@playerafar
#753
But I think he conceded that tablebasing is a non-starter from the outset.
The checkers paper he quotes and the method based on it that he proposes for solving chess are not tablebasing. I haven't seen anything where he concedes that his own method is a non starter.
" I haven't seen anything where he concedes that his own method is a non starter."
which I didn't claim.
But your comments about the size of memory that would be needed to solve for many pieces on the board look like icing on the cake to me.
Reinforcement of his concessions about tablebasing.
His silence on the matter is further concession too.
If you can't solve it - you can't solve it. Simple as that.
7 pieces 'solved'. More - no.
No estimates yet as to how long it would take to solve for 8.
No postings yet from the 'article' as to the time taken to get from 6 to 7.
The silence is telling. Concession.
This can be talked about as a lawyer thing - or objectively - or in many other variants. Idea: Mathematics isn't a lawyer thing. Not for this.
Nor is it a political thing ...
'Solved in five years !' is running for office? What do the polls say?
Nah ....
The weak solution is meant to contain less variations because variations with inaccurate play are excluded. Conversely, the strong solution includes positions arising after game-losing errors by either side.
Firstly. it's obvious that the first priority in "solving chess" is to try to identify the best moves, which should lead to drawn positions if played by both sides. So that's the so-called weak solution. But of course, before chess is "solved" it's impossible to know whether a line contains an error or not. This means that the entire distinction between weak and strong is a pseudo-distinction: ultimately pointless and meaningless.
I'm pretty sure the article is taken from something written as a bit of a joke, to get students thinking, as happens also in philosophy and also probably in law.
Weak and strong refer to the *outcomes* of the solutions...not to the difficulty of achieving them.
A weak solution for chess will tell you if chess is a draw from the starting position and how to do it from that position. An application of a strong solution for chess will "solve" any chess position given to it and tell you if it's a win, loss, or draw with best possible play. This makes a strong solution more useful (and for games of all types, not just chess).
"It's 2/2/2222, and chess has finally been solved! Who would have known that the Ponziani Opening of all openings would be a forced win? What will this do for the chess world, FabianoC#23?"
"Well, of course, this does mean in the short term that everyone will at first try to play the Ponziani...but that is effectively meaningless, since a human being could not possibly reproduce the forced win..."
"Indeed...what does it mean to you personally?"
Weak solution:
"Well, my 7 cycle clone ancestor Fabiano Caruana always wanted to know if Carlsen vs. Naroditsky 2029 was actually a salvageable draw for Carlsen in the pivotal game 31...but sadly we still don't know..."
Strong solution:
"Well, my 7 cycle clone ancestor Fabiano Caruana always wanted to know if Carlsen vs. Naroditsky 2029 was actually a salvageable draw for Carlsen in the pivotal game 31...and now we know that Naroditsky's unfathomable Na1 was perfect and Carlsen did not blow the world championship by making a mistake...Naroditsky took it from him with the move of the century!"
The tablebasing is the strongest standard mentioned so far.
All lesser solvings are a progressive diminishment in the standards.
Can be compared to the highest standard.
Right down to the very lowest ones ..
"its a draw - the game is a draw because 'we' say so" or
"people wouldn't play that" looks like another bottom-feeding standard.
But people who have learned from experience with tactics problems - know about 'counter-intuitive' moves.
And know about the blunders that 'dismissal' leads to.
@btickler
Thankyou for your explanation. I appreciate it very much, although I disagree with the logic behind what you're explaining, which is not your fault as you, presumably, didn't write it. I think it's a jumbled mess, however.
Could be the fault of the person refusing to grasp the logic too.
Or instead. Rather.
The problems with these distinctions (between strong and weak) is that they are hypothetical and in practice, it wouldn't be possible to discern between the weak and strong solutions, although the ultra-weak one stands apart because it isn't a solution at all. I put forward in Ponz's thread that it must be done algorithmically or not at all, but the algorithms have to work with real chess lines or they cannot be tested. The more I think about it, the more I suspect that the contents of this Wiki article have been concocted to try to get people to think.
I changed degrees. I completed year one of a computing degree but I was just too busy to do it. I switched to philosophy and managed to do the full time philosophy degree as a part time thing. I noticed that there were strong links between computing and philosophy. The computing lecturers and professors especially respected philosophy and tried to use it. Computer programming is basically Boolean Algebra. It's a logical process but it consists of commands rather than proposals. The Wiki article could actually be a joke subject within philosophy, hijacked by someone who believed it was realistic.
@Optimissed
It would be certainly be possible to discern the difference between between weak and strong solutions in practice. In the KBNK example I posted for you, if you consult any weak solution about how you should play from a mate in 32 position the answer is "don't know". If you consult a strong solution it will give you a move.
Also the weak solutions are for one side. If the solution is not for you and you ask it for a move, you get "don't know" anyway. A strong solution gives both sides moves.
The Wiki article is simply defining various terms that are generally agreed among game theorists. Nothing more subtle. They allow you to have a conversation where everybody understands what the others have said.
@Optimissed
It would be certainly be possible to discern the difference between between weak and strong solutions in practice. In the KBNK example I posted for you, if you consult any weak solution about how you should play from a mate in 32 position the answer is "don't know". If you consult a strong solution it will give you a move.
Also the weak solutions are for one side. If the solution is not for you and you ask it for a move, you get "don't know" anyway. A strong solution gives both sides moves.
The Wiki article is simply defining various terms that are generally agreed among game theorists. Nothing more subtle. They allow you to have a conversation where everybody understands what the others have said.
Thankyou. It's perfectly possible to have a conversation within those terms while knowing that they are logically invalid. Life is full of instances where the experts agree on nomenclature which is confusing and which doesn't help outsiders and makes it a closed shop. The outsiders can learn the jargon and participate.
In this particular instance, the jargon reinforces incorrect thinking. The major objection is that it's all hypothetical and couldn't possibly be brought into practice because it's assumptive, in that it assumes the solutions are known. In reality it would be impossible to distinguish between the weak and strong solutions. Impossible to set out to find either a weak or strong solution, because they're inseperable *until* the full solution has been found, in which case there'd be no point distinguishing them. You may just as well stick with as strong a solution as you can accomodate in your storage,
It's basically bad thinking but it hasn't been understood as such, because it's impossible to put it into practice. It's an hypothetical scenario, invented to make these people feel clever, as so much is.
The basic and simple explanation for this is that you have to find a large part of the strong solution in order to find the weak one, because you cannot know in advance whether a line is an error or not, before it's tested. The result is that only lines which emanate from nonsense positions should be rejected, as @tygxc was trying and perhaps failing to explain. There is no delineation between strong and weak solutions in practice and that's why the thinking's wrong.
"strong and weak 'solutions' " look like bait and switch.
Neither one is 'going to get it' anyway.
It looks like there's now a general concession that chess will never be table-base solved anytime soon.
In other words - it will not be solved in the foreseeable future.
That foreseeable future could change - if programming improves enough to either tablebase the task - or perform solving that's close enough.
From the opening - no moves - one position.
One ply - 20 positions. Two ply - 400 positions.
Then it starts getting much tougher.
Seems though - if all possible positions could be itemized - then 'solving' could come in after that.
Moves leading to positions instead of 'games'.
But that looks even harder than table-basing from the endgame end.
Because its still depending on moves instead of positions.
For example - pieces could move backwards - even to their original squares.
F-bishops sometimes do that - after castling and the rook moves.
I've seen it in GM games. even the c bishop could do it. A lot of pieces could.
Point: Its going to be too much. Too many moves to handle - too much multiplication.
Solving chess is only feasible right now as weakly solving, just like was done for checkers (8*8 draughts).
Strongly solving chess i.e. a 32-men table base would require to visit all 10^37 positions. That would take 10^28 seconds on 1 cloud engine and would require at least 10^37 bit of storage assuming only 1 bit draw/no draw per position and a 1 to 1 relationship between natural numbers 1 to 10^37 and the 10^37 positions in the sense like Tromp did. That is not feasible with present technology.
Weakly solving chess allows to prune non relevant positions and visiting only the square root of the legal and sensible positions, like was done for checkers, to account for positions rendered irrelevant by each pawn move and each capture.
Weakly solving chess allows also to prune the opening variations needing evaluation. If the Berlin is proven to draw for black against 1 e4, then it is not necessary to check if the Marshall, the Petrov, the Sveshnikov, the Najdorf, the French, the Caro-Kann draw as well or not. Hence only 19 ECO codes suffice instead of 200 ECO codes B00 to C99.
As said the Tromp count is way too high as it contains almost all insensible positions with multiple excess underpromotions that play no role in solving chess. Take a data base with 4 million games, that gives about 320 million sensible positions. Take a sample of 320 million positions as counted by Tromp, that leaves 95% illegal positions and at best 1 sensible position.
A legal position is a position that can result from the initial position by a proof game of legal moves. I tentatively propose a sensible position as a legal position where the proof game has e.g. an accuracy > 90% or an average centipawn loss < 10. None of the random samples by Tromp is sensible.
Even the Gourion paper gives too high an estimate: a random sample of 200 positions also contains many non sensible positions, mainly because of non sensible pawn structures like quadrupled pawns.
The 50-moves rule plays no role, forget it.
It is not necessary to double the number of Gourion positions. The side having the move can be inferred by counting the moves for both sides. Moreover any position with black to move can be converted to a diagram with white to move by switching colors, as endgame books conventionally do.
It is possible to cut the Gourion number in 2. As soon as both sides have lost castling rights, most often because both sides have castled, as is most often in 26-men tabiya, there is left/right symmetry. All positions with a white king on the left half of the board can be converted to an equivalent position with the white king on the right side of the board by switching wings, as endgame books conventionally do.
For all Gourion positions without any pawns, the number can be cut in almost 8 by applying symmetry. The position can be converted to an equivalent one with the white king confined to the triangle e1-e4-h1. The syzygy table base does that.
As to Stockfish against Stockfish at 60 h / move is like letting 2 toddlers play: If the calculation reaches a table base draw, then that means all moves of the black toddler were in retrospect good enough to hold the draw. As for the white toddler: we grant him takebacks starting with his last move and working backwards. That ascertains all his reasonable moves lead to no more than a table base draw.
The table base decides draw or not, not the evaluation function of Stockfish. The evaluation function of Stockfish merely serves to guide the search in a meaningful direction.
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"strong and weak 'solutions' " look like bait and switch.
Neither one is 'going to get it' anyway.
It looks like there's now a general concession that chess will never be table-base solved anytime soon.
In other words - it will not be solved in the foreseeable future.
That foreseeable future could change - if programming improves enough to either tablebase the task - or perform solving that's close enough.
From the opening - no moves - one position.
One ply - 20 positions. Two ply - 400 positions.
Then it starts getting much tougher.
Seems though - if all possible positions could be itemized - then 'solving' could come in after that.
Moves leading to positions instead of 'games'.
But that looks even harder than table-basing from the endgame end.
Because its still depending on moves instead of positions.
For example - pieces could move backwards - even to their original squares.
F-bishops sometimes do that - after castling and the rook moves.
I've seen it in GM games. even the c bishop could do it. A lot of pieces could.
Point: Its going to be too much. Too many moves to handle - too much multiplication.
If you wrote in English without trying to be cryptic, what you write might be vaguely comprehensible. As it is, <<"strong and weak 'solutions' " look like bait and switch.
Neither one is 'going to get it' anyway.>> looks like it means that the writer of the Wiki article is a troll who's trying to trick people but neither version takes the cake. I would say that's harsh.
From post #765
"That is not feasible with present technology."
Not only not feasible. Not possible. Not as things stand now.
Practical 'Possibility' only comes into existence - if means come into existence.
People flying wasn't possible - till the means were developed.
And 'weakly solving' is not solving - however many attempts there might be try to dress it up as such.
Chess grandmasters have been 'solving' positions - to a degree far beyond the rest of the population - for many decades.
Now - supercomputers have been 'solving' too.
And can process positions faster than grandmasters can.
But in both of those cases - the term 'solving' simply refers to an extremely small percentage of possible positions.
A miniscule percentage.
And that percentage of positions is so small - as to be Infinitesmal for practical purposes ... as far as 'all possible chess positions' are concerned.
The forum title would seem to refer to all of chess positions.
So whether you call it GM 'solving' or computer playing of positions or supercomputer 'examination' of solving ...
it doesn't refer to 'thorough' solving - that has actually occurred in tic tac toe and in checkers. Relatively simple compared with Go and Chess.
Much too simple - to premise anything on those simpler forms.
One could try to compare - verbally - except they don't really compare.
Just too great a gulf of difference in magnitudes.
The forum title also refers to 'here's why'.
But has that really been discussed yet ?
I would say no.
Because the 'progression of difficulty' hasn't really been explicitly discussed yet.
Some members have made selective quotes from a single internet website - but only with a result of promoting points of view.
To really express the 'here's why' - the mathematical buildup of difficulty as more pieces are added to endgame positions ... and the multiplication of positions as more moves are added to opening positions ... is what is at the heart of the matter.
Unwillingness to discuss such progressions by diverting to expeditions into 50 moves rules and exercises in computer jargon and battles over semantics and intense personal pingpong isn't going to get the true discussion done regarding the Gigantic mathematical buildup of obstacles to 'solved' in chess.
Solving chess is only feasible right now as weakly solving, just like was done for checkers (8*8 draughts).
Strongly solving chess i.e. a 32-men table base would require to visit all 10^37 positions. That would take 10^28 seconds on 1 cloud engine and would require at least 10^37 bit of storage assuming only 1 bit draw/no draw per position and a 1 to 1 relationship between natural numbers 1 to 10^37 and the 10^37 positions in the sense like Tromp did. That is not feasible with present technology.
Before offering to solve chess for us, it would be a good idea to understand a little of what is involved.
There are 12579944 positions in the KNNK endgame. To strongly solve any one of these, as the Nalimov and Syzygy tables do, it is necessary to visit only 736 of those positions.
You obviously have some learning difficulties. As Tromp has shown, there are at least 2.6x10⁴⁶ positions in competition rules chess (2.6x10⁹ times as many as the figure you repeatedly give). His work is sound.
You apparently can't even distinguish between a position and a diagram (but that is the least of your problems).
A 1-1 mapping of positions to bits would not be enough for even an ultra weak solution.
Weakly solving chess allows to prune non relevant positions and visiting only the square root of the legal and sensible positions, like was done for checkers, to account for positions rendered irrelevant by each pawn move and each capture.
Weakly solving chess allows for significant pruning of the number of positions visited, but not for any of the pruning you have postulated.
You haven't shown that it allows you to visit the square root of the number of legal positions ( √{2.6x10⁴⁶} let alone the square root of the legal and sensible positions (whatever "sensible" is supposed to mean).
Weakly solving chess allows also to prune the opening variations needing evaluation. If the Berlin is proven to draw for black against 1 e4, then it is not necessary to check if the Marshall, the Petrov, the Sveshnikov, the Najdorf, the French, the Caro-Kann draw as well or not. Hence only 19 ECO codes suffice instead of 200 ECO codes B00 to C99.
A proof of the statement would be in order.
As said the Tromp count is way too high as it contains almost all insensible positions with multiple excess underpromotions that play no role in solving chess. Take a data base with 4 million games, that gives about 320 million sensible positions. Take a sample of 320 million positions as counted by Tromp, that leaves 95% illegal positions and at best 1 sensible position.
I've shown you examples of multiple excess under-promotions that play a role in Sysygy's solution of seven man chess (and pointed out that these occur in practical games -though this consideration is strictly speaking irrelevant).
Are you sure it's the positions that are insensible?
A legal position is a position that can result from the initial position by a proof game of legal moves. I tentatively propose a sensible position as a legal position where the proof game has e.g. an accuracy > 90% or an average centipawn loss < 10. None of the random samples by Tromp is sensible.
Your proposed solution is not designed to take any account of accuracy.
Presumably you measure accuracy in terms of number of moves to mate. I've already shown you Syzygy playing perfectly but hugely inaccurately in #584 (have you got round to reading that post yet?). I could give you many more with a greater divergence from accuracy.
It is the norm for perfect play (and also practical play - though this consideration is strictly speaking irrelevant) to be not sensible in terms of your definition.
Your definition of sensible play/sensible position is in no way relevant to your proposed computation.
Even the Gourion paper gives too high an estimate: a random sample of 200 positions also contains many non sensible positions, mainly because of non sensible pawn structures like quadrupled pawns.
This is almost certainly perfect play by both sides.
If the starting position for the game is a White win, the position shown could almost certainly appear as part of a weak solution. A weak solution in that case must cater for any moves by Black, however odious you personally might find those moves.
The moves shown are clearly not accurate, but your proposed solution is not designed to produce accurate play. This could form part of your weak solution, in which case the final position could not be discounted.
You will note the final position contains quadrupled pawns.
The 50-moves rule plays no role, forget it.
You obviously have, in spite of many reminders.
The fact remains this plays an increasing role in closely matched positions in perfect play up to the 7 men we know about. We also know it plays a role in 8 man positions.
The only reason you think it should stop playing a role at 8 and beyond is you can't think of any cases where it would be relevant and you think your play is nearly perfect, so, if you can't think of it, it doesn't exist.
But I don't think you'd stand an earthly of mating under your own steam against SF14/Syzygy from this position under basic rules (SF14/Syzygy could). You certainly wouldn't under competition rules (and neither would SF14/Syzygy).
You think you'd get better with more men. I think that defies common sense.
It is not necessary to double the number of Gourion positions. The side having the move can be inferred by counting the moves for both sides.
What a croc of manure.
Whose move is it in this diagram - the third of Tromp's introductory diagrams (and the first which does not have a corresponding position with one of the players to move already excluded from his estimate of legal positions)?
or the one in #727 which you have conveniently ignored.
Moreover any position with black to move can be converted to a diagram with white to move by switching colors, as endgame books conventionally do.
This is true, but it's also true of checkers, so should already be taken account of in your (yet to be discussed) assumption that the time taken is proportional to the square root of the number of legal positions.
(I'm assuming the checkers paper refers to legal positions rather than equivalence classes of legal positions under black/white symmetry - I should check.)
It is possible to cut the Gourion number in 2. As soon as both sides have lost castling rights, most often because both sides have castled, as is most often in 26-men tabiya, there is left/right symmetry. All positions with a white king on the left half of the board can be converted to an equivalent position with the white king on the right side of the board by switching wings, as endgame books conventionally do.
This is true. @playerafar already suggested it in #259
"Another big cutdown could occur - with positions that are rotations and reflections of each other. "
but you appeared to reject it in your response #261
"The count of 3.8125 * 10^37 positions does not take symmetry into consideration. Left/right symmetry is broken by castling. Up/down symmmetry is broken by white pawns maching up and black pawns marching down."
so I have assumed you were not intending to take board symmetries into account in your program.
If you are, this would halve the effective number of positions in Tromp's count, reducing it to something over 1.3x10⁴⁶.
This would reduce the calculation time on your (yet to be discussed) basis below 200 millenia.
For all Gourion positions without any pawns, the number can be cut in almost 8 by applying symmetry. The position can be converted to an equivalent one with the white king confined to the triangle e1-e4-h1. The syzygy table base does that.
Yes, but no real saving beyond the above. The vast majority of positions have pawns.
As to Stockfish against Stockfish at 60 h / move is like letting 2 toddlers play: If the calculation reaches a table base draw, then that means all moves of the black toddler were in retrospect good enough to hold the draw. As for the white toddler: we grant him takebacks starting with his last move and working backwards. That ascertains all his reasonable moves lead to no more than a table base draw.
Not quite.
Here is a cut down version. The task is to reach the 4 man tablebases from a 5 man position.
The toddlers are SF12 and SF12 with different coloured hats.
The game reaches a 4 man tablebase draw. Black toddler's moves were good enough to hold the draw. White toddler can take back as many moves as he wants, but with two knights that's obviously going to lead to no more than a draw.
So you can stick it in your cut down solution as a draw? You could, but it's actually mate in 52 (under either set of rules).
If SF can't manage to successfully negotiate a single phase with 5 men on the board, how would you expect it to do negotiating 19 phases with 26 men on the board?
And there's that word "reasonable" again. You should have realised already from the numerous examples I've given that perfect play is usually unreasonable in your terms.
The table base decides draw or not, not the evaluation function of Stockfish. The evaluation function of Stockfish merely serves to guide the search in a meaningful direction.
Or not, as the case my be.
I read through that post by MARattigan ...
2.6x10⁴⁶ looks more like a realistic figure.
But even if it were 'only' 10 to the 27th power - we're still talking about a daunting number.
And Martin seems to understand the mathematics of the obstacles to thorough solving of chess.
He is one of at least five persons here who I would think know about factorials and combinations and the like.
But even for those who don't - everyone here probably understands simple multiplication quite well and is quite capable of appreciating how big a number you get when many double -digit numbers are multiplied together many times.
Capable - but not necessarily willing. 
There are many sub-projects regarding these types of computer project.
Supposedly - computers could be set to cutdown 'rotations and reflections' as Martin mentioned -
with various ideas in mind.
Whatever happened to Coolout? How we all miss him!
In the pre-engine era games were adjourned after 40 moves and 5 hours of play and play was then resumed the next morning after players and their seconds had analysed the position the whole night. They had neither engines nor table bases. They had only like 10 hours to analyse. Nevertheless they more often than not arrived at the truth about the position.
How did they do that? First they established who had the advantage, i.e. which side had to play for a win e.g. white and which side for a draw e.g. black. Then they looked at the position and its traits. Then they started analysis i.e. they played a game against themselves from the position. When the outcome was as desired for one side, then they started with takebacks for the other side, starting at the end.
It is this procedure that I propose to emulate with cloud engines and table bases to likewise find the truth about a 26-men tabiya. If you call a cloud engine with 10^9 nodes / second running for 60 hours / move a toddler, then your desktop at 10^6 nodes / second running for a few seconds is not even an embryo.
...
Firstly. it's obvious that the first priority in "solving chess" is to try to identify the best moves, which should lead to drawn positions if played by both sides. ...
No. It's just to identify the best moves. (Assuming you mean perfect play.)
It's irrelevant to the discussion whether or not I think that the best moves will lead to a draw and yet you don't even have the intelligence to understand that. I appreciate that you've found your operating level. Hope you enjoy it.