Will computers ever solve chess?

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Elroch
wtmgeo wrote:

Just by symmetry black CANNOT win if white chooses the opening move.

False reasoning. Chess is not a game where symmetry justifies this conclusion. White certainly cannot copy black's moves whatever he plays before that. Note that there are plenty of games with a symmetrical start position and symmetrical moves where the first player loses. (One example is Nim with the piles being 3-2-1). In chess, zugzwang is a well-known phenomenon and I bet it is possible to construct a symmetrical zugzwang position (the starting position is of course a symmetrical position).

I personally think a draw for all opening moves is unlikely. There is probably at least one winning, and maybe at least one losing, first move for white. But who knows.

Not you, to be frank!

 

wtmgeo

Black simply cannot be at an absolute advantage in chess if it moves second. It is absurd to suggest otherwise.

troy7915

 Yes, it can, potentially, nobody does know for sure right now.

 

 (Obs: The iPad anticipated the text differently., and I had to correct it.)

 

Elroch

Correct. It merely seems unlikely that white is in zugzwang.

troy7915

It seems unlikely according to what we know at the moment: which is very little compared to what we don’t know—given the huge number of possible games to be played.

eryxc

Yes

Elroch

To be fair, almost all possible games involve blunders on a large fraction of moves!

An interesting concept to chess players is how many perfect games there are (these are ones where the theoretical result of the start position gets preserved throughout - i.e. no blunders, in the precise sense). An estimate suggests this number is way more than the number of legal positions.

Another interesting number is the number of distinct positions that are reached in perfect games - clearly much smaller than the number of legal positions, firstly because it excludes all positions that have the "wrong" result, but secondly because a lot of positions with the right result are not going to turn up without blunders preceding them.

A further intuitively interesting concept is the minimum number of positions a perfect strategy needs to deal with if the opponent plays perfectly (but with complete freedom). This is practically interesting, because winning games after the opponent has blundered may be easier than preserving the correct result after the opponent has played perfectly.

It's worth noting that random positions are empirically very largely winning for one side so, if the perfect result is a draw (as most believe), almost all positions could only have a chance of appearing after a blunder.

cellomaster8
Stfu
eryxc
cellomaster8 wrote:
Stfu

You stop first then elroch

troy7915

Many blunders may not turn out to be blunders, but brilliant sacrifices with perfect play. Especially ‘weak’ moves, labeled so because, say, they fail to bring nothing for the side playing it, may turn out to be strong moves after all, if a strong continuation is eventually found.

  Take for instance 1. e4 c5 2. f4 d5 3. exd5 Nf6—a well-known gambit. After 4. Bb5+ Bd7  5. Bxd7+ Qxd7, 6. c4 e6, 7. Nf3? s labeled weak because it doesn’t bring anything for White. Although it is a clever way to keep the extra pawn for the moment, containing a little trap—after 7...exd5 White can regain the extra pawn with 8. Ne5 Qc8 8. cxd5, when Black cannot recapture on d5, due to (8...Nxd5?) 9. Nxf7! after which he will be a pawn down with little prospects—so he has to play 7...Be7 and castle, and after that exchange another pawn and regain one back, thus leaving White with pretty much nothing. But who knows? Somebody finds out a good continuation and ‘?’ becomes ‘!’ or even ‘!!’. 

  All the chess work is done in the dark, illuminating more and more of it. But the big picture is so vast that what we’re illuminating is only a very, very small corner. We know nothing, really.

 

  As for the number of perfect games, in the true sense of that word, ideally it is one.

 Best move for White from the very beginning, either bringing a win in the least number of moves with perfect opposition, or a loss in the biggest number of moves with best moves by Black, or a forced draw in the biggest number of moves—we must assume both sides are trying to win the perfect game, so they pose problems after problems, with the purpose of having the other side crack at some point—for both sides.

  But who knows? Perhaps no matter what the first move for White is, Black has a choice of moves with which he can either lose or win in the same number of moves. It seems unlikely though, if perfect opposition increases the number of moves to astronomical levels —it is very improbable to find to games with best opposition leading to the same result (win for either side or draw) in, say, 55 million and exactly 11 moves!!—but it is still not a certainty until all the permutations have been exhausted.

Elroch

It is true that our knowledge of what is good and bad is mostly imperfect and uncertain. The length of games is not an important factor to the theoretical situation: symmetry does not guarantee anything about the length of optimal variations after different moves (there are almost always going to be large numbers of these, generally with different lengths anyway (it is easy to be sure of this by looking at the situation where we do have perfect knowledge: in endgame tablebases.

troy7915

 The length of the games matters in deciding what a perfect game is. If White wins in 55.000 moves with perfect opposition, then winning in 55.014 moves with perfect resistance by Black, means that somewhere he slipped up!

wtmgeo

Ok, I think I understand what you are saying : that there are entirely symmetrical configurations of (a small number of) pieces for which is is known for certain that the side moving first is at an absolute disadvantage. And the statement is that, by extension, this may be true of the initial state of the chess board. Ok, I apologize for my categorical statements. 

troy7915

Zugzwang, hello? The opposition in pawn-king vs pawn endings, hello?

Elroch
troy7915 wrote:

 The length of the games matters in deciding what a perfect game is. If White wins in 55.000 moves with perfect opposition, then winning in 55.014 moves with perfect resistance by Black, means that somewhere he slipped up!

Not if you count 1 point for a win. There are no bonus points for being 14 moves quicker. According to the rules of chess, optimality is a matter of getting the right result, not the quickest way to that result.

pawn8888

Perhaps a perfect game would be for white to use it's slight opening advantage and play for a win, not making any mistakes. Black couldn't play a perfect game for a win because white would have to make a mistake first which would mean the game wasn't perfect. Maybe black's perfect game would be a draw.  

lfPatriotGames
pawn8888 wrote:

Perhaps a perfect game would be for white to use it's slight opening advantage and play for a win, not making any mistakes. Black couldn't play a perfect game for a win because white would have to make a mistake first which would mean the game wasn't perfect. Maybe black's perfect game would be a draw.  

If blacks perfect game is a draw, wouldn't that mean whites perfect game is a draw too? I'm assuming in all cases both sides play with no mistakes. If white starts out with an advantage and plays for a win and black can't stop it, then blacks perfect game is always a loss and never a draw.

Elroch

Yes, correct.

troy7915
Elroch wrote:
troy7915 wrote:

 The length of the games matters in deciding what a perfect game is. If White wins in 55.000 moves with perfect opposition, then winning in 55.014 moves with perfect resistance by Black, means that somewhere he slipped up!

Not if you count 1 point for a win. There are no bonus points for being 14 moves quicker. According to the rules of chess, optimality is a matter of getting the right result, not the quickest way to that result.

 

  The point is that if you play a longer game you allow more chances for your opponent, by giving yourself more room for error. The longer the game lasts the more resistance  your opponent puts up with perfect play and the less perfect your moves are.

  We are talking about perfection here. Like the road from A to B, it is the most direct route between two points. It is even more obvious when the difference between the number of moves is reduced dramatically, to a reasonable number that can be played in a normal game, like from 55.000 to 79 moves.

 

 But that being said, I can see your point as well, where only the final result counts, and so a move would be perfect regardless of how it gets the job done.

troy7915
pawn8888 wrote:

Perhaps a perfect game would be for white to use it's slight opening advantage and play for a win, not making any mistakes. Black couldn't play a perfect game for a win because white would have to make a mistake first which would mean the game wasn't perfect. Maybe black's perfect game would be a draw.  

 

  That scenario assumes that White starts the game with a slight advantage. In the big picture, we don’t know that for sure.