Will computers ever solve chess?

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JubilationTCornpone
Elroch wrote:
RCMorea wrote:
Flank_Attacks wrote:

.. Obviously, it's speculation ; But since, 'quantum' computers, are still in their development infancy ; Perhaps, there are already, mathematical projections, {or estimates} ; As to how long, it might take, a hypothetical, quantum 'supercomputer' ; Capable, of sorting through, mind-boggling, permutations ; Given that, the 'quantum' approach ; Has supposedly equal, daunting capabilities {!?! }

Quantum computers don't work like that.  They check all permutations at the same time.  A quantum computer with enough power solves chess instantly.  The problem is, "enough power" (meaning enough quantum bits, properly organized and powered) is still on the same order as has already been discussed. 

No, I believe you are wrong here. The computation that can be achieved with a quantum computer is exponential in the number of qubits. So if this resource was used efficiently, a thousand qubit quantum computer might be adequate for chess.

 

I suppose it depends what the exponent is.  If it is 2, then 1,000 only squares to 1,000,000, which is still a small number.  Meanwhile 10^45 still square-roots to 10^22, which remains far too big.  But if the exponent could be large enough then maybe...and actually I am not sure...

For example, could 64 squares be encoded in each of fifteen states (KQRBKP for both sides or empty) and then could all of that be considered at once due to quantum uncertainty?  Must admit I have no idea if it even works that way.  Maybe I'll try to read up on it.

JubilationTCornpone
 

I suppose it depends what the exponent is.  If it is 2, then 1,000 only squares to 1,000,000, which is still a small number.  Meanwhile 10^45 still square-roots to 10^22, which remains far too big.  But if the exponent could be large enough then maybe...and actually I am not sure...

For example, could 64 squares be encoded in each of fifteen states (KQRBKP for both sides or empty) and then could all of that be considered at once due to quantum uncertainty?  Must admit I have no idea if it even works that way.  Maybe I'll try to read up on it.

 

Answering myself, at least for the moment, and without taking a PhD level course at the border of CS and Physics, from what I can determine, quantum computers aren’t expected to be all that well suited to this problem.

Apparently the exponent we are dealing with is still 2.  That is to say 2 states per qubit.  Even considered all at once, this isn’t nearly as cool as if the number of states could be much larger.

Also apparently, quantum computers are not expected to be particularly good at solving problems involving sequence (which chess more or less is).  That is, you could possibly encode all the states in a very large number of qubits.  But then you still need to connect them up in meaningful sequence, which is just as hard as it ever was.

And lastly (lol, as if), you still need to be able to “read” the solution even if the quantum machine is capable of giving it, and it’s still as big as it ever was.

Sorry for the edits--the self-quoting wasn't working very well.

Flank_Attacks

.. At least, it takes a slightly different 'tack' in emphasizing, the importance, of this acknowledged, {Big}, technological, breakthrough !  [ :

https://www.extremetech.com/extreme/260215-alphazero-new-chess-champion-harbinger-brave-new-world-ai

vickalan

Thanks to everyone on this thread such as @RCMorea, @Flank_Attacks, @IfPatriotGames@winston_weng, @LawAndOrderKing, @s23bog, @NelsonMoore, @Elroch, @me_roma, @hairhorn, and plenty of others, all who are polite, and have thoughtful, insightful, and interesting comments. (of course I missed a lot of people, but this seems to be one of the most popular topics on chess.com). Interesting stuff!😊

DiogenesDue
Deedlit wrote:
 

Your claim that a game cannot be solved unless the entire area is traversed is false, and an easy way to see that it is false is the fact that there are a number of solved games for which traversing the entire game tree is completely unfeasible.  For example, checkers.

 

How big is the game tree of checkers?  Well, it's infinite, since theoretically you can keep moving pieces back and forth indefinitely.  Even if we bound the length of the game, like Shannon did for chess, we still get around 10^60 for a game of 80 plies or less.  This is a completely unfeasible number, both for storage and number of computations.  Yet checkers was solved back in 2007!

 

How did they do it?  Well, first of all it is the number of positions that is the relevant number for the difficulty of brute-forcing the game, not the size of the game tree.  But even then, there are about 5*10^20 positions in the game of checkers - still too many to have brute forced in 2007.  What they in fact did was search about 10^14 positions, with a storage requirement of 10^7 per computer.

 

Here's why you don't have to actually search every position.  To prove that checkers is a draw, you need two things: a strategy for the first player that always leads to a draw or a win, and a strategy for the second player that always leads to a draw or a win.  This proves that neither player can force a win against the opposing strategy.  Now, the strategy for the first player requires that you examine every possible play by the second player; but it does _not_ require that you examine every possible play by the first player! You only need to find one move at each step.

 

Theoretically, this could lead to a best-case scenario of about the square root of the number of positions as the required number of positions to be searched; in practice, things are likely to be a little worse.  But, the Schaeffer team was still able to reduce the number to about 10^14, which was a significant improvement.

 

Assuming an analogous reduction for chess, we could speculate that the approximately 10^45 positions would require about 10^30 positions traversed using 10^15 memory.  Certainly not feasible at the moment, and also not something we cannot rule out in the indefinite future.  Yes, this is speculative; the actual numbers could be higher, could be lower.  But that's the point - we really don't know.  What I know for sure is that it is not required to search all 10^45 positions.  So any argument of impossibility based on 10^45 computations/storage being required (or worse, 10^120) is not correct.

 

Another good example of a complex solved game is Go-Moku, played on a 15x15 board.  This has roughly 10^105 positions, and the number of games is much higher!

I see you conveniently skipped over my statement that brute force plus added shortcuts were used to solve all of Vickylan's list.  You posit a giant shortcut that still leaves this in "unsolvable in our lifetimes territory".  Perhaps, while trying to argue with me, you could also address Vickylan's claim that chess can be solved within 25-50 years, or sbog's claims that chess can be solved any day if only we have a breakthrough in storing arrays using vegetables wink.png...

Because I am not here to argue with fairly reasonable posts like yours.  I am here to debunk ridiculous diagrams and numbers pulled of of hindquarters.  If you want to assume a square root reduction, go ahead...but I'll be the one posting here in 25 years with a giant 72 font size "I told you so".  You are assuming an "analogous reduction" and a "best case scenario" that equates checkers with chess, but checkers is half the board size, and the pieces move in ways that are incredibly simplified (to the point of being binary before kings are on the board wink.png).

As for your 10^46.7 assertion, I've already posted about that long ago to refute Vickylan and some similar (but his are completely based on garbage assumptions) reductions to 10^30.  Which, as you admit, is still beyond not only current capabilities, but even reasonably expected future capabilities.

If you would like to officially join the other side of this argument, all you need to do is agree with Vickylan and say:

I think chess will be solved within our lifetimes.

Go for it.

vickalan
btickler wrote:

 

...Go for it.

 

I never said "I think chess will be solved within our lifetimes." Like so much else in your message, you like to invent nonsense, and seem to base your arguments on hyperbole and fantasy.😊

DiogenesDue
btickler wrote:
Deedlit wrote:

Hmm, this misunderstanding is repeated throughout this thread and in other discussions on solving chess.  There are not 10^120 different chess positions, that is an estimate of the number of chess games of average length (40 moves).  The number of chess positions is roughly 10^44, much less.  This is important for the matter of solving chess, since it is not necessary to search the same position more than once, so 10^44 serves as a maximum for the difficulty of the problem.

Further, it is not necessary to actually search through all 10^44 positions to solve chess, there are pruning methods available that can greatly reduce the number of searched positions, to roughly the square root in the optimum case.  To see why this is so, observe that, if chess is a draw, then solving chess would require finding a strategy for white that always leads to at least a draw, and a strategy for black that does the same.  To find a strategy for white, an algorithm may start with e4; if there is a drawing strategy for white starting with e4, then it is not necessary to search positions that can't be obtained starting with e4.  So a drawing strategy requires dealing with all the opponent's moves, but there is no need to examine all of your moves.

To see why some of these arguments for chess being insolvable are invalid, note that they would apply also to checkers.  Checkers has complexity roughly the square root of chess, with about 10^21 positions and about 10^50 to 10^60 games of average length.  If one needed to actually search through 10^60 games to solve checkers, that would obviously be too difficult as well.  Even searching through 10^21 positions would be beyond current capabilities.  But checkers was solved back in 2007!  If you read the details of their proof, they searched through about 10^14 positions using 10^7 memory, using the pruning techniques I mentioned before combined with a partial endgame tablebase.  This was just easy enough for them to be able to handle it.

Assuming a similar reduction for chess, one might guess it would take searching about 10^29 positions using a similar approach.  This is a blowup of difficulty by a factor of 10^15, obviously too much for current computers, but not something obviously too much for human civilization until the end of eternity!  Certainly, all this talk of "more than the number of atoms in the universe" is not relevant here.

10^15 times current computing power puts the solution well past the lifespan of anyone on this forum, or likely anyone that ever will read this forum before it is long gone ;).  Even if the model resulting in Moore's Law (computing power doubles very 2 years, essentially) were still in effect (it is not, it has slowed way down)...

So, ultimately, the argument is the same...whether the universe cannot hold the answer or not, the answer is just as unreachable for anyone musing about the problem right now.

Well, look at this ^^^ copied from page 32...

Re-read your old post.  Your previous post (not this quoted one) is comparing 10^60 games to 10^46.7 positions.  And you know it!  Checkers actual complexity is 10^21, reduced to 10^14 by "shortcuts".  If you want to compare 10^60, then you should be comparing it to the Shannon number, 10^120.

You flat out stated in your post on page 32 that to solve chess requires 10^15 times more computing power than solving checkers.  Now are you going to tell me that an increase in mankind's sum total of computing power is going to increase 10^15 times within the next 50 years?  Hell, 500 years?

captain222
Fixing_A_Hole wrote:
waffllemaster wrote:

This has been asked and talked about before.  The answer is no.

 

ifoody wrote:

Sadly yes. It may take some years, but the technology advances all the time, and if today's computer need 200 years to solve chess completley, in 10 years the will need 50 years, and maybe in some time solving games like chess will be something that every 8 years old kid can do with his personal computer at home.

But the answer is for sure, yes.

The problem with that logic is they currently need an absurd number like 10^50 years.  So in the future, when it gets 100x faster, they'll only need 10^48 years, and in the very far far far future, only 10^40 years.

And then there's the impracticality (more like impossibility) of storing the solution.

e.g. a little quiz.  If every position + its evaluation only took 1 bit of storage space, and every bit could be stored in the size of an atom, then how big would the storage device be?

A) Bigger than the moon.
B) Bigger than the sun.
C) More atoms than our solar system.
D) More atoms than our galaxy.

Answer is none of the above- More atoms than in the universe.  

Do you know how big an atom is? There's millions of atoms in a peice of dust.

syed700

vickalan
btickler wrote:
 
...Well, look at this on page 32..

 

What does that have to do with anything here? I never said "I think chess will be solved within our lifetimes." Like so much else in your message, you like to invent nonsense, and base your arguments on hyperbole and fantasy.😊

Elroch
RCMorea wrote:
Elroch wrote:
RCMorea wrote:
Flank_Attacks wrote:

.. Obviously, it's speculation ; But since, 'quantum' computers, are still in their development infancy ; Perhaps, there are already, mathematical projections, {or estimates} ; As to how long, it might take, a hypothetical, quantum 'supercomputer' ; Capable, of sorting through, mind-boggling, permutations ; Given that, the 'quantum' approach ; Has supposedly equal, daunting capabilities {!?! }

Quantum computers don't work like that.  They check all permutations at the same time.  A quantum computer with enough power solves chess instantly.  The problem is, "enough power" (meaning enough quantum bits, properly organized and powered) is still on the same order as has already been discussed. 

No, I believe you are wrong here. The computation that can be achieved with a quantum computer is exponential in the number of qubits. So if this resource was used efficiently, a thousand qubit quantum computer might be adequate for chess.

 

I suppose it depends what the exponent is.  If it is 2, then 1,000 only squares to 1,000,000, which is still a small number.

No, you have this upside down. "Exponential in N" means that the correct number is k^N, where N is a 1000 here. You can assume k is 2, but it doesn't matter much: the log to one base is proportional to the log to another. k^1000 is big (I chose 1000 to be generous).

 

DiogenesDue
vickalan wrote:
btickler wrote:
 
...Well, look at this on page 32..

 

What does that have to do with anything here? I never said "I think chess will be solved within our lifetimes." Like so much else in your message, you like to invent nonsense, and base your arguments on hyperbole and fantasy.😊

Ummm...can you recognize that a post that quotes someone else and then replies to it is not directed at you? wink.png

Your post is next.

JubilationTCornpone
Elroch wrote:
RCMorea wrote:
Elroch wrote:
RCMorea wrote:
Flank_Attacks wrote:

.. Obviously, it's speculation ; But since, 'quantum' computers, are still in their development infancy ; Perhaps, there are already, mathematical projections, {or estimates} ; As to how long, it might take, a hypothetical, quantum 'supercomputer' ; Capable, of sorting through, mind-boggling, permutations ; Given that, the 'quantum' approach ; Has supposedly equal, daunting capabilities {!?! }

Quantum computers don't work like that.  They check all permutations at the same time.  A quantum computer with enough power solves chess instantly.  The problem is, "enough power" (meaning enough quantum bits, properly organized and powered) is still on the same order as has already been discussed. 

No, I believe you are wrong here. The computation that can be achieved with a quantum computer is exponential in the number of qubits. So if this resource was used efficiently, a thousand qubit quantum computer might be adequate for chess.

 

I suppose it depends what the exponent is.  If it is 2, then 1,000 only squares to 1,000,000, which is still a small number.

No, you have this upside down. "Exponential in N" means that the correct number is k^N, where N is a 1000 here. You can assume k is 2, but it doesn't matter much: the log to one base is proportional to the log to another. k^1000 is big (I chose 1000 to be generous).

 

Interesting.  I started to write up an example of why you are wrong and proved to myself you are right.  It's 2^N.  In fact, at least at one point, I already knew this but was failing to apply it properly.

So...that would suggest all the positions could be examined within a probably feasible quantum computer.

I'm not sure that changes the answer because I don't actually understand some of the other objections I've come across, especially why quantum computers are said to be bad at problems involving sequence (I could guess that having encoded all these positions they still have to go through them in order, but it would only be a guess).  And would the existence of the machine itself count as a proof, if you couldn't store the output?

For sure, the very existence of quantum mechanics should keep anyone living in this world from being too sure they know the answer to anything.

DiogenesDue
vickalan wrote:
btickler wrote:

 

...Go for it.

 

I never said "I think chess will be solved within our lifetimes." Like so much else in your message, you like to invent nonsense, and seem to base your arguments on hyperbole and fantasy.😊

I have to apologize Vickylan...you never did state that explicitly.  You also never said 50 years.  You actually gave a bunch of ridiculous calculations and claimed it could be done in 18 years...check page 61.  You stated on 2 other occasions that chess could be solved in the next couple of decades.  Later you effectively recanted and said 200 years, with ironically even more specious reasoning, on page 109.  Since then you have kept your number to yourself for close to 100 pages.  What that shows anyone paying attention is that (A) you were full of crap to begin with, (B) you later realized you were full of crap but never admitted it, and (C) that now you have given up on even standing behind your retreat to 200 years number.  Because...you know you are wrong.  Just admit it.

I do apologize for giving you credit for 50 years when you believed an even more unreasonable 18-20.

Some of your quotes, in chronological order:

 

"On the other hand, if best play is a draw, chess won't be solved until the entire tree is checked. So we can only expect an answer in our lifetime if one side can force a win. But if perfect play is a draw, we probably won't know it within our lifetime."


"Checkers has been solved. Chess is a big leap, but it could happen within a decade or two."


"As for solving chess, there is some reason to believe it can happen within a decade or two."

 

"So chess might be able to be solved in 18 years."


"These are other advances that will help solve chess, compared to computers in 2007 when checkers was solved. I agree with Campter: Yes - chess may soon be solved."

 

"If I must make a guess, I would say Yes chess will be solved within 200 years or so."

 

The next time you claim "invented nonsense" or hyperbole on whatever subject, hopefully people will remember your blatant falsehood here. 

 

For fun:

You posted your silly tree diagrams on pages 65, 68, 116, 117, 127, and 145.

You posted your triangle diagram on pages 165 and 182.

You posted your Venn diagram on pages 146 and 184.

You posted your moving a sofa animated GIF on page 176...you haven't repeated yourself on that one yet.

DiogenesDue

While I was sifting through Vickylan's stuff, I also decided to take a look at s23bog's posts...here's a sample of bipolar manic episodes run amok:

"There is currently enough computing power on the planet to solve chess, and store the solution. It is a matter of priorities, however, and chess ranks pretty low for the VAST majority of people."
"Running a chess engine like a farm might be a worthwhile idea."
"There is a ton of mining, here in Chile. So, mining has been on my mind for a little while. Excessive heat can be a problem, from what I understand. I can't think of an effective way to collect the heat to be converted into a more usable form (like electricity?)."
"If you were to create a manager of engines ... kind of like a music conductor of chess engines ..."
"While the answer to the question is a single bit, the proof of the answer is not something people can really see with our eyes, or grasp with our minds."
"I am quite capable of taking a stance that may be wrong. Sometimes I do this to challenge others. Other times, it is just because I feel like motivating others. In this case, it is because I truly believe that white is the only one that can force a win from the initial position"
"I wouldn't mind losing my reputation. Was thinking what life would be like if I wasn't constantly messing things up. Undoubtedly, there would be plenty of people quite thrilled by my demise, but I would quickly be forgotten, I am sure. No benefit from any death is ever very long lived."
"Many position have been solved for chess. Tactics are a good example of a few. But in order to solve the game, we really need to solve for the 0 position. Considering that this position occurs with the absolute greatest of frequency, for about a thousand years, or so ... it stands to reason, that this position has "eaten up" the greatest amount of processing time. I think back to reading about Bobby Fischer thinking for 5 minutes before making his first move in game 6 of the 1972 match with Spassky."
"There only needs to be one way for white to force a win for there to be a forced win for white."
"I compared it before to threading a needle. The thread moves (black) and the needle moves (white), but they only need to line up one way to get the thread through the needle. One move for white from the initial position and one response for every black response to that one move for as many moves as it takes."
"I have made no such assumption. The only assumption I am making is that black cannot force a win."
"It isn't like it is that hard to get the rating up for a 2600 player."
"How about, as a path to finding out the actual solution, we were to create a tree of white wins, only? From there, it becomes a matter of seeing if you can stay on that tree without falling off of it."

"Using computers to solve chess would be tantamount to turning on a big electromagnet."

"You may have quoted a post, but it wasn't my post. I never said that there was no chance that black could force a win. I decided to take the position that black does not have a forced win, but, as I have stated, I am quite capable of taking positions that are wrong. Sometimes, I even take positions I don't believe are right."
"But, these mammoth complexes that you could build, need not be tethered to the earth."
"It is interesting to think of what actually is meant by "under the sun", since we revolve around the sun. From the perspective of someone actually ON the sun, it would be anything over the sun."
"I was thinking earlier of the time that computers take before deciding on a move. If the computer controls this, it would seem the computer has attained the ability to judge for itself."
"Does no one see any promise by dividing up the positions by pawn structure?"
"Let's say the data is like snow on a mountain face, and the spherical storage devices collect data from a mountain of users as it rolls down into a lake, where it gets melted into a big lake."
"Chess is like a tree. For the computer, we can think of the numbering system as the roots of the tree. Games played using a particular numbering system would be the roots of the tree."
"I present myself as I am, and usually people show me the door. I even recall the door actually being slammed shut once."
"For that matter, it isn't worth arguing about whether or not chess will be solved either. I don't find such endeavors very productive."
"I have declared war against the United States"

lfPatriotGames

I like the second one. Running a chess engine like a farm might be a worthwhile idea. Anyone that thinks that way can't be all bad.

vickalan
btickler wrote:

...You posted your triangle diagram on pages 165 and 182.

...You posted your Venn diagram on pages 146 and 184...

 

Lol, you went back more than a 100 pages and created a Table of Contents to prove that what you said I said, I never said!🤠

DiogenesDue
vickalan wrote:
btickler wrote:

...You posted your triangle diagram on pages 165 and 182.

...You posted your Venn diagram on pages 146 and 184...

 

Lol, you went back more than a 100 pages and created a Table of Contents to prove that what you said I said, I never said!🤠

Actually, your posts were pretty easy to parse, which is why I did a second pass for s23bog.  And, what you said was actually worse.  I consider it time well spent...not to convince you, but to show your lack of integrity to your audience at large.

DiogenesDue
LilBoat21 wrote:
CP6033 wrote:

 in the next 30-40 years no, 100-200 who cares? i mean none of us will be alive then.

Almost 4 years later Google made the most powerful chess engine ever.

Still TBD.

Johnkagey

ptd570 wrote:

Will there ever be a computer strong enough to solve chess to the point where white uses its half tempo advantage to always beat black no matter what moves black plays (in otherwords the same computer can never win with black even after a thousand random games against itself)

 

I beleive one day there will be a computer so strong and so big that it will solve chess completely but perhaps that is 50 or 100 years off, its possible to solve it but we may never see it even in a 100 years

the answer is no.The reason being that there are 20 possible first moves alone meaning the outc ok me can not be certain.