captures.
Make two lone Kings primary instead of 32 pieces on original squares.
The game becomes
solved' - when all analysis lead back To that position - not From it.
Could chess be solved in our lifetimes ?
Not without a very big boost in hardware/software/programming - or some really high-powered vitamin pills to extend life many thousands of years. (Or millions/billions of years)
#778
I do not understand how you can consider positions as counted by Tromp as sensible
I am quite certain such positions never ever need to be visited in solving chess.
The Gourion number 10^37 is a far better estimate.
10^37 would then be the number of positions to strongly solving chess i.e. a 32-men table base.
For weakly solving chess further reductions are possible, which make it feasible.
just mentioning: in the position in #789
e8(Q)# is double check with checkmate.
#778
I do not understand how you can consider positions as counted by Tromp as sensible
I am quite certain such positions never ever need to be visited in solving chess.
The Gourion number 10^37 is a far better estimate.
10^37 would then be the number of positions to strongly solving chess i.e. a 32-men table base.
For weakly solving chess further reductions are possible, which make it feasible.
Certainly the Gourion number is an underestimate for what is needed as promotion is a major part of chess. Multiple promotions are perfectly normal even in the tiny sample of master games (a few million). It is worth remembering that solving chess involves effectively looking at way more than 10^30 times as many games as all those ever seen, so it is to be expected that MUCH weirder things will happen sometimes.
Single underpromotions are even a feature of real chess games as the best moves (sometimes the sole best move), so may form part of a winning strategy from both sides. Multiple underpromotions are rare but known. It is intuitively plausible that no position with five underpromotions to rook could be best play by the promoter, but it is certainly necessary to deal with every single underpromotion the defender could do. No hand-waving is allowed. This is simply an example of the principle that you can't skimp - EVERY possibility for the defender needs to be addressed.
Again, the point that dealing with more than 10^30 times more potential games as all those ever seen thus far means this will include possibilities weirder than anything ever seen.
It is intuitively plausible that no position with five underpromotions to rook could be best play by the promoter.>>
Intuitively, it's a virtual necessity. Looking at the given position, we can say with 100% confidence that it wasn't achieved by best play. It may be an intuitive thing .... i.e. that proof is both extremely difficult and (should be) completely unnecessary.
Intuition is worthless for solving chess except where it points the way to an efficiency gain for the proof.
I would also suggest pondering on the fact that induction from a few million master/computer games is unreliable for the 10^43 branches of a possible game tree. Odd things happen rarely, so you don't see them in a tiny sample.
#793
The Gourion number is an overestimate.
The positions as randomly sampled by Tromp make no sense at all
7 white rooks
3 black rooks
2 black dark square bishops
5 black knights
I gave a proof game above.
If a cloud engine at 10^9 nodes / second during 60 hours per move is considered a "toddler", then the beings that reach the Tromp samples are not even embryos, maybe amoebes.
That is not odd, It is just stupid.
Besides for weakly solving chess not the full 10^37 positions need visiting, only a small fraction of these.
cutting off excess promotions doesn't look like a good cutdown.
Much better would be to say -
'here's what we solved and here's what we didn't solve' - and then specify the characteristics of each.
#793
The Gourion number is an overestimate.
The positions as randomly sampled by Tromp make no sense at all
7 white rooks
3 black rooks
2 black dark square bishops
5 black knights
I gave a proof game above.
If a cloud engine at 10^9 nodes / second during 60 hours per move is considered a "toddler", then the beings that reach the Tromp samples are not even embryos.
That is not odd, It is just stupid.
Besides for weakly solving chess not the full 10^37 positions need visiting, only a small fraction of these.
Nobody is suggesting there is any correlation between positions you would regard as sensible and Tromp's samples.
I suggest in #584 (have you read it yet) that there is also little correlation between between positions you would regard as sensible and positions that might occur in your calculation. @Elroch suggests the same more concisely in #778. (Have you read that yet?)
I didn't initally dub SF a toddler, but I think the term is apt for this application. The fact is I don't believe it would give the right answer from the 5 man "Tabya" I started from in #759 until it reached a mate at a search depth of 103 ply. One second a move on a ZX80 or 60 hours a move on a Summit would give the same result.
That's finding its way from a single 5 man position to the 4 man tablebases. What are the chances of success from all your 26 man Tabya to the 7 man tablebases if you limit it to 60 hours per move on a Summit? Thinking 100% - now that would be stupid.
Since you have changed your mind about the game you are intending to solve, this now corresponds with the game for which Tromp has produced a valid estimate of the number of legal positions. His estimate is between 2.6x10^44 and 2.9x10^44.
(Incidentally, since you did change your mind, should you not also have reduced the time you expect to need on your own basis to 6 months? You haven't anywhere conceded that your basis is wrong.)
What is your figure of 10^37? The Gourion number you mention gives the number of diagrams without excess promotion as 3.8521...x10^37. If you were attempting to round the index of 10 to the nearest integer that would be 10^38 and certainly if you were claiming it as an upper bound.
But you have adduced no rational argument to explain its relevance nor to say why only a small fraction of positions that result in those diagrams should be visited.
Elroch gives arguments in #778/#780 that the latter would not be true even of Tromp's set of legal positions. Could you not address those posts, instead of simply adopting the Bellman's stance and repeating yourself.
#797
A) "Nobody is suggesting there is any correlation between positions you would regard as sensible and Tromp's samples."
++ It is obvious that the Tromp samples play no role in solving chess and hence his number is 7 orders of magnitude too high for the purpose of assessing the feasibility of solving chess.
Hence the more recent Gourion number 10^37 is better suited for assessing the feasibility of solving chess.
B) "What are the chances of success from all your 26 man Tabya to the 7 man tablebases if you limit it to 60 hours per move on a Summit? Thinking 100% - now that would be stupid."
++ No, as said I propose to let the cloud engine play against itself and then validate by granting white takebacks. The initial tentative game is begin of proof, the takebacks are the proof.
C) "Since you have changed your mind about the game you are intending to solve"
++ I have not changed my mind, I have always said that the 50-moves rule plays no role.
The 50-moves rule can be considered unwritten for the purpose of solving chess.
D) "What is your figure of 10^37? The Gourion number you mention gives the number of diagrams without excess promotion as 3.8521...x10^37. "
++ D1) Gourion himself says it is an upper limit and he estimates 3*10^37.
D2) Moreover left/right symmetry after castling rights are lost e.g. by castling reduces a factor 2.
D3) Moreover for the pawnless positions symmetry reduces by a factor 8 (white king not on a long diagonal) to 4 (white king o a long diagonal).
D4) Moreover a random sample of 200 Gourion positions also reveals many that can play no role in solving chess because of unreasonable pawn structures like quadrupled pawns.
D5) The only correction in the other sense is that some positions with 4 queens can play a role and should be added to the count.
E) "But you have adduced no rational argument to explain its relevance nor to say why only a small fraction of positions that result in those diagrams should be visited."
++ There are 2 rational arguments.
E1) Each pawn move and each capture renders huge numbers of positions not reachable and thus irrelevant. Checkers was proved visiting only the square root of the number of legal and sensible positions. We do not know if for chess it is more or less than the square root. It is plausible to assume that it is about the square root for chess too. We will only know after it is done for 1 ECO code e.g. C67.
E2) It is not necessary to assess all 500 ECO codes. To prove black can draw against 1 e4 only 19 ECO codes suffice instead of the 200 B00 to C99. That is an additional reduction by a factor 10.
#797
A) "Nobody is suggesting there is any correlation between positions you would regard as sensible and Tromp's samples."
++ It is obvious that the Tromp samples play no role in solving chess and hence his number is 7 orders of magnitude too high for the purpose of assessing the feasibility of solving chess.
Hence the more recent Gourion number 10^37 is better suited for assessing the feasibility of solving chess.
You say stuff like this all the time. You try to make leaps of logic like an errant bullfrog, who misses the lilypad . Read the bolded statement a dozen times until it sinks in that the second portion does not follow from the first. You are making *two* bad leaps here in a single sentence...the first is "it is obvious", and the second follows "hence"...
*sploosh*
There's no "hence" involved since a supposition that Tromp's number is too high does nothing to validate the other number that is 7 orders of magnitude lower. You have two numbers you are working with, and are creating a false dichotomy here. If you had a 3rd study that said 10^22, you'd jump right to that one. You just want to eliminate as many orders of magnitude as you can, because it fits your Sveshnikov-fueled narrative. I could pick apart the other points, but that would just dilute the main message. Bad science, thy name is Tygxc 
...
Let's face it, if Stockfish were able to hit the 7 man tablebase from the opening position right now, in any opening or narrowed field whatsoever, you'd be declaring chess solved already...which would be like saying that XYZ variant of string theory is absolutely correct because a grad student's 5 page essay on the topic said so. Stockfish is a fatally flawed source of information for this purpose.
#807
"You say stuff like this all the time." ++ Yes, because it is true.
"the second portion does not follow from the first."
++ Yes, it does. Tromp arrived at 10^44 legal positions. The vast majority of his positions has multiple excess underpromotions that makes these positions irrelevant for solving chess. Gourion arrived at 10^37 and that is a much better estimate for the number of positions that can be visited in solving chess. Hence for the purpose of assessing the feasibility of solving chess the Tromp number is 10^44 / 10^37 = 10^7 times = 7 orders of magnitude too high.
"If you had a 3rd study that said 10^22, you'd jump right to that one."
++ Yes, that is right: I gave 4 arguments D1, D2, D3, D4 why the Gourion number 10^37 is too high for the purpose of assessing the feasibility of solving chess and 1 argument D5 why it is too low.
"it fits your Sveshnikov-fueled narrative."
++ Yes, that is right. GM Sveshnikov was a world authority on chess analysis without and with engines. His work on B33 (which bears his name), B32, B22, and C02 is legendary.
"if Stockfish were able to hit the 7 man tablebase from the opening position right now, in any opening or narrowed field whatsoever, you'd be declaring chess solved already"
++ No, the first game from the 26-men tabiya to the 7-men table base is not proof, but begin of proof. The retractions of the white moves complete the proof. Stockfish is just the generator of the positions 26 -> 25 -> 24 -> 23 -> 22 -> ... 7 men in a reasonable way.
Do you realise it is not a proof that white can achieve a specified result unless you consider EVERY position black can reach? i.e. every black move. The only way you can avoid dealing with black underpromotions is by avoiding positions where black can promote. Likewise for multiple under promotions.
Sounds easy? Yeah, easy, like beating Stockfish 14.
#809
In the initial position white is a tempo up, that is an advantage, hence white tries to win and black tries to draw.
If a sequence of moves leads to a draw, then that retroactively validates all black moves: they were good enough to achieve the goal: to draw.
On the other hand if the sequence of moves leads to a draw, then it might be that white somewhere missed a winning move. Hence all white moves need validation by examining takebacks.
Multiple promotions are rare. 1-2 promotions per game are common, but 10 promotions as in the first Tromp sample position not.
Excess promotions are rare. Usually a pawn promotes to a piece already taken. 2 excess promotions usually to a 3rd and a 4th queen happen but rarely. 10 excess promotions never happen.
Underpromotions are rare. When a pawn promotes, then it is in 99.9% of cases to a queen. In rare cases it is a knight, e.g. to promote with check. In rare cases it is to a rook or to a bishop, to avoid stalemate. 10 underpromotions never happen.
10 excess underpromotions never happen, that is why the random sampled positions as counted by Tromp play no role in solving chess and why thus the Gourion number 10^37 is a better estimate than the Tromp number to assess the feasibility of solving chess.
I believe it's that kind of figure, or more.