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Main
Date: 29 Jan 2008 03:38:07
From:
Subject: with perfect play, should it be 1-0, 0-1, or a draw?
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If White and Black both play perfectly, who wins? Or is it a draw?
I'd be interested to know how chessplayers' opinions on this question
are distributed.
Personally I think White wins, because he starts with a clear
advantage.
I suspect most people might think the game is a draw.
Michael
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Date: 08 Feb 2008 16:33:43
From: help bot
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
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On Feb 8, 11:59 am, David Richerby <[email protected] >
wrote:
> To continue this little conversation with myself, I note that
> Wikipedia says that Nunn says that, er, I'll start again.
>
> KRN-KNN is a rather exotic sort of an endgame, that is unlikely to
> occur in real play. On the other hand, for an ending as natural as
> KQP-KQ, Wikipedia says,
>
> ``Tablebases have shown that this can be won in many more positions
> than was thought, but the logic of the moves is presently beyond
> human understanding'',
Where many humans fail in understanding such
things is in taking the wrong approach to them; for
example, in assuming that a direct attack is the only
way to attack.
Take the Trojan Horse, for instance. The Greeks
could not "direct-attack" their way in, but all the
same, they did have another method, and were
st enough to find it.
In the famous example of KQ vs. KBB -- which
was pronounced a draw by the leading authorities of
the day -- they forgot to consider that, if Black (i.e.
the weaker side) had an "ideal fortress" position, all
one need do is transfer the move to him, and kerpow:
the perfect fortress is not so perfect anymore!
The same principle applies to other forms of
fighting (i.e. Em. Lasker: "chess is a fight"). I
saw a video once of one of the Ultimate Fighting
Championships, and the guy who won was on
his back, getting the sh*t pounded out of him,
but his assailant was so busy "winning" he left
himself open to a decisive choke hold!
-- help bot
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Date: 08 Feb 2008 16:21:31
From: help bot
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
On Feb 8, 8:43 am, David Richerby <[email protected] >
wrote:
> > In KRN-KNN, are the programs winning when grandmasters would draw, or
> > drawing when they would lose, or both?
>
> KRN-KNN is won (in most cases) for the side with the rook. However,
> in many cases, the forced win takes over 200 moves, almost always, the
> game would be drawn by the 50-move rule. In practice, the ending
> never occurs but, if it did, humans would agree a draw (assuming that
> a piece wasn't immediately lost) and the computer would go on to win
> (assuming that the opponent didn't claim his draw by the 50-move
> rule).
In a situation where it is the endgame table-base
versus a human player, it seems very likely that a
poor defense by the human could result in no
50-move rule draw, but rather, a legitimate win for
the program.
As far as I can recall from my own games, this
ending has never occurred; but then, that might be
in part due to a deliberate avoidance of this kind
of simplification, since I always must win, and
because my opponents aren't st enough to
trade off all the pawns!
-- help bot
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Date: 08 Feb 2008 01:35:11
From: help bot
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
On Feb 6, 1:50 pm, Larry Tapper <[email protected] > wrote:
> > But isn't the leading edge of theory mostly variations on lines
> > popular in current practice? It doesn't necessarily represent best
> > play up to, e.g., move 35.
>
> Yes, I agree. The main purpose of deep preparation is not to make a
> modest contribution toward the general solution of chess, but to
> figure out what to play against Kropotkin.
>
> I think it's well understood that many playable and interesting lines
> can remain stagnant theoretically for decades just because they are
> unfashionable. John Watson gives several instructive examples of this
> phenomenon in his book Modern Chess Strategy.
>
> The point I wish to make, however, is that when a line _is_
> fashionable and therefore analyzed deeply by leading GMs, the work
> they do is most likely worth something objectively, in the sense that
> a perfect computer would view most of their efforts with qualified
> approval.
In many cases, the GMs may do 90% correct
analysis, but all it takes to debunk an opening
line is *one* improvement. I see this all the
time when analyzing games with a computer.
Tonight I went over an old game between
Bobby Fischer and Tigran Petrosian, and was
surprised when the daggone machine refused
to follow the main lines -- long presumed to be
forcing -- of the um, Pelikan(?) Sicilian. A few
more seconds, I kept thinking... then it will
finally "see" that it must play the book move
here... but no. The same thing happened in
the exchange Ruy Lopez between BF and BS
from 1992-- the computer refused to "cooperate".
But I will say this: in the first game mentioned
above BF played very, very well in the middle-
game, frequently matching the computer when
there were perhaps 30+ legal moves to choose
from! A real tough cookie, that guy was.
Still, when you see GMs losing to computers
at pawn odds -- after gaining a crushing edge
due to some programmers' misguided efforts to
interfere -- it is hard to take seriously any claims
to near-perfection in human analysis. Much of
it is built upon the flawed framework of prior
human analysis, just presumed to be correct.
Even what passes for computer-checked work
these days is often shallow stuff-- not even
remotely close to old-school correspondence
chess analysis work.
Jose Capablanca was right: [computers should]
learn the game backwards, starting with the
endgame [table-bases]. I am still working on
increasing the number of atoms in the "known"
universe, to satisfy the numb-skulls who can't
accept reality and who are in denial over the
data storage end of solving chess. Look-- there's
another atom! Right there, behind that distant
black hole; that's my next hard drive!
-- help bot
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Date: 06 Feb 2008 16:23:00
From:
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
On Feb 6, 5:29=A0pm, Larry Tapper <[email protected] > wrote:
> On Feb 6, 11:15=A0am, David Richerby <[email protected]>
> wrote:
[...]
> It is true that grandmasters could conceivably look like ignoramuses
> from the point of view of an omniscientchesscomputer, but I'm
> inclined to doubt that the gap is _that_ wide. Opening theory, for
> example, is dismayingly =A0deep nowadays =A0--- possibly Kramnik had his
> Corus game with Aronian prepared up to move 35! And this theory
> represents a sort of massive collective effort on the part of highly
> skilled and motivated inquirers. This isn't conclusive but surely it
> counts for something.
A perfect player would not even need the concept of "opening theory",
which is based on the misting up of the tree of possibilities. Ditto
those humans who have mastered noughts and crosses (tictactoe) need no
such concept.
Michael
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Date: 06 Feb 2008 16:17:46
From:
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
On Feb 6, 4:15=A0pm, David Richerby <[email protected] >
wrote:
> <[email protected]> wrote:
> > As for the argument that "grandmaster play has shown no evidence
> > that White can, with best play, keep his advantage, therefore it
> > seems unlikely that that would happen even withperfectplay" - I
> > wouldn't ascribe any appreciable weight to this. This is because
> >perfectplay wold be *way* stronger than the greatest play by
> > grandmasters.
>
> This depends on how much you think that current grandmaster play is
> resemblesperfectplay. =A0If you believe that grandmaster play is very
> much likeperfectplay but with a few mistakes thrown in, then you can
> try todrawconclusions aboutperfectplay from grandmaster play.
[...]
> On the other hand, it might be that grandmaster play is nothing likeperfec=
tplay.
>
> Consider what we know about endgames. =A0Tablebases tell us that
> grandmasters can play KRP-KR endings pretty-much perfectly. =A0We
> understand the tablebases and know why the right move is the right
> move. =A0On the other hand, the tablebase for KRN-KNN looks, in most
> cases like completely random moves -- nobody can understand it. =A0In
> this case, grandmaster play looks nothing likeperfect.
Sounds like we know how to spot the difference in this type of
endgame, whereas maybe we wouldn't in the middlegame or opening. The
difference, whether spottable or not, comes from the huge difference
in the number of positions analysed.
In KRN-KNN, are the programs winning when grandmasters would draw, or
drawing when they would lose, or both?
Michael
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Date: 08 Feb 2008 13:43:19
From: David Richerby
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
<[email protected] > wrote:
> David Richerby <[email protected]> wrote:
>> Consider what we know about endgames. Tablebases tell us that
>> grandmasters can play KRP-KR endings pretty-much perfectly. We
>> understand the tablebases and know why the right move is the right
>> move. On the other hand, the tablebase for KRN-KNN looks, in most
>> cases like completely random moves -- nobody can understand it. In
>> this case, grandmaster play looks nothing likeperfect.
>
> Sounds like we know how to spot the difference in this type of
> endgame, whereas maybe we wouldn't in the middlegame or opening. The
> difference, whether spottable or not, comes from the huge difference
> in the number of positions analysed.
>
> In KRN-KNN, are the programs winning when grandmasters would draw, or
> drawing when they would lose, or both?
KRN-KNN is won (in most cases) for the side with the rook. However,
in many cases, the forced win takes over 200 moves, almost always, the
game would be drawn by the 50-move rule. In practice, the ending
never occurs but, if it did, humans would agree a draw (assuming that
a piece wasn't immediately lost) and the computer would go on to win
(assuming that the opponent didn't claim his draw by the 50-move
rule).
But if you look at perfect play in this ending, it just seems to be
completely random. Nobody can work out what's going on because,
whatever the subgoals might be (for example, in KBN-K, they'd be
driving the king to the edge, then driving him to the right corner,
then mating), they take twenty or thirty or forty moves to achieve.
You can see the longest win at the following URL
http://www.xs4all.nl/~timkr/chess2/diary_3.htm
or play through it (a reflected version of the same thing) at
http://www.gothicchess.com/endings/chess_krnknn/game.htm
It makes no sense at all. The pieces just bounce around for move
after move after move.
Incidentally, I've seen elsewhere that there's a 290-move mate in
KRRN-KRR (seven-man). See the following link for discussion and
an example of the longest mate:
http://www.stmintz.com/ccc/index.php?id=456178
Dave.
--
David Richerby Surprise Toy (TM): it's like a fun
www.chiark.greenend.org.uk/~davidr/ child's toy but not like you'd expect!
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Date: 08 Feb 2008 13:44:32
From: David Richerby
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
David Richerby <[email protected] > wrote:
> KRN-KNN is won (in most cases) for the side with the rook.
I forgot to say -- about 78% of cases, according to Wikipedia.
http://en.wikipedia.org/wiki/Endgame_tablebase
Dave.
--
David Richerby Indelible Voodoo Cat (TM): it's like
www.chiark.greenend.org.uk/~davidr/ a cuddly pet that has mystical powers
but it can't be erased!
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Date: 08 Feb 2008 16:59:39
From: David Richerby
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
David Richerby <[email protected] > wrote:
> David Richerby <[email protected]> wrote:
>> KRN-KNN is won (in most cases) for the side with the rook.
>
> I forgot to say -- about 78% of cases, according to Wikipedia.
>
> http://en.wikipedia.org/wiki/Endgame_tablebase
To continue this little conversation with myself, I note that
Wikipedia says that Nunn says that, er, I'll start again.
KRN-KNN is a rather exotic sort of an endgame, that is unlikely to
occur in real play. On the other hand, for an ending as natural as
KQP-KQ, Wikipedia says,
``Tablebases have shown that this can be won in many more positions
than was thought, but the logic of the moves is presently beyond
human understanding'',
citing Nunn's _Secrets of Minor Piece Endings_.
http://en.wikipedia.org/wiki/Endgame#Effect_of_tablebases_on_endgame_theory
Dave.
--
David Richerby Natural Poisonous Goldfish (TM): it's
www.chiark.greenend.org.uk/~davidr/ like a fish but it'll kill you in
seconds and it's completely natural!
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Date: 06 Feb 2008 10:50:40
From: Larry Tapper
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
On Feb 6, 1:21=A0pm, Mike Murray <[email protected] > wrote:
> On Wed, 6 Feb 2008 09:29:48 -0800 (PST), Larry Tapper
>
> <[email protected]> wrote:
> > Opening theory, for
> >example, is dismayingly =A0deep nowadays =A0--- possibly Kramnik had his
> >Corus game with Aronian prepared up to move 35! And this theory
> >represents a sort of massive collective effort on the part of highly
> >skilled and motivated inquirers. This isn't conclusive but surely it
> >counts for something.
>
> But isn't the leading edge of theory mostly variations on lines
> popular in current practice? =A0It doesn't necessarily represent best
> play up to, e.g., move 35.
>
Yes, I agree. The main purpose of deep preparation is not to make a
modest contribution toward the general solution of chess, but to
figure out what to play against Kropotkin.
I think it's well understood that many playable and interesting lines
can remain stagnant theoretically for decades just because they are
unfashionable. John Watson gives several instructive examples of this
phenomenon in his book Modern Chess Strategy.
The point I wish to make, however, is that when a line _is_
fashionable and therefore analyzed deeply by leading GMs, the work
they do is most likely worth something objectively, in the sense that
a perfect computer would view most of their efforts with qualified
approval.
LT
> >Actually that's not the way I remember it myself. It seems to me that
> >back in the 80s I heard many people say, as if it were an obvious
> >fact, that a computer could never play chess better than its
> >programmer. But generally speaking, these skeptics were not chess
> >masters, they were just interested laypeople who had various axes to
> >grind against the notion of strong AI.
>
> I used to snigger at books such as Dreyfus' "What Computers Can't Do:
> The Limits of Artificial Intelligence".
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Date: 08 Feb 2008 08:25:08
From: David Richerby
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
Larry Tapper <[email protected] > wrote:
> The point I wish to make, however, is that when a line _is_
> fashionable and therefore analyzed deeply by leading GMs, the work
> they do is most likely worth something objectively, in the sense
> that a perfect computer would view most of their efforts with
> qualified approval.
There's no such thing as `qualified approval' by a perfect computer.
To the perfect computer, any line is either winning, losing or
drawing.
Dave.
--
David Richerby Accelerated Expensive Beer (TM): it's
www.chiark.greenend.org.uk/~davidr/ like a refreshing lager but it'll
break the bank and it's twice as fast!
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Date: 06 Feb 2008 09:29:48
From: Larry Tapper
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
On Feb 6, 11:15=A0am, David Richerby <[email protected] >
wrote:
> <[email protected]> wrote:
> > As for the argument that "grandmaster play has shown no evidence
> > that White can, with best play, keep his advantage, therefore it
> > seems unlikely that that would happen even with perfect play" - I
> > wouldn't ascribe any appreciable weight to this. This is because
> > perfect play wold be *way* stronger than the greatest play by
> > grandmasters.
>
> This depends on how much you think that current grandmaster play is
> resembles perfect play. =A0If you believe that grandmaster play is very
> much like perfect play but with a few mistakes thrown in, then you can
> try to draw conclusions about perfect play from grandmaster play.
> That said, you'd have to give an argument that differentiated between
> `White's mistakes mean that he draws games he should win' and `Black's
> mistakes mean that he loses games he should draw.' =A0(The latter seems
> more likely, since defending often requires making only moves, while
> attacking usually has more flexibility.)
>
> On the other hand, it might be that grandmaster play is nothing like
> perfect play.
A well-framed answer, I think.
It is true that grandmasters could conceivably look like ignoramuses
from the point of view of an omniscient chess computer, but I'm
inclined to doubt that the gap is _that_ wide. Opening theory, for
example, is dismayingly deep nowadays --- possibly Kramnik had his
Corus game with Aronian prepared up to move 35! And this theory
represents a sort of massive collective effort on the part of highly
skilled and motivated inquirers. This isn't conclusive but surely it
counts for something.
Help bot's comment on the grandmaster consensus was that he recalled
grandmasters insisting that computers would never reach master level.
So what do they know?
Actually that's not the way I remember it myself. It seems to me that
back in the 80s I heard many people say, as if it were an obvious
fact, that a computer could never play chess better than its
programmer. But generally speaking, these skeptics were not chess
masters, they were just interested laypeople who had various axes to
grind against the notion of strong AI. The strong players I knew
during that transition period tended to agree that the eventual
triumph of the silicon beasts was inevitable, though there was
disagreement about how long it would take.
Larry T.
>
> Consider what we know about endgames. =A0Tablebases tell us that
> grandmasters can play KRP-KR endings pretty-much perfectly. =A0We
> understand the tablebases and know why the right move is the right
> move. =A0On the other hand, the tablebase for KRN-KNN looks, in most
> cases like completely random moves -- nobody can understand it. =A0In
> this case, grandmaster play looks nothing like perfect.
>
> Dave.
>
> --
> David Richerby =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0=
=A0Devil Chainsaw (TM): it's likewww.chiark.greenend.org.uk/~davidr/=A0 =A0=
=A0 =A0 =A0 a lethal weapon that's possessed
> =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =
=A0 =A0 =A0 =A0 =A0 by Satan!
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Date: 08 Feb 2008 08:22:34
From: David Richerby
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
Larry Tapper <[email protected] > wrote:
> A well-framed answer, I think.
Thank you.
> It is true that grandmasters could conceivably look like ignoramuses
> from the point of view of an omniscient chess computer, but I'm
> inclined to doubt that the gap is _that_ wide. Opening theory, for
> example, is dismayingly deep nowadays --- possibly Kramnik had his
> Corus game with Aronian prepared up to move 35! And this theory
> represents a sort of massive collective effort on the part of highly
> skilled and motivated inquirers. This isn't conclusive but surely it
> counts for something.
It's hard to say. Perhaps grandmasters are, so to speak, getting
really, really good at making fire by rubbing two sticks together,
discovering all kinds of advanced techniques for how to shape the
sticks and what angle to rub them at. And somebody's going to come
along and invent the match.
> It seems to me that back in the 80s I heard many people say, as if
> it were an obvious fact, that a computer could never play chess
> better than its programmer.
Well, they were, frankly, idiots. Not because they were subsequently
proven to be very wrong but because they were committing a basic error
of reasoning. This is like saying that a robot can never run faster
than its designer or, as Turing put it, like saying that no animal
could possibly eat something bigger than itself.
Or maybe, since you say they weren't generally strong chess players,
they didn't realise that a large part of playing good chess is
checking that you're not going to lose material, which is a largely
routine process.
Dave.
--
David Richerby Surprise Pants (TM): it's like a
www.chiark.greenend.org.uk/~davidr/ well-tailored pair of trousers but
not like you'd expect!
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Date: 08 Feb 2008 15:38:11
From: David Kane
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
"David Richerby" <[email protected] > wrote in message
news:6Sp*[email protected]...
> Larry Tapper <[email protected]> wrote:
>> A well-framed answer, I think.
>
> Thank you.
>
>> It is true that grandmasters could conceivably look like ignoramuses
>> from the point of view of an omniscient chess computer, but I'm
>> inclined to doubt that the gap is _that_ wide. Opening theory, for
>> example, is dismayingly deep nowadays --- possibly Kramnik had his
>> Corus game with Aronian prepared up to move 35! And this theory
>> represents a sort of massive collective effort on the part of highly
>> skilled and motivated inquirers. This isn't conclusive but surely it
>> counts for something.
>
> It's hard to say. Perhaps grandmasters are, so to speak, getting
> really, really good at making fire by rubbing two sticks together,
> discovering all kinds of advanced techniques for how to shape the
> sticks and what angle to rub them at. And somebody's going to come
> along and invent the match.
Perhaps Mercury is home to a thriving colony of orangutans, living
underground. Perhaps the human lifespan can be doubled by properly aiming
He-Ne laser beams at the proper complex combination of taste
buds on the human tongue. Perhaps Knights really are much stronger than
Rooks, but you just have to know how to use them properly.
Fanciful speculations lacking a basis in reality are never worth much.
They key with chess is that we have a largely consistent story - computers
and tablebases etc are *not* refuting theory except for some extremely
rare positions, most of which there has never been any reason
for humans to analyze.
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Date: 06 Feb 2008 10:21:13
From: Mike Murray
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
On Wed, 6 Feb 2008 09:29:48 -0800 (PST), Larry Tapper
<[email protected] > wrote:
> Opening theory, for
>example, is dismayingly deep nowadays --- possibly Kramnik had his
>Corus game with Aronian prepared up to move 35! And this theory
>represents a sort of massive collective effort on the part of highly
>skilled and motivated inquirers. This isn't conclusive but surely it
>counts for something.
But isn't the leading edge of theory mostly variations on lines
popular in current practice? It doesn't necessarily represent best
play up to, e.g., move 35.
>Actually that's not the way I remember it myself. It seems to me that
>back in the 80s I heard many people say, as if it were an obvious
>fact, that a computer could never play chess better than its
>programmer. But generally speaking, these skeptics were not chess
>masters, they were just interested laypeople who had various axes to
>grind against the notion of strong AI.
I used to snigger at books such as Dreyfus' "What Computers Can't Do:
The Limits of Artificial Intelligence".
|
| |
Date: 06 Feb 2008 06:04:43
From:
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
On Feb 4, 6:42=A0pm, Larry Tapper <[email protected] > wrote:
> On Feb 1, 6:15=A0pm, [email protected] wrote:
>
> > I still think it's a win.
>
> > What's your opinion, disregarding issues of proof and the feasibility
> > thereof?
>
> > Michael
>
> For what it's worth, grandmasters who are asked this
> question will typically tell you that chess is probably
> a draw. There are some exceptions though, for example
> the correspondence champion and computer pioneer Hans
> Berliner, =A0who was famous for insisting that White has a
> winning advantage.
>
> I think it's a draw myself. If you look in the rgcm
> Google archives, you'll find several old threads with
> sometimes astonishingly heated debates on the subject.
I'm not sure that a grandmaster's opinion necessarily carries more
weight than a non-grandmaster's on this topic.
The argument that "White starts with an advantage, and therefore with
best play ought to be able to keep it and convert it to a win" doesn't
prove anything, but its weight is surely non-zero.
As for the argument that "grandmaster play has shown no evidence that
White can, with best play, keep his advantage, therefore it seems
unlikely that that would happen even with perfect play" - I wouldn't
ascribe any appreciable weight to this. This is because perfect play
wold be *way* stronger than the greatest play by grandmasters.
Michael
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Date: 06 Feb 2008 16:15:31
From: David Richerby
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
<[email protected] > wrote:
> As for the argument that "grandmaster play has shown no evidence
> that White can, with best play, keep his advantage, therefore it
> seems unlikely that that would happen even with perfect play" - I
> wouldn't ascribe any appreciable weight to this. This is because
> perfect play wold be *way* stronger than the greatest play by
> grandmasters.
This depends on how much you think that current grandmaster play is
resembles perfect play. If you believe that grandmaster play is very
much like perfect play but with a few mistakes thrown in, then you can
try to draw conclusions about perfect play from grandmaster play.
That said, you'd have to give an argument that differentiated between
`White's mistakes mean that he draws games he should win' and `Black's
mistakes mean that he loses games he should draw.' (The latter seems
more likely, since defending often requires making only moves, while
attacking usually has more flexibility.)
On the other hand, it might be that grandmaster play is nothing like
perfect play.
Consider what we know about endgames. Tablebases tell us that
grandmasters can play KRP-KR endings pretty-much perfectly. We
understand the tablebases and know why the right move is the right
move. On the other hand, the tablebase for KRN-KNN looks, in most
cases like completely random moves -- nobody can understand it. In
this case, grandmaster play looks nothing like perfect.
Dave.
--
David Richerby Devil Chainsaw (TM): it's like
www.chiark.greenend.org.uk/~davidr/ a lethal weapon that's possessed
by Satan!
|
| | | |
Date: 06 Feb 2008 09:55:33
From: David Kane
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
"David Richerby" <[email protected] > wrote in message
news:ZTC*[email protected]...
> <[email protected]> wrote:
>> As for the argument that "grandmaster play has shown no evidence
>> that White can, with best play, keep his advantage, therefore it
>> seems unlikely that that would happen even with perfect play" - I
>> wouldn't ascribe any appreciable weight to this. This is because
>> perfect play wold be *way* stronger than the greatest play by
>> grandmasters.
>
> This depends on how much you think that current grandmaster play is
> resembles perfect play. If you believe that grandmaster play is very
> much like perfect play but with a few mistakes thrown in, then you can
> try to draw conclusions about perfect play from grandmaster play.
I don't think that play need be anything close to perfect in order
to draw conclusions. Collectively, humanity/computers have explored
chess' move tree and, from those explorations, we can draw
conclusions. The only way that it would make sense to discount
past explorations is to hypothesize that every time humans or
computers have stumbled on the path to White's (or Black's) win,
that they didn't *realize* that they had an advantage and hence
didn't explore it further. This strikes me as extremely unlikely for a game
like chess.
> That said, you'd have to give an argument that differentiated between
> `White's mistakes mean that he draws games he should win' and `Black's
> mistakes mean that he loses games he should draw.' (The latter seems
> more likely, since defending often requires making only moves, while
> attacking usually has more flexibility.)
>
> On the other hand, it might be that grandmaster play is nothing like
> perfect play.
>
> Consider what we know about endgames. Tablebases tell us that
> grandmasters can play KRP-KR endings pretty-much perfectly. We
> understand the tablebases and know why the right move is the right
> move. On the other hand, the tablebase for KRN-KNN looks, in most
> cases like completely random moves -- nobody can understand it. In
> this case, grandmaster play looks nothing like perfect.
I don't think that is relevant. Those tablebases confirm that, in general,
KRN is stronger than KNN, in conformity with the general chess principle
that Rooks are worth more than Knights. GMs don't concern themselves
with this simply because these types of positions are only rarely produced
by chess' move tree.
To make your case, you need to provide examples of *surprising* wins.
>
>
> Dave.
>
> --
> David Richerby Devil Chainsaw (TM): it's like
> www.chiark.greenend.org.uk/~davidr/ a lethal weapon that's possessed
> by Satan!
|
| |
Date: 05 Feb 2008 20:11:39
From: help bot
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
On Feb 4, 1:42 pm, Larry Tapper <[email protected] > wrote:
> For what it's worth, grandmasters who are asked this question will
> typically tell you that chess is probably a draw.
Yeah, but the dismal record of grandmasters
when making such guesses is not sufficient
for us to conclude anything; after all, it's very
possible for even the worst prognosticators to
occasionally get something right.
Long ago (or so it seems), these grandmasters
were adamant in their denials regarding whether
a chess computer or program would *ever* be
able to defeat a master (later modified to GM).
In essence, the answer was always "of course
not, you fools, because "we" are so amazingly
st!!". Food for thought... .
-- help bot
|
| |
Date: 05 Feb 2008 09:11:25
From: Larry Tapper
Subject: Re: all the cheese in Canada
|
Phil Innes writes:
PI > ...Secondly, if logic is these days divorced from mathematics, yet
remains in play in philosophy, I am afraid that the mere enumeration
of data is insufficient to resolve the issue by mathematics, since
otherwise you might as well try to prove the existance of Canada by
mathematics, or where cheese is located in Canada.
Oh, sorry to hear that, nobody had told me about the divorce. You
learn all sorts of things on the Internet.
I wonder, was the divorce nasty or amicable? Who got custody of the
field known as "mathematical logic"? Is mathematics now taking a walk
on the wild side, dispensing with the notion of formal proof?
LT
|
| | |
Date: 05 Feb 2008 15:20:28
From: Chess One
Subject: Re: all the cheese in Canada
|
"Larry Tapper" <[email protected] > wrote in message
news:61985973-69f7-4927-87df-4e65f637c527@l16g2000hsh.googlegroups.com...
>
> Phil Innes writes:
>
> PI> ...Secondly, if logic is these days divorced from mathematics, yet
> remains in play in philosophy, I am afraid that the mere enumeration
> of data is insufficient to resolve the issue by mathematics, since
> otherwise you might as well try to prove the existance of Canada by
> mathematics, or where cheese is located in Canada.
>
> Oh, sorry to hear that, nobody had told me about the divorce. You
> learn all sorts of things on the Internet.
>
> I wonder, was the divorce nasty or amicable? Who got custody of the
> field known as "mathematical logic"? Is mathematics now taking a walk
> on the wild side, dispensing with the notion of formal proof?
You talking with yourself Larry? Or about the issue of finite games, the
role of math, any particular instance of anything you know enough about to
write other than rhetorically. If you can't do, you know, sod off! There is
enough shit on these newsgroups these days without cult-math showing up to
suggest it has hairs on its chest.
Maybe you just forgot some content to your message? Since you don't contest
mine, but vague-out. Some people would think that indicates you couldn't
answer, but protest anyway. Fair?
PI
> LT
>
>
|
| |
Date: 04 Feb 2008 10:42:24
From: Larry Tapper
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
On Feb 1, 6:15=A0pm, [email protected] wrote:
> I still think it's a win.
>
> What's your opinion, disregarding issues of proof and the feasibility
> thereof?
>
> Michael
For what it's worth, grandmasters who are asked this question will
typically tell you that chess is probably a draw. There are some
exceptions though, for example the correspondence champion and
computer pioneer Hans Berliner, who was famous for insisting that
White has a winning advantage.
I think it's a draw myself. If you look in the rgcm Google archives,
you'll find several old threads with sometimes astonishingly heated
debates on the subject.
LT
|
| |
Date: 04 Feb 2008 03:00:16
From: Wlodzimierz Holsztynski (Wlod)
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
On Feb 3, 9:47 am, David Richerby <[email protected] >
wrote:
>
> I think it was Turing who observed that a perfect game of chess
> between Mr White and Mr Black would proceed in one of three ways:
>
> 1. Mr White announces, `I resign',
> 2. Mr Black announces, `I resign' or
> 3. Mr White asks, `Would you like a draw?' and Mr Black says, `Yes.'
It is a corollary to the general Zermelo's theorem
about finite games. It predates Turing.
Wlod
|
| | |
Date: 05 Feb 2008 12:12:48
From: David Richerby
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
Wlodzimierz Holsztynski (Wlod) <[email protected] > wrote:
> David Richerby <[email protected]> wrote:
>> I think it was Turing who observed that a perfect game of chess
>> between Mr White and Mr Black would proceed in one of three ways:
>>
>> 1. Mr White announces, `I resign',
>> 2. Mr Black announces, `I resign' or
>> 3. Mr White asks, `Would you like a draw?' and Mr Black says, `Yes.'
>
> It is a corollary to the general Zermelo's theorem about finite
> games. It predates Turing.
The general theory says that, with perfect play, the result of the
game is either a win for white, a win for black or a draw. But I
think it was Turing who phrased it in this way, with the two players
not even bothering to make any moves.
Dave.
--
David Richerby Frozen Evil Sword (TM): it's like a
www.chiark.greenend.org.uk/~davidr/ razor-sharp blade but it's genuinely
evil and frozen in a block of ice!
|
| | |
Date: 04 Feb 2008 08:00:41
From: Chess One
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
"Wlodzimierz Holsztynski (Wlod)" <[email protected] > wrote in message
news:e1fc788b-c7bd-46f9-9f22-7bdd6d4b263a@e23g2000prf.googlegroups.com...
> On Feb 3, 9:47 am, David Richerby <[email protected]>
> wrote:
>
>>
>> I think it was Turing who observed that a perfect game of chess
>> between Mr White and Mr Black would proceed in one of three ways:
>>
>> 1. Mr White announces, `I resign',
>> 2. Mr Black announces, `I resign' or
>> 3. Mr White asks, `Would you like a draw?' and Mr Black says, `Yes.'
>
> It is a corollary to the general Zermelo's theorem
> about finite games. It predates Turing.
>
> Wlod
To interest you both, here is a 16th definition of Finite Games - which
differentiates predictive theory, from the play itself:-
"One obeys the rules in a finite game in order to play, but playing does
not consist of only obeying the rules.
The rules of a finite game do not constitute a script. A script is
composed according to the rules but is not identical to the rules. The
script is the record of the actual exchanges between players - whether acts
or words - and therefore cannot be written down beforehand. In all true
finite play the scripts are composed in the course of the play.
This means that //during the game// all finite play is dramatic, since
the outcome is yet unknown. That the outcome is not known is what makes it a
true game. The theatricality of finite play has to do with the fact that
there is an outcome.
Finite play is dramatic, but only provisionally dramatic. As soon as it
is concluded we are able to look backward and see how the sequence of moves,
though made freely by the competitors, could have resulted only in this
outcome. We can see how every move fit into a sequence that made it
inevitable that this player should win.
The fact that a finite game is provisionally dramatic means that it is
the intention of each player to eliminate its drama by making a preferred
end inevitable. It is the desire of all finite players to be //Master
Players//, to be so perfectly skilled in their play that nothing can
surprise them, so perfectly trained that every move in the game is foreseen
at the beginning. A true Master Player plays as though the game is already
in the past, according to a script whose every detail is known prior to the
play itself."
//James P. Carse.
Phil Innes
|
| | | |
Date: 05 Feb 2008 12:16:03
From: David Richerby
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
Chess One <[email protected] > wrote:
> "One obeys the rules in a finite game in order to play, but playing
> does not consist of only obeying the rules..." -- James P. Carse.
Thank you but we were discussing games as an exercise in mathematics,
not philosophy. But I now see where your confusion about the nature
of finite and infinite games comes from.
Dave.
--
David Richerby Broken Beer (TM): it's like a
www.chiark.greenend.org.uk/~davidr/ refreshing lager but it doesn't work!
|
| | | | |
Date: 05 Feb 2008 11:26:53
From: Chess One
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
"David Richerby" <[email protected] > wrote in message
news:dxD*[email protected]...
> Chess One <[email protected]> wrote:
>> "One obeys the rules in a finite game in order to play, but playing
>> does not consist of only obeying the rules..." -- James P. Carse.
>
> Thank you but we were discussing games as an exercise in mathematics,
> not philosophy. But I now see where your confusion about the nature
> of finite and infinite games comes from.
You do not understand what Carse proposes, that if the nature of a true
finite game is, a priori, unpredictable, wherefore the imperative in the
title of this thread - ie, 'should'?
Secondly, if logic is these days divorced from mathematics, yet remains in
play in philosophy, I am afraid that the mere enumeration of data is
insufficient to resolve the issue by mathematics, since otherwise you might
as well try to prove the existance of Canada by mathematics, or where cheese
is located in Canada.
As to cheese :: so to chess.
Mathematics does not assess all, ony the quantifiable aspects of any system.
Mathematics can even not theoretically assess all, since it is impossible to
create a 1 :: 1 map.
These are functions of logic, semantically phrased. The implication is that
the resolution of chess may not have to do with mathematics any more than
the location of the Canadian cheese.
Phil Innes
>
> Dave.
>
> --
> David Richerby Broken Beer (TM): it's like a
> www.chiark.greenend.org.uk/~davidr/ refreshing lager but it doesn't
> work!
|
| | | | | |
Date: 06 Feb 2008 13:43:47
From: David Richerby
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
Chess One <[email protected] > wrote:
> "David Richerby" <[email protected]> wrote:
>> Chess One <[email protected]> wrote:
>>> "One obeys the rules in a finite game in order to play, but playing
>>> does not consist of only obeying the rules..." -- James P. Carse.
>>
>> Thank you but we were discussing games as an exercise in mathematics,
>> not philosophy. But I now see where your confusion about the nature
>> of finite and infinite games comes from.
>
> You do not understand what Carse proposes
I do not claim a full understanding of what Carse has written. But I
understand it well enough to know that it is not relevant to the
current discussion. However, if you believe that Carse's proposal of
game as a metaphor and analytical tool for life is relevant to the
solution of chess, you do not understand what he was written, either.
> Secondly, if logic is these days divorced from mathematics, yet
> remains in play in philosophy
Logic is not divorced from mathematics.
> Mathematics does not assess all, ony the quantifiable aspects of any
> system. Mathematics can even not theoretically assess all, since it
> is impossible to create a 1 :: 1 map.
Huh?
> These are functions of logic, semantically phrased.
As far as I can see, that sentence is devoid of semantic content.
> The implication is that the resolution of chess may not have to do
> with mathematics any more than the location of the Canadian cheese.
The solution of chess is precisely a quantifiable aspect of a
mathematical system. It is absolutely a question of mathematics.
Other aspects of chess, such as whether it will make any difference if
we know the game-theoretic outcome of the game, are not questions of
mathematics.
Dave.
--
David Richerby Miniature Old-Fashioned Smokes (TM):
www.chiark.greenend.org.uk/~davidr/ it's like a pack of cigarettes but
it's perfect for your grandparents
and you can hold in it your hand!
|
| | | | | | |
Date: 06 Feb 2008 09:33:42
From: Chess One
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
"David Richerby" <[email protected] > wrote in message
news:35d*[email protected]...
> Chess One <[email protected]> wrote:
>> "David Richerby" <[email protected]> wrote:
>>> Chess One <[email protected]> wrote:
>>>> "One obeys the rules in a finite game in order to play, but playing
>>>> does not consist of only obeying the rules..." -- James P. Carse.
>>>
>>> Thank you but we were discussing games as an exercise in mathematics,
>>> not philosophy. But I now see where your confusion about the nature
>>> of finite and infinite games comes from.
>>
>> You do not understand what Carse proposes
>
> I do not claim a full understanding of what Carse has written. But I
> understand it well enough to know that it is not relevant to the
> current discussion.
Perhaps then, you cannot contest Carse to the extent that you say it is not
relevant - especially since he says that prior determination by any means,
including mathematics removes chess from being a finite game.
You see, I simply represent his point that mathematics need to relate to
something in the real world, which you have called 'philosophy' and I have
called logic.
Secondly, it may not be relevant /to you/. And as I wrote before, if you
think you can prove the existance and whereabout of cheese in Canada by
mathematics, then, you are right, logic and philosophy are not'relevant' for
you.
Below you cannot understand what you address, seemingly never before having
encountered the 1:1 model paradigm. Therefore, someone like yourself who
will not admit a logical proposition to your deliberations, will try to
prove one could construct a 1:1 map.
The other half of the sentence to which you reply, "Huh?" states that your
own field of interest, mathematics, is concerned with quantification, by
which we mean, to make numbers thereof.
It is a statement of limits in philosophy, since by only making the numbers
thereof, you have no idea if you represent 99% of the topic or just 1% of
it - in fact, the quantification can be forgotten for what it is, a
reduction, but believed to decribe the whole thing, 1:1.
Which is why mathematicians should get out more, and look at some cool
pictures. There is one titled: "This is not a hat."
> However, if you believe that Carse's proposal of
> game as a metaphor and analytical tool for life is relevant to the
> solution of chess, you do not understand what he was written, either.
>
>> Secondly, if logic is these days divorced from mathematics, yet
>> remains in play in philosophy
>
> Logic is not divorced from mathematics.
>
>> Mathematics does not assess all, ony the quantifiable aspects of any
>> system. Mathematics can even not theoretically assess all, since it
>> is impossible to create a 1 :: 1 map.
>
> Huh?
>
>> These are functions of logic, semantically phrased.
>
> As far as I can see, that sentence is devoid of semantic content.
Maybe consult what semantics means? It means 'meaning'.
>> The implication is that the resolution of chess may not have to do
>> with mathematics any more than the location of the Canadian cheese.
>
> The solution of chess is precisely a quantifiable aspect of a
> mathematical system. It is absolutely a question of mathematics.
Those are metaphysical assertions, either true or untrue. They are not
logical propositions.
> Other aspects of chess, such as whether it will make any difference if
> we know the game-theoretic outcome of the game, are not questions of
> mathematics.
Another suppositional statement with a'whether...if' formation followed by a
metaphyscial 'we' and continuing to an assertion that "game-theoretic
outcome" is even knowlable.
By assertion all you say may or may not be true, and the simple substitution
reveals the way you describe it, is apart from any logical content:
The solution of where cheese is in Canada is precisely a quantifiable aspect
of a
mathematical system. It is absolutely a question of mathematics.
Phil Innes
> Dave.
>
> --
> David Richerby Miniature Old-Fashioned Smokes
> (TM):
> www.chiark.greenend.org.uk/~davidr/ it's like a pack of cigarettes
> but
> it's perfect for your
> grandparents
> and you can hold in it your hand!
|
| | | |
Date: 04 Feb 2008 08:39:27
From: Mike Murray
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
On Mon, 4 Feb 2008 08:00:41 -0500, "Chess One" <[email protected] >
wrote:
> Finite play is dramatic, but only provisionally dramatic. As soon as it
>is concluded we are able to look backward and see how the sequence of moves,
>though made freely by the competitors, could have resulted only in this
>outcome. We can see how every move fit into a sequence that made it
>inevitable that this player should win.
>
> The fact that a finite game is provisionally dramatic means that it is
>the intention of each player to eliminate its drama by making a preferred
>end inevitable. It is the desire of all finite players to be //Master
>Players//, to be so perfectly skilled in their play that nothing can
>surprise them, so perfectly trained that every move in the game is foreseen
>at the beginning. A true Master Player plays as though the game is already
>in the past, according to a script whose every detail is known prior to the
>play itself."
>
> //James P. Carse.
>
>Phil Innes
Almost seems Carse is speaking of Master Annotators rather than
Players.
|
| |
Date: 01 Feb 2008 15:15:30
From:
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
On Feb 1, 11:05 am, David Richerby <[email protected] >
wrote:
> Chess One <[email protected]> wrote:
> > I think we do not know if chess can be classified as a
> > finite game, since it is so complex that even
> > the /classification/ eludes us. Can any mathematico
> > here affirm or contradict the previous sentence?
>
> We've already been through this a hundred times. You
> evidently don't understand the answer but that doesn't
> mean that the question is still open.
>
> Chess is, strictly speaking, an infinite game. Although
> there are a finite number of possible positions, there
> are plays that go on forever, for example by the players
> moving their knights in and out.
...with neither player claiming a draw.
It becomes finite if the 50-move rule is changed so that a draw is
automatic after 50 moves by both players without a capture or pawn
move.
> So, if chess is a forced win for either side, the winning
> strategy will never involve repeating a position or
> making more than fifty consecutive moves between pawn
> moves and captures [...] [T]here can only be a finite
> number of moves in a perfectly played game.
This is true. Checkmate would occur before move X, where X is an
integer for which an upper bound should not be too difficult to find.
If chess is a draw with perfect play, the drawing strategy *will*
involve repeating a position, claiming a draw after 50 moves without a
capture or pawn move, or causing there to be insufficient material -
and whichever of these it does involve, will occur within a finite
number of moves. Otherwise it's just pushing wood...
Although it might also be said that if chess is a draw with perfect
play, a game between two perfect players might as well end in a draw
before a move is played! :-)
I still think it's a win.
What's your opinion, disregarding issues of proof and the feasibility
thereof?
Michael
|
| | |
Date: 03 Feb 2008 17:47:07
From: David Richerby
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
<[email protected] > wrote:
> David Richerby <[email protected]> wrote:
>> Chess is, strictly speaking, an infinite game. Although there are
>> a finite number of possible positions, there are plays that go on
>> forever, for example by the players moving their knights in and
>> out.
>
> ...with neither player claiming a draw.
>
> It becomes finite if the 50-move rule is changed so that a draw is
> automatic after 50 moves by both players without a capture or pawn
> move.
Well, yes but, technically, that's a different game. The rest of my
post argued that it's analytically equivalent because perfect play
will result in immediately claiming a draw whenever one has the option
because the opponent would never let you claim a draw if he had a way
of winning. Thus, we may as well assume that the draws are automatic
(though I didn't explicitly say that).
> If chess is a draw with perfect play, the drawing strategy *will*
> involve repeating a position, claiming a draw after 50 moves without
> a capture or pawn move, or causing there to be insufficient material
Not necessarily. It could end in stalemate from some positions. :-P
> Although it might also be said that if chess is a draw with perfect
> play, a game between two perfect players might as well end in a draw
> before a move is played! :-)
I think it was Turing who observed that a perfect game of chess
between Mr White and Mr Black would proceed in one of three ways:
1. Mr White announces, `I resign',
2. Mr Black announces, `I resign' or
3. Mr White asks, `Would you like a draw?' and Mr Black says, `Yes.'
(Technically, one should only offer a draw on one's own move so we can
disregard the case where Mr Black offers the draw.)
> I still think it's a win.
>
> What's your opinion, disregarding issues of proof and the feasibility
> thereof?
As I think I've already said in this thread, I think it's most likely
that it's a draw and, if not, it's most likely that White has the win.
Dave.
--
David Richerby Pickled Cheese T-Shirt (TM): it's like
www.chiark.greenend.org.uk/~davidr/ a fashion statement that's made of
cheese but it's preserved in vinegar!
|
| |
Date: 30 Jan 2008 11:21:44
From:
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
On Jan 29, 4:22 pm, Sanny <[email protected] > wrote:
> On Jan 29, 4:38 pm, [email protected] wrote:
>
> > If White and Black both play perfectly, who wins? Or is it a
> > draw?
>
> > I'd be interested to know how chessplayers' opinions on this
> > question are distributed.
>
> > Personally I think White wins, because he starts with a clear
> > advantage.
>
> > I suspect most people might think the game is a draw.
>
> > Michael
>
> If Both are a perfect player of Equal Match. Say Master/Advance
> Level at GetClub Chess then I think
>
> 90% chance it will be Draw.
> 8% White Wins
> 2% Black Wins.
> It will depend on Opening the White/Black Chooses. There are 100s
> of Openings and Each are perfect. So for Each opening we will have
> different results.
No, I am talking about two hypothetical perfect players, not two
players at "master" or "advanced" level.
Maybe only one first move by White is "perfect", necessarily leading,
against perfect play by Black, to the best available result for White.
Maybe several do. No-one knows!
No-one even knows what that result is. It may be a win by White; it
may be a draw. We can only speculate.
It may conceivably be a win by Black. In that case, of course, ANY
first move by a perfect player with the White pieces will lead to a
loss against a perfect player with the Black pieces - so the idea of a
"perfect" first move by White stops making sense! White would start
with a losing position.
I think you were answering a question different from the one I asked!
To put the question in other words: take the starting position - is it
a) a win for White, b) drawn with best play, or c) a win for Black?
There are no other possibilities.
Michael
|
| | |
Date: 31 Jan 2008 11:14:15
From: David Richerby
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
<[email protected] > wrote:
> Maybe only one first move by White is "perfect", necessarily
> leading, against perfect play by Black, to the best available result
> for White.
Note that, if chess is a forced win for one player or the other, the
concept of `perfect play' for the loser is moot.
My personal opinion is that chess is most likely a draw. If it's not
a draw, it's most likely a win for white but I don't totally discount
the possibility that it's a win for black.
Dave.
--
David Richerby Nuclear Lotion (TM): it's like a
www.chiark.greenend.org.uk/~davidr/ soothing hand lotion that's made
of atoms!
|
| | | |
Date: 31 Jan 2008 11:37:10
From: Chess One
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
|
"David Richerby" <[email protected] > wrote in message
news:RNf*[email protected]...
> <[email protected]> wrote:
>> Maybe only one first move by White is "perfect", necessarily
>> leading, against perfect play by Black, to the best available result
>> for White.
>
> Note that, if chess is a forced win for one player or the other, the
> concept of `perfect play' for the loser is moot.
>
> My personal opinion is that chess is most likely a draw. If it's not
> a draw, it's most likely a win for white but I don't totally discount
> the possibility that it's a win for black.
In Finite and Infinite Games, Carse explains finite games as though which
can usually be determined to be win draw or loss, and some which absolutely
provide the first player with that result.
I think we do not know if chess can be classified as a finite game, since it
is so complex that even the /classification/ eludes us. Can any mathematico
here affirm or contradict the previous sentence?
Secondly, in previous conversations some people thought that chess was
finite, but requiring thousands of years of human attention in order to
prove any win - and therefore, in terms of human life spans, it seemed
a-finite. No-one thought it was an infinite game, since those typically
evolve themselves in the play! Example, new rules are introuduced or mutated
as the game progresses.
Phil Innes
>
> Dave.
>
> --
> David Richerby Nuclear Lotion (TM): it's
> like a
> www.chiark.greenend.org.uk/~davidr/ soothing hand lotion that's
> made
> of atoms!
|
| | | | |
Date: 01 Feb 2008 11:05:53
From: David Richerby
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
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Chess One <[email protected] > wrote:
> I think we do not know if chess can be classified as a finite game,
> since it is so complex that even the /classification/ eludes us. Can
> any mathematico here affirm or contradict the previous sentence?
We've already been through this a hundred times. You evidently don't
understand the answer but that doesn't mean that the question is still
open.
Chess is, strictly speaking, an infinite game. Although there are a
finite number of possible positions, there are plays that go on
forever, for example by the players moving their knights in and out.
We should agree, although it's not stated in the rules for obvious
practical reasons, that any infinite play is a draw.
However, chess is analytically equivalent to a finite game. The
fifty-move rule and the threefold repetition rule mean that ``I claim
a draw'' is, in effect, a move in the game. When analyzing chess,
we're interested in best-possible play. Thus, neither player will
give the possibility of a draw when they have a forced win because the
opponent would immediately claim that draw because ``I claim a draw''
is better than playing a move that leads to a loss.
So, if chess is a forced win for either side, the winning strategy
will never involve repeating a position or making more than fifty
consecutive moves between pawn moves and captures. Since any game can
contain only a finite number of pawn moves (they only move forwards
and will, eventually, hit the other end of the board) and only a
finite number of captures (there are only thirty pieces on the board,
apart from the kings, and each can only be captured once), there can
only be a finite number of moves in a perfectly played game.
Thus, for the purpose of deciding whether chess is a forced win for
either side, chess is a finite game. This is good news, since it is
well-known that every finite two-player game of perfect information is
determined: either one player has a forced win or the game is a forced
draw.
> Secondly, in previous conversations some people thought that chess
> was finite, but requiring thousands of years of human attention in
> order to prove any win - and therefore, in terms of human life
> spans, it seemed a-finite.
Dude, a-finite isn't a word. Something that isn't finite is, by
definition, infinite. There's no room for an alternative notion
between ``finite'' and ``infinite''.
But, yes. While chess is effectively finite, it does seem that it
would take an unfeasibly large amount of time to determine which
player has a winning strategy and what that strategy is. This is
nothing unusual. There are clearly a finite number of grains of sand
in the Sahara but it would take an infeasible length of time to count
them, even if you could somehow stop them blowing away.
> No-one thought it was an infinite game since those typically evolve
> themselves in the play!
There is absolutely no requirement that an infinite game evolve in
play! I can't think of a single infinite game that has been analyzed
in mathematics that ``evolves'' in this way. Indeed, mathematically,
a game (finite or infinite) is defined by:
i) a set of possible positions;
ii) a list of pairs of positions (X,Y) such that there is a move
transforming position X to position Y; and
iii) a list of positions that are won for each player.
The rules are fixed at the start and never change.
Dave.
--
David Richerby Frozen Toy (TM): it's like a fun
www.chiark.greenend.org.uk/~davidr/ child's toy but it's frozen in a block
of ice!
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Date: 31 Jan 2008 23:32:50
From: Kenneth Sloan
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
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Chess One wrote:
>
> I think we do not know if chess can be classified as a finite game,
Chess is finite.
This comforts the theoretician.
Chess is very, very, very, very, big.
This concerns the practitioner.
--
Kenneth Sloan [email protected]
Computer and Information Sciences +1-205-932-2213
University of Alabama at Birmingham FAX +1-205-934-5473
Birmingham, AL 35294-1170 http://KennethRSloan.com/
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Date: 01 Feb 2008 11:07:41
From: David Richerby
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
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Kenneth Sloan <[email protected] > wrote:
> Chess One wrote:
>> I think we do not know if chess can be classified as a finite game,
>
> Chess is finite.
>
> This comforts the theoretician.
>
> Chess is very, very, very, very, big.
>
> This concerns the practitioner.
Au contraire. It comforts the practitioner a great deal, since it
means that people can expect to play interesting games of chess for a
long time to come.
Dave.
--
David Richerby Solar-Powered Chicken (TM): it's like
www.chiark.greenend.org.uk/~davidr/ a farm animal but it doesn't work in
the dark!
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Date: 29 Jan 2008 08:22:23
From: Sanny
Subject: Re: with perfect play, should it be 1-0, 0-1, or a draw?
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On Jan 29, 4:38=A0pm, [email protected] wrote:
> If White and Black both play perfectly, who wins? Or is it a draw?
>
> I'd be interested to know how chessplayers' opinions on this question
> are distributed.
>
> Personally I think White wins, because he starts with a clear
> advantage.
>
> I suspect most people might think the game is a draw.
>
> Michael
If Both are a perfect player of Equal Match. Say Master/Advance Level
at GetClub Chess then I think
90% chance it will be Draw.
8% White Wins
2% Black Wins.
Play Chess at: http://www.GetClub.com/Chess.html
It will depend on Opening the White/Black Chooses. There are 100s of
Openings and Each are perfect So for Each opening we will have
different results.
Bye
Sanny
Play Chess at: http://www.GetClub.com/Chess.html
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