Chess will never be solved, here's why

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Avatar of DiogenesDue
stancco wrote:

Exactly.

99.7% of all possible positions are not relevant.

Okay, so that leaves with 10^41 positions.  What's your next step?

Avatar of stancco
tygxc wrote:

#3927

"99.7% of all possible positions are not relevant."
++ Only 10^17 positions of the 10^44 legal positions are relevant.
That is 1 position in 10^27 positions.
  0.0000000000000000000000001% of legal positions is relevant.
99.9999999999999999999999999% of legal positions is irrelevant.

I know.

I was rather figurative.

Avatar of leaniske
Computer>brain.
Avatar of DiogenesDue
tygxc wrote:

#3905

"I just understand that all your shortcuts require determinations to reduce the 10^44 positions "
++ No, there are no determinations needed at all. Only a tiny fraction of the 10^44 legal positions shows up during the solving process. Losing Chess has been weakly solved with only 10^9 positions not 10^44.
Look at the 3 sampled positions counted into the 10^44
https://github.com/tromp/ChessPositionRanking
It is clear that errors must have been made to reach those positions.

"Your arbitrary reductions will require a massive amount of computation to apply your arbitrary criteria to each position simply to eliminate it from consideration."
++ You still do not get it. I do not apply criteria and I do not need any computation to reduce positions, they just do not show up during the solution.

"More like a watered down attempt at a forward moving tablebase to meet the retrograde analysis in the middle." ++ That is how Checkers and Losing Chess have been weakly solved.
Have you read how they have done it?
http://magma.maths.usyd.edu.au/~watkins/LOSING_CHESS/LCsolved.pdf

https://www.cs.mcgill.ca/~dprecup/courses/AI/Materials/checkers_is_solved.pdf 
They did not start from the set of legal positions and then reduced that. They started from the initial position and then calculated towards the table base and at the end they had weakly solved it and then they counted they had visited 10^14 resp 10^9 positions in the process.

"you are not working backwards from mate" ++ I am not trying to strongly solve chess and compile a 32-men table base, that is not feasible.

I have read about the checkers solution, "Losing Chess" would be a waste of time.  Checkers reduced from ~10^20 down to 10^14.  And the solution did not just use the Chinook engine.  So, naturally, that means you can just go from 10^44 to 10^17 for chess and use only Stockfish wink.png...

Avatar of DiogenesDue
Optimissed wrote:

You're all three wrong in your different ways.

When asked to give a reason why I shouldn't be able to know that chess is drawn, haiuku couldn't get past the idea of "because it's unknown". When asked what could cause the equalising tendency in chess to mysteriously reverse, the answer was "because Relativity wasn't predicted". When told that there's no comparison because chess is a defined and finite system **in the way it operates as opposed to the search tree**, there was the verbal equivalent of a blank stare.

tygxc believes that anyone disagreeing with the definitions of the technical jargon he prefers to employ is showing they don't understand it, even though he's shown that he never even attempts to understand things he didn't know, preferring to reject them. I include tygxc here because although he also thinks chess is drawn, his confused ideas on the subject and an insistence that "the definitions are good" make it difficult.

bickler is a tricky combination of both of them, who cherry-picks what he wants, to win arguments he wants to engage with, for whatever reason; and constantly deflects and avoids good arguments, meaning that he doesn't engage. Instead, a constant engagement with tygxc means that he avoids the discussion proper and that seems to be a deliberate strategy, aimed at giving an impression rather than producing anything substantial.

No-one has shown that I am not reasonably entitled to believe that I know that chess is drawn with best play. One might remark that there was no proper opposition and that a contrary argument could be better represented by cleverer people. But I can assure you (anyone who is so bored that they're reading this) that a discussion with more able people would mean that there was a good chance chance of them understanding and perhaps agreeing with at least some of the points I've raised.

When the opponent disagrees with everything, that seems to be a childish technique, tending to demonstrate that the discussion goes above the head. Disagreement with everything implies, in practice, understanding of very little. So the argument has been concluded, as far as I'm concerned. No-one here has shown that I cannot know, without doubt, that chess is drawn with best play.

Does any of us actually need to be here for any of this fantasizing?  Please clean up after you are done...

Avatar of Elroch
tygxc wrote:

#3911

"The lines that no one has explored down to the tablebases yet, are unkown elements."
++ Many positions with more men than 7 are known draws or losses as well.
Many endgames with opposite colored bishops are known draws.
Many positions with huge material differences like a queen up are known wins.

"how do we know that the positions in S are draws?"
++ For all positions of 7 men or less and even some positions with 8 men it is known from the table base. For some endgames like opposite colored bishops it is known from analysis. For some middlegame positions with huge imbalance it is known from experience and from logic.

"you have no reason to believe that there will ever be a reliable proof." ++ A matter of money.

"All analyses will be impossible to check." ++ And for Checkers and Losing Chess?

"To me the only real proof is an exhaustive one" ++ Connect Four has been solved independently in two different ways: an exhaustive one by Allen and a set of 7 rules by Allis.
I believe weakly solving chess will be a combination of both.

"If one million mathematicians do all agree that T is a theorem, they might all be mistaken."
++ This has been heavily debated for the Four Color Theorem, but in the end it was agreed.

"A statement like "chess is a draw because of the equalizing tendency" really cannot be considered scientific, or nearly as reliable as a computer-assisted proof by exhaustion."
++ That is vague.
However: white is 1 tempo up, experience shows 3 tempi are worth 1 pawn, 1 pawn is enough to win a game by queening it, 1 tempo is not enough to win, makes sense.

Also: 1 e4 e5 2 Ba6 white is a bishop down. A bishop is worth 3 pawns. A bishop is enough to win. 1 e4 e5 2 Ba6 is a win for black. That is without an exhaustive calculation to checkmate in all lines.

This is a tremendous advance in chess theory. All through history, chess players have believed that sacrifices were sometimes valid and you have refuted those centuries of chess knowledge by the sheer power of assertion.

More generally, until now it has been believed that "proof by assertion" is a fallacy, and now you have raised it to a valid reasoning technique!

Imagine the things that can be achieved by this approach. Inspired by your lead, I have managed to both prove and disprove the Riemann hypothesis in the space of a minute. This proved mathematics to be inconsistent but then I saved the day by declaring it to be consistent!

Avatar of Elroch
Optimissed wrote:

I clicked on Elroch's link.

<<<<Chess theorists have long debated how enduring White's initiative is and whether, if both sides play perfectly, the game should end in a win for White or a draw. George Walker wrote in 1846 that, "The first move is an advantage, ... but if properly answered, the first move is of little worth".[29] Steinitz, the first World Champion, who is widely considered the father of modern chess,[30][31][32] wrote in 1889, "It is now conceded by all experts that by proper play on both sides the legitimate issue of a game ought to be a draw."[33] Lasker and Capablanca, the second and third World Champions, agreed.[34][35][36] Reuben Fine, one of the world's leading players from 1936 to 1951,[37] wrote that White's opening advantage is too intangible to be sufficient for a win without an error by Black.[38]>>>>

But the above is improperly described in its introduction. The ensuing isn't evidence of  even the beginnings of a debate. Each past Master is expressing certainty that it's drawn.

ie, "is sufficient"
"is now conceded"
"is of little worth"

No hint of a maybe amongst them.

The same players were wrong in their reasoning in every game of chess they lost over the board, despite committing their full efforts and using a lifetime of experience. At some point in every lost game they played a move which they believed was best and which lost.

Their knowledge and understanding was imperfect, therefore it is ridiculous to suggest they have any basis for certainty in assessments of the initial position in chess, without incorporating any more reasoning than their inductive chess knowledge.

The wiser position is that of Fischer, a stronger player than any of them - strong confidence, not certainty.

Avatar of tygxc

#3939
"sacrifices were sometimes valid "
++ Of course sacrifices are sometimes valid. But 1 e4 e5 2 Ba6 is no such time.
That is also why the good assistants are needed.

"Give me five years, good assistants and the latest computers
- I will bring all openings to technical endgames and "close" chess." - GM Sveshnikov (+)

The task of the good assistants i.e. (ICCF) (grand)masters is to launch calculations preferably from 26-men positions, but also to end calculations in clearly drawn, or clearly won positions, where they would agree on a draw or where they would resign in a real (correspondence) game.

1 pawn is enough to win.
The plan is to queen the pawn.
In the initial position white is up 1 tempo.
3 tempi = 1 pawn.
You cannot queen 0.33 pawn.
1 tempo is not enough to win.
The game-theoretic value of the initial position is a draw.

After 1 e4 e5 2 Ba6 white is up a bishop.
1 bishop = 3 pawns.
1 pawn is enough to win.
The plan is to queen the pawn.
1 bishop is enough to win.
The plan is to trade the bishop for a pawn.
The position after 1 e4 e5 2 Ba6 is a win for black.

That is simple human logic from simple human knowledge.

Now try the same with brute force by exhaustion

So 1 e4 e5 2 Ba6 is a forced checkmate in 82 moves.
But what if white plays differently?
Then white loses in a different way.


Avatar of ScroogeMcBird
tygxc wrote:

#3939
"sacrifices were sometimes valid "
++ Of course sacrifices are sometimes valid. But 1 e4 e5 2 Ba6 is no such time.
That is also why the good assistants are needed.

"Give me five years, good assistants and the latest computers
- I will bring all openings to technical endgames and "close" chess." - GM Sveshnikov (+)

The task of the good assistants i.e. (ICCF) (grand)masters is to launch calculations preferably from 26-men positions, but also to end calculations in clearly drawn, or clearly won positions, where they would agree on a draw or where they would resign in a real (correspondence) game.

1 pawn is enough to win.
The plan is to queen the pawn.
In the initial position white is up 1 tempo.
3 tempi = 1 pawn.
You cannot queen 0.33 pawn.
1 tempo is not enough to win.
The game-theoretic value of the initial position is a draw.

After 1 e4 e5 2 Ba6 white is up a bishop.
1 bishop = 3 pawns.
1 pawn is enough to win.
The plan is to queen the pawn.
1 bishop is enough to win.
The plan is to trade the bishop for a pawn.
The position after 1 e4 e5 2 Ba6 is a win for black.

That is simple human logic from simple human knowledge.

Now try the same with brute force by exhaustion

So 1 e4 e5 2 Ba6 is a forced checkmate in 82 moves.
But what if white plays differently?
Then white loses in a different way.


I keep hearing people quoting advanced statistics or whatever to say that Chess is a "draw" before the first move, as if movement isn't required. White has to move, Black has to move. Humans don't play perfect chess and computers don't compete in open events. Thus, whether Chess is "solved" by computers or not doesn't really matters.

Sure, there are vehicles capable of going at supersonic speeds, but we still have olympic sprinting. Humans aren't displaced by machines when it comes to organized competition *because they aren't allowed to enter and their skills are not 100% transferable to humans*.

 

Avatar of tygxc

#3948
"whether Chess is "solved" by computers or not doesn't really matters."
++ Well, yes and no.
Weakly solving chess requires a proof tree of a billion positions, that is 10 million perfect games. Nobody can memorise 10 million games. However, when somebody has memorised say 10,000 perfect games, he would have a big advantage.

Avatar of mpaetz
Optimissed wrote:


No-one has shown that I am not reasonably entitled to believe that I know that chess is drawn with best play. One might remark that there was no proper opposition and that a contrary argument could be better represented by cleverer people. But I can assure you (anyone who is so bored that they're reading this) that a discussion with more able people would mean that there was a good chance chance of them understanding and perhaps agreeing with at least some of the points I've raised.

     Of course you are entitled to believe whatever you please on any subject. You can believe that chess is a draw with best play (I concur). You can believe that Britannia still rules the waves. You can believe that Helios draws the sun across the sky in his chariot every day. You can believe you are the best-informed and smartest person commenting in these forums.

     But it should be apparent that what you cannot do is convince everyone else here to agree with your beliefs or give your comments greater respect than their own beliefs.

Avatar of DiogenesDue
tygxc wrote:

#3939
"sacrifices were sometimes valid "
++ Of course sacrifices are sometimes valid. But 1 e4 e5 2 Ba6 is no such time.
That is also why the good assistants are needed.

"Give me five years, good assistants and the latest computers
- I will bring all openings to technical endgames and "close" chess." - GM Sveshnikov (+)

The task of the good assistants i.e. (ICCF) (grand)masters is to launch calculations preferably from 26-men positions, but also to end calculations in clearly drawn, or clearly won positions, where they would agree on a draw or where they would resign in a real (correspondence) game.

1 pawn is enough to win.
The plan is to queen the pawn.
In the initial position white is up 1 tempo.
3 tempi = 1 pawn.
You cannot queen 0.33 pawn.
1 tempo is not enough to win.
The game-theoretic value of the initial position is a draw.

After 1 e4 e5 2 Ba6 white is up a bishop.
1 bishop = 3 pawns.
1 pawn is enough to win.
The plan is to queen the pawn.
1 bishop is enough to win.
The plan is to trade the bishop for a pawn.
The position after 1 e4 e5 2 Ba6 is a win for black.

That is simple human logic from simple human knowledge.

Now try the same with brute force by exhaustion

So 1 e4 e5 2 Ba6 is a forced checkmate in 82 moves.
But what if white plays differently?
Then white loses in a different way.

You do understand that all the point valuations you are using are approximations, right?  Not absolutes you can use in any calculations whatsoever.

If you set pawns to 1 point by default in the starting position, then all other values are fluid.  The value of a tempo, the value of every other piece, and the value of the pawn itself in a given position.  The statistical valuations at scale are only accurate for the current level of engine play... which is flawed.  

What is the value of the pawn at a2 in this position?

It's 9.  The value of the pawn at a2 is 9.  Or, more correctly, the value of this pawn is the same as the value of a queen's default value, because it already *is* effectively a queen.

What does Stockfish say?  7.5 using chess.com, until the horizon closes in further.  8.7 using the desktop version at 30 ply (over 1 minute).  In the simplest of positions, the engine is 3.33% off with about 3 minutes calculation.  Now extrapolate this to your method...how long did you want each "relevant" position to be analyzed for again...?

Avatar of dashadow333

so true

Avatar of DiogenesDue
Optimissed wrote:
You can believe you are the best-informed and smartest person commenting in the forums

Not necessarily best informed.

Surreal, isn't it?  

Avatar of DiogenesDue
Optimissed wrote:

Your entire universe is surreal, so yes it must be.

Not even this page, never mind "the forums".

Avatar of Elroch
btickler wrote:

What does Stockfish say?  7.5 using chess.com, until the horizon closes in further.  8.7 using the desktop version at 30 ply (over 1 minute).  In the simplest of positions, the engine is 3.33% off with about 3 minutes calculation.  Now extrapolate this to your method...how long did you want each "relevant" position to be analyzed for again...?

I think it does not use the value 9 for a queen. Even after the queen is on the board it rates it 8.x.

This is strange as winning a pawn in 2 or 3 moves is trivial. But it is worth remembering it is adjusting with other positional factors (activity of kings, pawn control of the centre). 

All complete nonsense - it's surprising the thing can play chess at all. wink.png

Avatar of DiogenesDue
Elroch wrote:

I think it does not use the value 9 for a queen. Even after the queen is on the board it rates it 8.x.

This is strange as I winning a pawn in 2 or 3 moves is trivial. But it is worth remembering it is adjusting with other positional factors (activity of kings, pawn control of the centre). 

All complete nonsense - it's surprising the thing can play chess at all.

The point is that the valuations are fluid, and that engines' valuations are off by a factor that completely precludes Tygxc's premise when applied at that scale.  The number of pre-filtered eliminated positions by mistaken criteria would be gigantic, and the number of misevaluations of chosen positions would also be gigantic.  You might as well march a million duckling babies over a stormdrain grating and then count the 937,000 you have left and declare it a million ducklings, problem solved.

I'm sure no engine uses integer values for any pieces other than pawns in the starting positions anymore.  Engine improvements are sometimes derived from specific ideas, but often are just tweakings of values that are experimented with and found to work against other engines.  In that sense, engines are simply evolving to play better against other engines and human players, not to play chess perfectly.  Only when they hit the tablebase do they consistently achieve perfect play.

Avatar of TheNumberTwenty

@tygxc I was speaking of chess GAMES, not chess positions... It's actually also amazing how high just the number of positions is, 32 soldiers on 64 squares can create a number that human beings could hardly imagine without some grand scale comparison.

Avatar of haiaku
tygxc wrote:

"The lines that no one has explored down to the tablebases yet, are unkown elements."
++ Many positions with more men than 7 are known draws or losses as well.
Many endgames with opposite colored bishops are known draws.
Many positions with huge material differences like a queen up are known wins.

"Missing the point" fallacy.

"how do we know that the positions in S are draws?"
++ For all positions of 7 men or less and even some positions with 8 men it is known from the table base. For some endgames like opposite colored bishops it is known from analysis. For some middlegame positions with huge imbalance it is known from experience and from logic.

Quoting out of the context and missing the point.

"you have no reason to believe that there will ever be a reliable proof." ++ A matter of money.

First of all, it is an epistemological matter.

"All analyses will be impossible to check." ++ And for Checkers and Losing Chess?

As above.

"To me the only real proof is an exhaustive one" ++ Connect Four has been solved independently in two different ways: an exhaustive one by Allen and a set of 7 rules by Allis. I believe weakly solving chess will be a combination of both.

Both are exhaustive. See the last section in this post.

"If one million mathematicians do all agree that T is a theorem, they might all be mistaken."
++ This has been heavily debated for the Four Color Theorem, but in the end it was agreed.

Missing the point.

"A statement like "chess is a draw because of the equalizing tendency" really cannot be considered scientific, or nearly as reliable as a computer-assisted proof by exhaustion."
++ That is vague.

In the second an third section of my previous post I addressed the problems with that statement. As for the reliability, an overgeneralization from a small sample of positions and games has a high probability to be proven false. We can make the following example (maybe someone else here already made it or a similar one, I do not recall well): we have 10²⁰ balls in a basket, few red, the other white; we pick randomly 10000000 balls; the red balls are 1/100000000000 (10⁻¹¹) of the total; the probability p to pick only white balls is approximately p = 0.99999999993. If we do not know a priori that there are red balls in the basket, by inductive reasoning we could well conclude that there is no red ball at all.

Computer-assisted proofs can be affected by glitches, but those proofs can be reproduced, there are methods to verify them, the probability that a glitch occur must be multiplied by the probability that the occurrence is crucial to the proof... In sum, they are much more reliable.

@Optimissed spoke of "full paradigm" for chess, but besides the fact that the word "paradigm" can be used in different ways, if the paradigm is the product of inductive reasoning, it has the same limits of the inductive reasoning.

++ That is vague.
However: white is 1 tempo up, experience shows 3 tempi are worth 1 pawn, 1 pawn is enough to win a game by queening it, 1 tempo is not enough to win, makes sense.

Overgeneralization and missing the point.

Also: 1 e4 e5 2 Ba6 white is a bishop down. A bishop is worth 3 pawns. A bishop is enough to win. 1 e4 e5 2 Ba6 is a win for black. That is without an exhaustive calculation to checkmate in all lines.

Overgeneralizations. And in that position my Lc0, after 25 million nodes (which is not bad for "her", as you know), still gives White 3.9% chances of winning.

In order to logically use knowledge A to prove something, you have to show that A is already proven; to prove A you can use logic and other proven knowledge B, and so on, down to axioms. Axioms are taken as always true, logic is taken as always true, so if you use them to prove something, that thing is taken as always true. That's what an exhaustive proof is: it is valid in any case. Unfortunately, the knowledge you plan to use is not always true and it is not proven that it would be, with optimal play, because optimal play has not been determined yet. The alpha-beta algorithm is always true: it is proven that it produces the same results of a minimax, so you can use it to cut off lines as soon as the search reaches the endgame. But knowledge as "a bishop is worth 3 pawns" is not always true, it is not exhaustive, so one can use it only for move ordering, when solving chess, not to cut off lines.

Avatar of ScroogeMcBird

Who will prove they understand numbers the best? I will have to keep reading to find out!

Forget about the Observer's Paradox! This is a contest among men to see who has the biggest, most powerful brain. Silly pawns. Your worth is fluid at best.