Chess will never be solved, here's why

Obviously ignoring definitions in common dictionaries, that do not nor can include all the specific and technical uses of some words, I think that the following is a very good example of how "any opposition" is considered in our context. In fact, the authors use just van den Herik's (cited in the references) definition of weakly solved, explaining later its meaning:

  "Weakly solved means a strategy [ . . . ] has been determined for the initial position
to achieve the game-theoretic value against any opposition. [ . . . ]
   In terms of prunings in branch and bound tree search, a sound pruning condition when solving a weaker solution concept may not hold in stronger ones. This is caused by the removal of the assumption of optimal/perfect plays when dealing with stronger solution concepts. For example in alpha-beta prunings, when the min player obtains an A-costs which is lower than the lb (i.e. max player's last found best), we cannot immediately backtrack if we want to tackle weakly solved solutions, where we assume the max player is the adversary. The reason behind is that we cannot assume the max player must play a perfect move. We have to consider all moves for the max player. The situation is similar if we assume the min player is the adversary." (emphasis mine)

https://www.researchgate.net/publication/262296151_Consistencies_for_Ultra-Weak_Solutions_in_Minimax_Weighted_CSPs_Using_the_Duality_Principle

@MARattigan, I can understand your point about using that definition (e. g. a perfect strategy to gain... a loss?). There is no problem if we consider that if the game is, let's say, a win for White, it has to be proven that White can actually win (the strategy must not work only for the losing side). But indeed, other ways to state the concept may be clearer.

What then would you make of this article published in the ICGA journal roughly concurrently.

In particular the opening paragraph of the conclusion (p. 196):

The checkers computations will continue, albeit at a slower pace. Idle machines will be used to solve additional openings, with the goal of eventually solving all three-move checkers openings. Without additional computing resources, however, this will take many years. 

My problem is that the definition doesn't say who the strategy is for. If it means a strategy for both players it should say that.

But even if you do make the assumption that the strategy in question means a strategy for both sides there is still a problem.

A weak solution of this position, for example would have to look something like the accompanying moves.

The game theoretical value is a draw, so the Syzygy tablebase would not do for White's strategy according to van den Herik's definition,  because it would produce a win if Black played anything but KxN and the definition insists on a draw.

Variations on van den Herik's definition are prevalent in the literature, but what is actually used is not the stated definition, but rather the one I gave.

You don't find anyone questioning whether the tablebases give a weak solution of the positions they deal with.

I have to admit I don't know checkers enough to be sure wheter they neglected some necessary openings or not. In that paper they say that the vast majority of those around 400 openings can be eliminated for transpositions or alpha-beta cutoffs, some others result bounded, but they do not state clearly if really everything that matters has been considered. Indeed, I think that nine men's morris has been "solved" with some approximations. On the other hand, you rightly pointed out that we cannot trust 100% any solution produced by decades of computing; so the question is: how much approximation can be considered tolerable? I am afraid that just saying that will unleash @tygxc 's creativity...

Remember a proof never has to deal with a line that involves a move by each side that is not in one of the strategies. So you need to deal with all first moves by black (I believe black moves first in checkers). But then for each first move that is not in the strategy for black you can ignore all the lines where white then also plays a move that is not in its strategy.

In chess terms, you need to deal with 1. a4 for white, but if the white strategy always plays 1. e4 you only need to deal with one move against 1. a4 (because this position only occurs in the black strategy).

This is a large reduction of the opening book. Same for the three move checkers openings. There are about 300 of these and somewhere I recall that only 19 openings were dealt with, which happens to be a tad more than the square root, as one would naively estimate.

Issue:  "I can interpret data any way I want"
And then - assert that misinterpretation publically.
Issue: "If I interpret it as correct - then it is not misinterpretation because I say so."
How would anybody tell @tygxc to go against himself ?  

It would be like telling somebody to abandon their religion.

So what makes this situation so special ?
It seems to be - that every time @tygxc is refuted and exposed - he will retort (including with referring to Dr. van den Herik) and feel and maintain that he has accurately rebutted all disagreement.
Including with the double ++ signs. 
(which are used in chess reference data to signify big winning advantage)

Some really 'nervy' stuff - like that it 'doesn't matter' about the computers' maximum ops per second ...
So there's actually two discussions ...

I agree that 1) a4 can't be discounted - 
but I thought @Elroch agreed to that too.
But the precise issue there - well it probably went by me.

Well, I was focussing on the actual amount you reduce the opening book when you solve chess like checkers was solved.

• You need to deal with 20 positions generated after 1 ply
• Suppose white's strategy says play 1.d4. Then you need to deal with all black's replies to 1.d4. That is 20 positions. You also need to deal with just 1 reply to all the other 19 first moves.
• So the total 2-ply positions you need to deal with is 39 out of the 400 legal positions after one move by each side.
• It gets fiddly to go further, but at every ply you will be making large savings. Somewhat short of square root in total.

Chess is a gathering of the mind to its original state of nothingness, the board represents the mind, each square an idea, the pieces the obstacles of illusions. I remember when the chess board were black and white, like the pieces, therefore, testing your concentration. Now, we have green and white boards, books on openings and defenses, computers, and pre-moves.The human has lost its mind to study and A.l.s, no longer using his/her mind as intended. In Chess, why do I have to study any openings or defenses, I considered that a lost to the game of Chess and the creative aspect of the mind. No books on chess, however, notations by the opponents fair in understanding your opponent's thoughts and approach to certain play on board. One may solve a chess puzzle but Chess as expression of a creative mind will never be solve, not even by AI. Let's stay human the mechanical approach to anything is but folly.

Seems to me that if you're to prove a position is drawn you have to prove neither side can win.

If say you have a strategy for White that provably avoids a loss (in chess) that begins 1.e4, that doesn't prove that White cannot win with 1.a4.

To prove that you would need to consider moves by both Black and White that don't occur in White's strategy.

So I'm not following.

It may depend on definitions used implicitly. The game theoretic value of that game is a draw. A weak solution provides the game-theoretic value of the initial position and a strategy that guarantees at least that value (actually "at least" is even redundant, because the game-theoretic value is the minimum outcome that can be achieved with optimal play). So anything White plays after any first Black's move is indeed an optimal White's strategy for a weak solution, because Black cannot win. But since Syzygy tablebases are a strong solution, the game-theoretic value of all the legal positions from start to finish and a strategy to achieve that value are known, so If Black does not capture, the position becomes a win for White and an optimal White's strategy for a strong solution must achieve victory. Nontheless, since White cannot lose, her strategy for a strong solution is also good for a weak solution. So yes, there are implicit nuances in Allis and van den Herik's definitions that for practical purposes it maybe better to explicit.

I add that if an optimal strategy for White is known, indeed it is also known what is the best opposition Black can offer. In fact, the optimal strategy for White must work for all Black moves, so we know that the best opposition she can offer is the capture, in that position; therefore, we can determine an ideal game, where both sides do their best to achieve the draw (the game value of the starting position).

I think your last sentence is correct, @MARattigan!  

For 1. a4 you need to deal with one response for black that you can prove forces a draw. That's all. (Assuming 1. a4 is not in white's strategy and chess is a draw).

White's strategy is one move for each possible position that he could see.  Black's strategy is similar. 

So White's strategy deals with 1 initial position and 39 positions after black's first move (see reasoning in previous post).  This makes no assumptions about black's play.

Likewise, Black's strategy deals with all 20 positions after white's first move but far fewer than the total number after his second (because he only needs deal with positions reached by strategy moves by him). And so on.

The fact that both players reduce the positions like this means that a position that can only be reached by both players playing at least one non-strategy move can be ignored, since neither strategy requires it. For example if 1. d4 d5 are strategy moves, the position 1. e4 e5 can be ignored.

Another idea for 'weak solution'.
Instead of arbitrarily having only four candidate moves at each turn -
go by numerical evaluation parameters instead.
Opinion:  plus or minus 6 is Crushing.  In Stockfish.
Issue:  Has the computer been allowed to run long enough ?
I've seen Stockfish change its mind after a time. 
From plus to minus.  And a lot too.
But I've seen that time exceed 30 seconds !  
Uh oh ! ...  getting back into trouble again !  

There's the idea of supercomputers running in parallel.
So if you've got over 100 supercomputers in the room - they can each consider a move of a single position.
I can't recall seeing a position in my games that would have had 100 move options.
Middlegames are often in the fifties and endgames in the thirties.
But some of the move options are Ridiculous.
Running in parallel - the computers can tag-team each other as positions transpose into each other.

Stuck at this point, which seems to be a jumble of party related points. If, between you, you still can't decide on average numbers of candidate moves (I suggested five) then why is this fantasy being discussed with such earnestness and seriousness? That's really the point of this thread .....

Continuing with my idea (instead of being baited by whoever) -
instead of going by candidate number of moves (ridiculous when you consider how many candidates there might be - and how comparable they might be too)
- go by computer evaluation number instead.
Would it work?  I'm not saying it would or would not work.
I'm suggesting its worth some discussion.
I recall from the days when I played postal chess (several decades ago) -
I'd make written lists of all the legal moves available for my move.
Then - I'd make three columns:  They were 
Candidates (sometimes ten or more) - intermediate -
and - too obviously losing or inferior.

Then I'd start calculating and comparing the candidates -
but sometimes there was a snag - and it turned out that some or all of them were pseudo-candidates ...
at that point - the real candidates had to be found and compared from the intermediate list along with 'survivors' from the first list.
At no time did any move ever emerge from the 'ridiculous' list.  

Point:  computers would be very good at such lists.
Issue - the computer may on occasion be able to isolate one move - for example the opponent plays QxQ.  Now is there a big percentage of the time where you can justify any other move but the only Recapture ??
The computer would know when you could or couldn't.
Anytime an opponent takes a piece of your's - a big percentage of the time you're taking back.
Point:  its pruned down to just one move in many instances.

And:  Would it be rare that the computer would have 20 comparable candidate moves?  
1) a4 should stay in.   But e4 e5 Ba6??   In weak solving I'd say its reasonable to knock that out.  Much much More Reasonable than only having four candidate moves ...  which is numb and arbitrary.

Photo

Regarding @tygxc and his 'bravery' ...
He is pushing a kind of 'devil's advocacy' and that in turn is a service rather than a minus.
It results in @MARattigan and @Elroch and @haiaku and @btickler all systematically refuting and exposing and debunking his arguments - which in turn illustrates the issues of the forum subject.  
So @tygxc deserves some 'credit' there.
He asserts himself - stumbles - but they're right there !  

I agree that identifying a strategy with the proof tree it provides and considering two separate strategies (one for each player), the union of the two strategies will not contain moves that are not part of either strategy. About the solution for checkers, though, what may leave some doubts to me is that, 1) as for chess, an optimal strategy and a game-theoretic value for checkers was not known, so in finding that optimal strategy, the evaluation function might not be able to discover the best lines immediatly; 2) more important to me is that "the vast majority [of openings] can be eliminated due to transpositions and alpha-beta cutoffs."[1] If the leaf nodes are tth or tbh, then ok, they have the true value of the nodes and they can apply alpha-beta to cut off llines; but if that means that they just did not check because the evaluation function at some depth said those positions are almost certanly a loss or a win (like e.g. a -6 or +6 in chess, using the pawn value as a measure of the advantage) while other openings almost certainly would lead to a draw, then indeed some approximations would have been made. Reading the better known paper, the authors say that the alpha-beta search (nominal depths 17-23 plies) used in Chinook was not designed to solve checkers, and it occasionally determined a proven win or loss; If Chinook did not find a proven result, then a second program with a different search algorithm (a Df-pn search) was invoked. At the end of page 3 [2], they say that "the rest [of the openings] can be proven to be irrelevant by an Alpha-Beta search". So it seems that the Alpha-Beta search was enough to hit a TT or the endgame with a win or a loss, otherwise it would have invoked the other algorithm and they would say "by a Df-pn search", instead.

@MARattigan, in the other paper you referenced, they say that "some opening results are bounded (≤ Draw). We only needed the bound to prove the root value. At the time of this writing, ongoing computations are working on turning these bounds into proven results (Loss or Draw)". That's the explanation imo for what we can find in the conclusion of that paper ("machines will be used to solve additional openings").

[1] https://icga.org/icga/journal/contents/Schaeffer07-01-08.pdf

[2] https://researchgate.net/publication/231216842_Checkers_Is_Solved