True or false? Chess will never be solved! why?

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pdela

There are quantum criptography protocols that don't rely in "mathematical hardness" but his security is guranteed by Physics laws. In fact Anton Zeilinger, encourage Austrian national bank to implement them. This dates back to 2004

http://www.nature.com/nature/journal/v428/n6986/full/428883b.html

Ziryab
EricFleet wrote:
Ziryab wrote:

of course a significant portion of the 10^43 positions are trivial. the seven piece tablebases were released about five years ahead of several predictions because they excluded certain trivial positions, such as five queens of the same color. Such a reduction of the problem also made it possible for these tablebases to fit into a mere 140 TB of storage. You could put them on your hard drive.

You have quite the hard drive... And even if 99.99% are trivial (I doubt it is nearly that high), you still have 10^39 posions left :)

No, my hard drive is only 1 TB. I have to store the six piece TBs on an external. But, maybe our friend who believes that math will solve everything has such a hard drive.

zborg

Tic-Tac-Toe, solved.  Checkers, solved.

Chess...don't hold your breath, or your head will explode.

Regardless, please stop making bald assertions about "technology" that hasn't been invented.  Those assertions are better used in the AGW and Evolution threads.

End of Story, yet again ??  Of course not...Onward Christian Soldiers.

The_Ghostess_Lola

It's true that AntiChess (Must Take ?) has been solved.

zborg
The_Ghostess_Lola wrote:

It's true that AntiChess (Must Take ?) has been solved.

"Must Take" is the same principle as Checkers.  That's an easy one.  Wink

P.S.  I once saw a chicken in a cage, at an Italian street fair in NYC, beat a human at Tic-Tac-Toe.  I broke out into a sweat, because I was up next against that bird.

Thankfully, I held the draw.

P.S.  Chess is a draw, but nobody can prove it.

End of Story, yet again ??

MuhammadAreez10

Chess is not going to be solved for at least half a century.

MuhammadAreez10

(End of story?)

Ziryab
owltuna wrote:

I have a 250Tb drive on my Atari 800XL. It's in the garage right now, solving chess. Has been chugging along since 1982, should be done any day now.

+1

watcha

I have looked into Shannon's formula and it is the number of possible shufflings of the pieces in the starting position. Since at the cost of 4 pawns you can promote all other pawns, giving you 12 new pieces to the existing ones, there is room for additional variety. It is true that not all possible positions will be legal, but a huge number of random positions where there are not too many pawns on board will be legal. So the number of legal positions may be more than Shannon's number which is 4.6*10^42 as calculated from the original formula below:

http://www.wolframalpha.com/input/?i=64%21%2F%2832%21*8%21%5E2*2%21%5E6%29

Some credible looking estimates put an upper bound of 10^46 on the number of possible ways to place a legal collection of chessmen on the board resulting in a legal position:

http://mathoverflow.net/questions/138133/what-proportion-of-chess-positions-that-one-can-set-up-on-the-board-using-a-leg

The number of legal positions may very well be on the order of the number of water molecules in all of Earth's oceans:

http://www.wolframalpha.com/input/?i=molecules+in+volume+of+Earth%27s+oceans

so if you can store a position in one water molecule, you need a memory of the size of all of Earth's oceans.

On the other hand it is also true, that the number of bits of information that can be present in the space occupied by a human brain ( caution: this is just a physical limit, the actual brain can not store this amount of useful information ), is also on the order of the number of legal chess positions:

http://en.wikipedia.org/wiki/Bekenstein_bound

A very clever device making use of quantum states may theoretically store much more than a few bits per molecule, so the size of the required memory can be anywhere between the size of Earth's oceans and the size of a human brain.

The brute force solution to this problem ( which is the only known method as of now ) is an incredibly difficult one, but not exactly impossible.

TheGrobe

There was some prior work (that I'd done) in this thread that a contemplated a minimal storage model for positions.  I can't find it now, but I seem to recall it was just under six bytes per position.

TheGrobe
watcha wrote:

The brute force solution to this problem ( which is the only known one as yet ) is an incredibly difficult one, but not exactly impossible.

Theoretically, it is entirely possible given no limits to the time and space we have available to us.  It is in the practical implementation of such an algorithm and the storage of the result where the trouble comes into paradise.

watcha

I do not underestimate the creativity of humans.

When I say the solution is not exactly impossible, I mean a practical solution.

electricpawn

What would the "solution" to chess look like over the board? A series of moves that guarantees a draw? A set of strategems and guidelines like My System? We have that now. Since no human has the ability to defeat the best chess engines, couldn't we say that from a practical perspective chess has already been solved?

Chessmentor2
electricpawn wrote:

What would the "solution" to chess look like over the board? A series of moves that guarantees a draw? A set of strategems and guidelines like My System? We have that now. Since no human has the ability to defeat the best chess engines, couldn't we say that from a practical perspective chess has already been solved?

Checkers is fully solved like connect four, that is, there are perfect sequences of moves that always lead to a win or a draw and which cannot lose.

Perfect sequences from start to finish might exist for chess, but they haven't been found yet, not at least by brute force computer analysis (like in the case of checkers). The amount of possible piece combinations in chess is gigantic.

 

Most popular chess endgames have been solved a long time ago though, and perfect plays exist where it is impossible to get any other result than win or draw.

starrynight14
shockinn wrote:
starrynight14 wrote:

Is chess really just a problem to be solved?  I thought there were often a variety of move choices and options of styles to play.


What a loose comment to make. Have you even bothered to read a single of the one million posts in this thread?

If you aren't interested in my comment why are you even replying?  It just sounds like arrogance really.

I've read some posts, I'm not reading all of them.

TheGrobe

You've read some posts, but based on your comment you haven't understood the question.  I think that was shockinn's point.

If you aren't interested in understanding the question why are you even replying?  It just sounds like arrogance really.

starrynight14
TheGrobe wrote:

You've read some posts, but based on your comment you haven't understood the question.  I think that was shockinn's point.

If you aren't interested in understanding the question why are you even replying?  It just sounds like arrogance really.

I think you are very limited in how you want to look at the question, which seems like arrogance.

Even if a computer somehow had a best move for every postion how would that exactly affect people playing each other without using computers?  The obsession with computers solving something isn't really very relevant to what people get out of chess.  But if you want to keep to your limited viewpoint do so, but don't insult people who have a wider view. 

TheGrobe

It's not about viewpoints, it's about established definitions.  If you want to re-define what it means to solve a game I guess that's your prerogative, but it means that you're comments aren't going to be relevant to the discussion at hand which contemplates whether the game will be solved in the standard mathematical sense of the word.

It's not a limited viewpoint, or arrogance, it's precision.

TheGrobe

Well, first you have to define stuff.

starrynight14
electricpawn wrote:

What would the "solution" to chess look like over the board? A series of moves that guarantees a draw? A set of strategems and guidelines like My System? We have that now. Since no human has the ability to defeat the best chess engines, couldn't we say that from a practical perspective chess has already been solved?

Even if some perfect sequences (ideal moves by both players) are found that wouldn't be relevant to human play as there would have to be a rule to stop that happening in tournament play so that it would be a properly competed contest.  I can understand using computers to find out ways to improve human play, but to use them to find a 'solution' to or kill chess I find pretty pointless.