Has chess openings been solved? In other words has it been determined
what the single best response is to each position that can occur in say
the first 10 moves of a game?

Has chess openings been solved? In other words has it been determined
what the single best response is to each position that can occur in say
the first 10 moves of a game?

Depends on what is understood by "the single best response".

It has been proved mathematically that chess (belonging to a class of games
with certain properties) is solvable in the sense that every (legal)
position can be calculated (in a finite number of steps) to be either a win
for white, a draw, or a win for black. One can understand the property "is a
win for white" intuitively by thinking of a guaranteed path to victory no
matter what black does. "is a draw" similarly loosely means that white has a
path to at least a draw, while black has the same.

However, not many chess positions have been calculated to a definitive
conclusion compared to the total number of legal chess positions. Among the
non-calculated positions is the starting position and practically all "chess
opening positions", so in this strict sense, chess openings have not been
solved.

While it's not very likely that "early" positions are ever going to be
calculated to a definitive conclusion, one can always make a more or less
educated guess at their principal state. A majority of "chess people" seems
to think that chess (or rather, the starting position) is a draw, as are
positions arising from the most popular ways of playing the opening. Hans
Berliner on the other hand believes chess is a win for white.

Whatever is the final, correct answer, note that thinking in this way
entails that by "best response" we should simply mean a move that does not
lead to a position of another principal state. For instance, it may very
well be that all of white's legal 1st moves lead to principally drawn
positions, while none of them lead to won positions. In this case, all
white's possible 1st moves are "best" moves.

From this observation we can infer that thinking in terms of "principally"
best moves is usually not the best way to optimize results in pratical play,
especially not in the opening phase. Indeed, chessplayers instead normally
talk about moves leading to "better winning chances in practical play" than
other moves.

This can only be a contextual and subjective definition. There is no
consensus about what opening moves to recommend as "optimal winning chance
enhancing moves". Some moves have been weeded out as "practically inferior"
though. For instance, most chess players would probably agree that 1. e4
leads to better practical winning chances than 1. f3, even though it has
never been disproved that they both lead to principally drawn positions.

On Fri, 25 Feb 2005 13:26:31 +0100, "Alkelele"
alkelele-funnyA-tdcadsl.dk wrote:

It has been proved mathematically that chess (belonging to a class of games
with certain properties) is solvable in the sense that every (legal)

One position in Checkers/draughts occurring after three half-moves has
recently been proven to be a draw. That's something, but that's a
LONG way from what the OP asked.

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Jud McCranie wrote:
"Alkelele" alkelele-funnyA-tdcadsl.dk wrote:
It has been proved mathematically that chess (belonging to a class of
games with certain properties) is solvable in the sense that [...]

One position in Checkers/draughts occurring after three half-moves has
recently been proven to be a draw. That's something, but that's a
LONG way from what the OP asked.

That's nothing. Four positions in chess occurring after three half-moves
were proven to be won years and years ago.


Dave.

--
David Richerby Pickled Disgusting Gnome (TM): it's
www.chiark.greenend.org.uk/~davidr/ like a smiling garden ornament but
it'll turn your stomach and it's
preserved in vinegar!

On 25 Feb 2005 23:48:05 +0000 (GMT), David Richerby
wrote:

One position in Checkers/draughts occurring after three half-moves has
recently been proven to be a draw. That's something, but that's a
LONG way from what the OP asked.

That's nothing. Four positions in chess occurring after three half-moves
were proven to be won years and years ago.

I hope you're joking.

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"chessisbest" wrote

Has chess openings been solved? In other words has it been determined
what the single best response is to each position that can occur in say
the first 10 moves of a game?

"White wins in X moves against any defense" results in what
computer scientists call a "combinatorial explosion:" There are
simply too many combinations of possible moves. All you can
do is investigate winning lines of play. ("White loses in X moves"
is easy.)

--
Craig Franck

Cortland, NY

"Jud McCranie" wrote in message
...
On 25 Feb 2005 23:48:05 +0000 (GMT), David Richerby
wrote:

One position in Checkers/draughts occurring after three half-moves has
recently been proven to be a draw. That's something, but that's a
LONG way from what the OP asked.

That's nothing. Four positions in chess occurring after three half-moves
were proven to be won years and years ago.

I hope you're joking.


He is not joking - Work it out.

Regards

On Sat, 26 Feb 2005 07:23:13 -0000, "Terry"
wrote:

I hope you're joking.


He is not joking - Work it out.

I'm not saying that he is joking about fools mate, but the implication
that it is on the order of magnitude of showing the checkers position
after three half moves was a draw.

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I'm pretty sure he was joking. You should assume so too. It'll be
easier on you blood pressure. ;-)

On Sat, 26 Feb 2005 19:39:10 -0600, David Vancina "djvchess at
comcast dot net" wrote:

I'm pretty sure he was joking. You should assume so too.

Yes, I did.

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