Adorjan's books analyse white/black wins as much from a psychological basis,
as anything else - that we have an expectation [or even obligation] to do
better with white and different expectation with black [getting a draw is
good!]. But there is no objective basis in chess for either attitude!

Indeed, GM Adorjan contradicts himself repeatedly in his
labored attempts to suggest that White has no advantage
whatever, followed by his voluntary "admission" that White
can magically induce a draw, followed by reversion back to
his first position, etc. In sum, he *sometimes* admits White
an advantage, but always insists it is not sufficient to win.

Adorjan even says that we are conditioned to always prosecute our chess from
white's point of view - and that all chess diagrams are presented as if you
were sitting behind the white pieces, eg. and this reinforces the conscious
perception of 'white to move and win.'

To a certain extent, perhaps. But I have replayed many of
the games of Paul Morphy -- from the book's White perspective --
where I kept getting the sh*t kicked out of my White pieces!
I think his opponents had a very different idea.

Players overconcentrate their study with what to do with the white pieces,

I see no evidence of this; if anything, players tend to study
harder for the Back side, because they *think* it is far more
difficult to play. Many, many chess books are written as a
repertoire for Black, and such books are best sellers.

At this point, it would be wise to note that many, many of
GM Adorjan's numerous contentions are left wholly
unsupported in the article. Even his analogies are inept;
either he or else his translator confounded football for
another sport, etc. The whole piece was put together rather
carelessly, especially with regard to the whole White/Black
draw idea.


and this imbalanced study coupled with received expectations of what to do
with white or black, creates a self-fulfilling result.

One should not overlook the initiative in attempting to
explain the imbalance in terms of results. An over-
simplification would be: 1.e4 e5 2.Nf3 (threatens Nxe5)
.... Nc6 (meets the threat), etc.

--------

IMO, the lower level play tends toward a smaller advantage
to the player of the White pieces, while the high-level results,
and perhaps results in high-level correspondence play, would
tend more toward the 60/40ish split. The reason is that at the
low levels, many games are decided almost at random, and in
addition, the initiative -- or rather having the move -- is just as
much a chance to blunder as it is to forward any particular
strategy. Likewise, the top players are the very ones who
will see a draw as Black being a sort of "turnover" of the ball,
not unlike a fumble in football.

I'm not certain exactly when that article was written, but at
least as far back as Paul Morphy there were players who did
*not* play for a draw as Black. More recently, I could cite GM
Tal, GM Fischer, GM Kasparov (except his matches with his
arch-nemesis), etc. In fact, the tendency to readily accept a
draw as Black seems connected to the idea that White has
more margin for error, for attempting to make something out
of the near-nothing or not-quite-something he gets in moving
first. Black, it is believed, must walk a narrower path or else
risk losing. Players prefer to "spend" their risk-tokens at
those times where they believe they can survive a small error
and yet still draw.

-- help bot

On Feb 22, 5:33 pm, "Chess One" wrote:

At present, I have *finally* achieved a position requiring
a deep think. Two pawns ahead, I need to select the
right follow-up or my attack will falter. This is in fact, the
very first time I have seen fit to set up a chessboard and
men. All my games at GetClub and all my games at
RedHotPawn have been played rather offhandedly, up
'till now. (Even so, I am considered a "star" at GetClub.)

Perhaps you could recruit IM Innes in this endeavor?
He has the latest, greatest chess program ever: Rybka,
which undoubtedly can improve on my actual moves
about 90% of the time.

Even a master such as myself

A master, eh? So they finally demoted you from nearly
an IM. 'Bout time! The creature claims you have no FIDE
rating at all -- not even 1200+. Sometimes I wonder if you
are in this world or one of your own making, where ratings
are handed out like candy-canes at Christmas!


can improve upon a 1300-beater such as Kennedy,

So true. I saw him at the Showbiz Pizza Quads, and
did he ever. But NM Wiseman put him in his place! The
poor fella probably lasted no more than 30 moves, with
his sorry French "suicide" Defense. Then again, the
Wiseman killed any and all folks back then, especially
the dumb ones what tried the French!

who is deeply puzzled by his position, and uncertain of the theme which can
conclude the game.

I used a real chessboard, and lo' and behold, it was
soon determined that EVERY line of attack won perforce!
All that mattered was that my big, bad Queen jump into
the fracas -- never mind the loss of a paltry Rook! Now
I'm havin' trouble connectin' to RedHot, so as I can finish
the poor victim off, quick an' painless like. Every single
game so fer is a win fer me, an' rightly so!


That, though, is not the problem, since the question is about Jason, the
on-line 16xx player,

That was back when he was just a kid! Now he's all
growed up and smart-like, see? Now he's about eight
feet tall, and reely big an' *strong*. (People tells 'im ta
use deoderant, but he won't never listen!)


and would not necessarily understand what I say.

No loss, fer you ain't said nothin' worth notin' fer a long
time!


More importantly, doesn't care to hear it.

Personally, I think he's afeard you'll open a can o'
whoopass on him, beatin' him in under ten moves or
so.


Jason has not the slightest interest in improving his chess,

Can't be done, so I'm told! He's THAT good. Says so
his self.

-- help bot

Chess One wrote:
"David Richerby" wrote:
I don't know if any mathematician has ever seriously proposed which
of these two states, potential :: action, is superior from any
theoretical model.

Again, what's this double-colon you're using?

Its an advanced colon, as used by ... well, no jokes occur to me. It
is very like a single colon, though more signalled.

A colon isn't grammatical at that point in that sentence, either!
Does it, in fact, mean `and'?


Chess is not even conveniently describable /as a process/ as a
Finite or Infinite Game.

Chess is trivially describable as an infinite game by omitting the
three drawing rules (dead position, three-fold repetition, 50-move
rule). It is then easy to prove that it suffices to consider only
finite games because of the drawing rules.

But finite is itself an arguable determination.

No it isn't! A collection of objects is finite if, and only if, you
can (in principle) count them (1, 2, 3, 4...) and stop at some number,
having counted all the objects. So, the number of pieces on a
chessboard is finite, as is the number of grains of sand in the Sahara
Desert.


Is it used synonymnously for 'theoretical',

No.

even though there are more moves than atoms in the universe

Even though there are more chess games than atoms in the universe.
This means that the finiteness of chess is of largely theoretical
interest, since knowing that it's finite doesn't help much in
practice. But `finite' does not mean `theoretical'.


but there is no /fixed/ prescription for when pawn promotions become
a consideration to actual play - and 'continuing the play' is what
happens in balanced or even dynamically unbalanced positions -

You've misunderstood the phrase `continuing the play' and are trying
to apply it outside its context. That context is a particular class
of infinite games. Infinite games are often defined as follows.
The two players

Or two or more, but yes...

For the purposes of the theory of games of perfect information, any
finite number of players is equivalent to two. Perfect information
means that all the players have full information about the position
(i.e., know where all of everyone's pieces are and any other relevant
facts).

Why does it suffice to consider two-player games? Suppose we have n2
players. We can analyze the game from the point of view of player 1
by assuming that some super-human plays the moves for players 2, ...,
n himself. If player 1 can beat the super-human, he can also beat any
collection of ordinary people acting individually. Likewise for each
of the other players.

(This doesn't apply for games of imperfect information because, in
such a game, player 2 and player 3 cannot effectively co-operate
because they don't know where each other's pieces are or there is some
other key fact they don't know. But the super-human knows where all
the pieces are for players 2, ..., n, so he should be more powerful.)


The tricky part of inifinite games is that the rules themselves
evolve, so that some moves may condition new rules. This may except
alternating moves. This is a quibble, but still...

No, no, no! NO! There is nothing in the concept of `infinite game'
that means the rules change. Further, every game where the rules are
allowed to change is equivalent to one where the rules are static:
suppose we have rule sets 1, 2, ... (this may be finite or infinite).
Just make the number of the rule set currently in operation part of
the position and produce a master rule set that says, in effect, `If
the current rule set is number 1, you're allowed to do this; if it's
number 2, you can do this; ...' So we never need to even consider
games with changing rules in order to develop a theory of how games
work.


(Not all infinite games work like this. Consider the following
game, the name of which I'm afraid I don't recall. The game is
defined by a set S of real numbers between, but not including, 0
and 1. We start with `0.' written on a piece of paper and take
turns to add one digit to the end of the number written so far. I
win if the infinitely long decimal we produce is in S; you win if
it isn't.)

This again is an aside, but is this infinite, or simply an
undetermined linear extension of a theme?

This is genuinely infinite. The technical term for for your
`undetermined linear extension' is `unbounded'. An unbounded finite
game is one where there's no limit to how long a game can last but
every game must eventually finish. Eventually, there is some move
that is played that is the last move of the game. An infinite game is
one where there are necessarily an infinite number of moves: the game
will never finish and there is no last move. After every move,
another must be made.

[Technical note to any mathematicians reading: yes, I'm aware that not
all infinite ordinals are limit ordinals but introducing the idea of
games of length omega+1 in the current discussion will just confuse
everyone.]

An example of an unbounded game is as follows. I think of a number
(an ordinary, positive integer: 1, 2, 3, ...) and you try to guess it.
After each guess, I tell you whether my number is smaller than or
greater than your guess and the game continues until you get the
correct number. On the assumption that your guesses are consistent
with the information I've given you (so you never guess 10 at any
point after I've told you the number is less than three, for example),
the game is unbounded but not infinite.

It is not infinite because there are only finitely many numbers
smaller than the one I chose. If I choose the number `n', there are
only n-1 numbers smaller than it so, if you don't repeat a guess,
after n guesses, you must have either found out my number or guessed
something bigger than it. If you guessed something bigger (say, some
number `m'), there are only finitely many (m-1, in fact) numbers
smaller than it so, after at most m-1 more guesses, you must have hit
on the right number. There's no way that the game can go on
forever but, on the other hand there's no bound on how long the game
can be: I can choose an arbitrarily large number and your guesses can
be 1, 2, 3, ... .

(The condition I stated is critical: without it, the game becomes
potentially infinite as you could just guess `1' every time, even
though I tell you that the number is bigger.)


and there are no fixed number of moves to any game of chess,
except as metaphysically decided by others.

What on earth is the word `metaphysically' doing in the middle of
that sentence? This has nothing to do with metaphysics.

I use the word in its technical sense - 'without person'

Oh. `Non-corporeal' might have made your meaning clearer. Anyway,
what does `there are no fixed number of moves to any game of chess,
except as decided by others without person' mean? The number of moves
in a game of chess is decided (antagonistically) by the players
themselves.


In this sense the game of chess is decided not by the players [the
persons] but by non-players implementing their determination of
rules.

I disagree. Ultimately, it's the players who implement the rules. An
arbiter can say, `You're not using the rules that we agreed so I do
not consider what you are doing to be part of the tournament,' but he
can't implement the rules for them.


Can any mathematician or logician suggest even an objective basis
for determining the result of chess as Finite/Infinite [?] game.

Yes. It's a finite game so, as far as a mathematician or logician
(raises hand) is concerned, the objective basis is `analyze each of
the possible cases in turn.' If you want to know whether there's a
practical way of doing it, you're straying into the realms of
computer science.

Which is to say, of logical method extrapolated to the Nth by brute
force projection. Yet what is the answer to even hypothesised
projections?

I'm sorry -- I don't understand the question.


Can the statement, "black always wins" be refuted

Yes. Consider the game 1.e4 e5 2.Bc4 Bc5 3.Qh5 a6 4.Qxf7#. The
statement `Black always wins with perfect play' can be refuted, in
principle, by case analysis.

Though its also true that black can mate quicker than white - so
perhaps the explicit statement 'with best play' needs to be added,
and if so, is there any answer?

Yes, `with best play' needs to be added to make the question
non-trivial. The answer is that, in principle, the statement `with
best play, Black always wins' can be refuted if, and only if, it is
false. If it is true, clearly, it cannot be refuted; if it is false,
it can be refuted by demonstrating that, with best play, the game is
drawn or won by White.

Whether there is a practical refutation, I do not know. But, again,
as soon as you start asking for practicalities (rather than mere
existence), you're straying into the world of computer science.


or can it be shown to be unprovable?

No because it is not unprovable.

shrug So can you prove with best play - instead of one-sided
manipulation to invoke worst play - that your assertion is true?

`Unprovable' has a technical meaning. A statement is unprovable if
there exists no proof of its truth or falsity. (Goedel's famous
incompleteness theorem says that any system powerful enough to
formalize a system called `first-order arithmetic' can either prove
something that is false or cannot prove something that is true. The
effect is that any such system that cannot prove any falsehood must be
unable to prove some truths: these are said to be `unprovable'.)

I have shown how one could, in principle, prove or disprove the
assertion (depending on whether it is true or false) so it is not
unprovable.

As for whether there exists a practical (dis)proof, I don't know.


Dave.

--
David Richerby Mexi-Ghost (TM): it's like a haunting
www.chiark.greenend.org.uk/~davidr/ spirit that comes from Mexico!

In article ,
David Richerby wrote:
Even though there are more chess games than atoms in the universe.

We don't know *that*. "Visible" universe perhaps?

For the purposes of the theory of games of perfect information, any
finite number of players is equivalent to two. [...]
Why does it suffice to consider two-player games? Suppose we have n2
players. We can analyze the game from the point of view of player 1
by assuming that some super-human plays the moves for players 2, ...,
n himself. If player 1 can beat the super-human, he can also beat any
collection of ordinary people acting individually. Likewise for each
of the other players.

Yes, but when one player can beat all the others combined is the
uninteresting [and unusual] case. Interesting games in this sense are
those when each player could be defeated by a coalition of the others
[which will "almost always" happen if the game is in reasonable balance,
in some sense]. In this case, the outcome of the game is determined as
much by social factors [which players are "friends"] as by the theory.
Try 3-player Nim some time ....

Note also that if a game is not zero sum [eg "Prisoner's Dilemma"],
then you can make it so by adding an extra player who sole role is to act
as "banker". [Or "society" in PD.] But this will turn "most" 2-player
non-ZS games into unstable 3-player games [even if they are PI].

Further note: even if a game is mathematically ZS, it may not be
so in terms of the utility of the result. This is more relevant to
probabilistic games, however. But even in deterministic games, you are
not required to assume that your opponent will play perfectly, and you
may rationally prefer a move that wins #1000 unless your opponent finds
exactly the right response, but then wins only #0.99, to a move that wins
#1.00 no matter what the response. Scope also for an essay on the topic
of "randomising" vs "simplification" by which a strong player aims to
confuse a position which is drawn [or even losing] in order to give an
opponent a chance to go wrong, vs [eg] sacrificing back almost all of a
large advantage in order to reach a K&P ending which is a guaranteed win
vs an easily won position in which the opponent has fiddling chances.
It can be hard to determine what is "perfect play" in such cases. This
is a concept which is ill-understood, as yet, by the computers.

[Technical note to any mathematicians reading: yes, I'm aware that not
all infinite ordinals are limit ordinals but introducing the idea of
games of length omega+1 in the current discussion will just confuse
everyone.]

Not *everyone*! But it's perhaps worth noting that there are
perfectly playable games with infinite [in various senses] values, and
["of course"] with infinitesimal values. Some of these are relevant
to chess [eg there are K&P endings most easily understood in terms
of infinitesimal, but strictly positive, games].

--
Andy Walker, School of MathSci., Univ. of Nott'm, UK.

"David Richerby" wrote in message
...
Chess One wrote:
"David Richerby" wrote:
I don't know if any mathematician has ever seriously proposed which
of these two states, potential :: action, is superior from any
theoretical model.

Again, what's this double-colon you're using?

Its an advanced colon, as used by ... well, no jokes occur to me. It
is very like a single colon, though more signalled.

A colon isn't grammatical at that point in that sentence, either!
Does it, in fact, mean `and'?

David, my real comments on the two proposition are at the bottom, but in
between we encounter the dangers of transference.

The term " :: " indicates among philosophic types that it is not a colon
used as in writing, but used in writing in the same way as a colon is used
in mathematics, that is, one suggests a ratio, or proportional relationship,
rather than alternative listings of items with or without stated
relationship, as normally used in writing.

Chess is not even conveniently describable /as a process/ as a
Finite or Infinite Game.

Chess is trivially describable as an infinite game by omitting the
three drawing rules (dead position, three-fold repetition, 50-move
rule). It is then easy to prove that it suffices to consider only
finite games because of the drawing rules.

But finite is itself an arguable determination.

No it isn't! A collection of objects is finite if, and only if, you

a metaphysic! is the you any you, or a hypothetical you? an 'if-you' which
may not actually exist! or could not exist. [pain in the ass, no? these
logical formations in writing, but their advantage of symbol displacements
is that impossible 'you's' can be discerned. In math the positied term could
go unchallenged, and it doesn't concern anyone if it is a hypothetical value
of 'you'. But in writing of actual 'you' values it must relate to what is
possible, not metaphysically supposed.

Otherwise the sort of person referenced as 'you' may or may not exist, and
such statements do not even imply they /could/ exist. But this renders the
formulation undifferentiated from either the impossible or the imaginary.

can (in principle)

is 'if you can (in principle)' a conditional statement where the 'if' means
'when' rather than 'if you could', and the '(in principle)' is a known
principle than than a supposition?

otherwise in formal logic you posit an hypothesis which, true, /would/ be
finite, but is not known if it actually exists. this is why finite is
arguable - to wit: to whom?

example: red and blue are colours. The 'and' does not tell us if they are
the same colour, as in the case if we had written 'light blue and azure are
colours'

if c is the category, 'a colour', then the statements:-
a=c
b=c
does not mean a=b except in relationship to c, which is to say, they are
equal only in set-theory, and the term "=" does not mean 'same' as in
identical, but 'equivalent quality' related to their set, which is not the
only set they can belong to...

count them (1, 2, 3, 4...) and stop at some number,
having counted all the objects. So, the number of pieces on a
chessboard is finite, as is the number of grains of sand in the Sahara
Desert.

but time is not finite. and if time taken exceeds time permitted, eg, the
entirety of an individual's life, or beyond the extent of the life of the
entire universe for all people, then the term finite runs into trouble -
since know other time is available or knowable to cite as a possibility

Is it used synonymnously for 'theoretical',

No.

even though there are more moves than atoms in the universe

Even though there are more chess games than atoms in the universe.
This means that the finiteness of chess is of largely theoretical
interest, since knowing that it's finite doesn't help much in
practice. But `finite' does not mean `theoretical'.

Except of course in the terms I pose above - especially if 'you' were to
attemtp to solve anything, then it can be that 'you' lack sufficient finite
time to solve it. This is also true of collective efforts, where finite runs
into time available for all people

So if you were to answer that chess would be finite if there were infinite
time to solve it, do we not encounter a paradox common in Large Number
Theory? There are conditions where only from infinity we can define finite.
But if we acknowledge we have no infinity available to us, is what would be
finite, actually so?

Do the parallel lines oscillate, [what does not?] is their amplitude such
that they cross over?

but there is no /fixed/ prescription for when pawn promotions become
a consideration to actual play - and 'continuing the play' is what
happens in balanced or even dynamically unbalanced positions -

You've misunderstood the phrase `continuing the play' and are trying
to apply it outside its context. That context is a particular class
of infinite games. Infinite games are often defined as follows.
The two players

Or two or more, but yes...

For the purposes of the theory of games of perfect information, any
finite number of players is equivalent to two. Perfect information
means that all the players have full information about the position
(i.e., know where all of everyone's pieces are and any other relevant
facts).

Okay

Why does it suffice to consider two-player games? Suppose we have n2
players. We can analyze the game from the point of view of player 1
by assuming that some super-human plays the moves for players 2, ...,
n himself. If player 1 can beat the super-human, he can also beat any
collection of ordinary people acting individually. Likewise for each
of the other players.

Okay, given our suppositional super-human, but still if all other players do
not act 'individually, but gang up...

(This doesn't apply for games of imperfect information because, in
such a game, player 2 and player 3 cannot effectively co-operate
because they don't know where each other's pieces are or there is some
other key fact they don't know. But the super-human knows where all
the pieces are for players 2, ..., n, so he should be more powerful.)

But positing super-human ability must mean something to do with process, and
again this assumes that other players are now relegated to less process or
ability. And this is to subvert the equation of 'best play' into a
relativity, a socio-drama of participants.

The tricky part of inifinite games is that the rules themselves
evolve, so that some moves may condition new rules. This may except
alternating moves. This is a quibble, but still...

No, no, no! NO! There is nothing in the concept of `infinite game'
that means the rules change.

I am sorry, but this was a factor Carse provided for Infinite Games - of
course their can be others, but I am citing Carse who launched the IG ship.

Further, every game where the rules are
allowed to change is equivalent to one where the rules are static:
suppose we have rule sets 1, 2, ... (this may be finite or infinite).
Just make the number of the rule set currently in operation part of
the position and produce a master rule set that says, in effect, `If
the current rule set is number 1, you're allowed to do this; if it's
number 2, you can do this; ...' So we never need to even consider
games with changing rules in order to develop a theory of how games
work.

The very rules of nature seem to contradict this assertion. Is any new thing
possible by anticipating it from the sum of its parts? I think so, it is our
awareness of the interrrelationship of the parts which is new, and also an
awareness of the dynamic of the whole shebang [this is almost a statement
about science this past quarter century]compared with the previous rules we
had related to our, then, understanding. Now we attain to seeing the
relationship of the part to the whole, we also have a holistic paradign to
include in our awareness. The original 'rules' of behavior may not be
discarded, but included in a greater dynamic.

Psychology eg, has much to do with what goes on in people, whereas
anthropolgy with what goes on between people.


(Not all infinite games work like this. Consider the following
game, the name of which I'm afraid I don't recall. The game is
defined by a set S of real numbers between, but not including, 0
and 1. We start with `0.' written on a piece of paper and take
turns to add one digit to the end of the number written so far. I
win if the infinitely long decimal we produce is in S; you win if
it isn't.)

This again is an aside, but is this infinite, or simply an
undetermined linear extension of a theme?

This is genuinely infinite. The technical term for for your
`undetermined linear extension' is `unbounded'. An unbounded finite
game is one where there's no limit to how long a game can last but
every game must eventually finish.

Or evolve, said Darwin.

Eventually, there is some move
that is played that is the last move of the game. An infinite game is
one where there are necessarily an infinite number of moves:

yes in a way, but not necessarily because the moves are infinite in number,
but the rules governing moving can change. you probably know about
probability theory, the more complex the equation, the less forseeable or
predictable the result? This is straight Godel

there is also the implicit factor in your statement that although there is
linear play the game will continue linear, and since this tends to
contradict nature, by which i also mean physics! then such assertions are
questionable these days

it is not as much as if what you say is not true, but not possible in this
world, and therefore some care might be taken with these terms finite and
infinite, since again we encounter the paradox of even deciding what is
finite without referring to what is infinite

this great interested my author, Dr. Carse, who incidentally is a professor
of religion who would, I should imagine, get on ratehr well with Bohm.

the game
will never finish and there is no last move. After every move,
another must be made.

[Technical note to any mathematicians reading: yes, I'm aware that not
all infinite ordinals are limit ordinals but introducing the idea of
games of length omega+1 in the current discussion will just confuse
everyone.]

An example of an unbounded game is as follows. I think of a number
(an ordinary, positive integer: 1, 2, 3, ...) and you try to guess it.
After each guess, I tell you whether my number is smaller than or
greater than your guess and the game continues until you get the
correct number. On the assumption that your guesses are consistent
with the information I've given you (so you never guess 10 at any
point after I've told you the number is less than three, for example),
the game is unbounded but not infinite.

yes I understand what is considered unbounded in mathematics, yet that is
not to address chess, but hypothetical possibilities which may or may not
apply to chess, or indeed to any application! so while you may raise
possibilities of unbounded finites, these are not abstracted - that is, not
ab stracto, not 'taken form' any in vivo or real circumstance necessarily,
but from a hypothetical universe of relationships

It is not infinite because there are only finitely many numbers
smaller than the one I chose. If I choose the number `n', there are
only n-1 numbers smaller than it so, if you don't repeat a guess,
after n guesses, you must have either found out my number or guessed
something bigger than it. If you guessed something bigger (say, some
number `m'), there are only finitely many (m-1, in fact) numbers
smaller than it so, after at most m-1 more guesses, you must have hit
on the right number. There's no way that the game can go on
forever but, on the other hand there's no bound on how long the game
can be: I can choose an arbitrarily large number and your guesses can
be 1, 2, 3, ... .

(The condition I stated is critical: without it, the game becomes
potentially infinite as you could just guess `1' every time, even
though I tell you that the number is bigger.)

Sorry - I think analogous suppositions are abridged too far :0
They are rather indulgences which may or may not have any application to the
nature of chess. To say they could is not to say they do.

and there are no fixed number of moves to any game of chess,
except as metaphysically decided by others.

What on earth is the word `metaphysically' doing in the middle of
that sentence? This has nothing to do with metaphysics.

I use the word in its technical sense - 'without person'

Oh. `Non-corporeal' might have made your meaning clearer.

No. The statement, 'you are wrong' is metaphysical, since the missing words
are 'In my opinion. There is no subject to the sentence, no person. Nothing
to do with corporeal factors, all to do with specific ownership. It is a
term used in logic. It does not imply that the person speaking has any
experience whatever, and especvially no bio-organic sense of what they
address. Heiddegger called such statements 'pathic' ones [and added, as if
conducted by idiots].

There is nothing 'wrong' about supposing things weith no knowledge, except
when this is confused with the knowledge that is based on experience.
Denying any personal involvement has the implicit criticism of it that what
is spoken abnout metaphysically may not be spoken about in any other way!
That is not a paradox, merely funny!

Anyway,
what does `there are no fixed number of moves to any game of chess,
except as decided by others without person' mean? The number of moves
in a game of chess is decided (antagonistically) by the players
themselves.

But not by prescription. Players don't collude that one or the other is
mated at move 17. The number of moves is decided by the previous moves and
is indeterminate.

In this sense the game of chess is decided not by the players [the
persons] but by non-players implementing their determination of
rules.

I disagree. Ultimately, it's the players who implement the rules. An
arbiter can say, `You're not using the rules that we agreed so I do
not consider what you are doing to be part of the tournament,' but he
can't implement the rules for them.

Sorry - I attemtped to say too briefly something about the influence of ex
cathedra decisions. I'll let it pass.


small snip on similar theme

Can the statement, "black always wins" be refuted

Yes. Consider the game 1.e4 e5 2.Bc4 Bc5 3.Qh5 a6 4.Qxf7#. The
statement `Black always wins with perfect play' can be refuted, in
principle, by case analysis.

Though its also true that black can mate quicker than white - so
perhaps the explicit statement 'with best play' needs to be added,
and if so, is there any answer?

Yes, `with best play' needs to be added to make the question
non-trivial. The answer is that, in principle, the statement `with
best play, Black always wins' can be refuted if, and only if, it is
false. If it is true, clearly, it cannot be refuted; if it is false,
it can be refuted by demonstrating that, with best play, the game is
drawn or won by White.

Okay - there are the means. What is our answer?

Whether there is a practical refutation, I do not know. But, again,
as soon as you start asking for practicalities (rather than mere
existence), you're straying into the world of computer science.

Gawd! They don't even know an emulation from the real. That's not even
science, and resembles cargo-cultism.

or can it be shown to be unprovable?

No because it is not unprovable.

shrug So can you prove with best play - instead of one-sided
manipulation to invoke worst play - that your assertion is true?

`Unprovable' has a technical meaning.

Yes.

A statement is unprovable if
there exists no proof of its truth or falsity. (Goedel's famous
incompleteness theorem says that any system powerful enough to
formalize a system called `first-order arithmetic' can either prove
something that is false or cannot prove something that is true.

BTW - you read Oxford Murders? All about Goedel and complexity, and even
IQ][

The
effect is that any such system that cannot prove any falsehood must be
unable to prove some truths: these are said to be `unprovable'.)

And...

I have shown how one could, in principle, prove or disprove the
assertion (depending on whether it is true or false) so it is not
unprovable.

You have introduced a suppositional condition to answer the question, but
ended with a determinate. If I said one could answer the question, but did
not answer the question, then this would be a self-refuting tautology, as if
my statement was to deny itself by its own terms.

As for whether there exists a practical (dis)proof, I don't know.

Yeah.

Phil


Dave.

--
David Richerby Mexi-Ghost (TM): it's like a
haunting
www.chiark.greenend.org.uk/~davidr/ spirit that comes from Mexico!

"Dr A. N. Walker" wrote in message
...
In article ,
David Richerby wrote:
Even though there are more chess games than atoms in the universe.

We don't know *that*. "Visible" universe perhaps?

True. My chess partner an engineer is much worried by the Special Theorum,
where is this universe with all its mass? He asks.

For the purposes of the theory of games of perfect information, any
finite number of players is equivalent to two. [...]
Why does it suffice to consider two-player games? Suppose we have n2
players. We can analyze the game from the point of view of player 1
by assuming that some super-human plays the moves for players 2, ...,
n himself. If player 1 can beat the super-human, he can also beat any
collection of ordinary people acting individually. Likewise for each
of the other players.

Yes, but when one player can beat all the others combined is the
uninteresting [and unusual] case. Interesting games in this sense are
those when each player could be defeated by a coalition of the others
[which will "almost always" happen if the game is in reasonable balance,
in some sense]. In this case, the outcome of the game is determined as
much by social factors [which players are "friends"] as by the theory.
Try 3-player Nim some time ....

Note also that if a game is not zero sum [eg "Prisoner's Dilemma"],
then you can make it so by adding an extra player who sole role is to act
as "banker". [Or "society" in PD.] But this will turn "most" 2-player
non-ZS games into unstable 3-player games [even if they are PI].

Further note: even if a game is mathematically ZS, it may not be
so in terms of the utility of the result. This is more relevant to
probabilistic games, however. But even in deterministic games, you are
not required to assume that your opponent will play perfectly, and you
may rationally prefer a move that wins #1000 unless your opponent finds
exactly the right response,

Just to interject a moment, since ordinary citizens may be confused, these
are all asides and suppositions to the 2 plain questions, no? Alternate
universe questions, not chess answers.

but then wins only #0.99, to a move that wins
#1.00 no matter what the response. Scope also for an essay on the topic
of "randomising" vs "simplification" by which a strong player aims to
confuse a position which is drawn [or even losing] in order to give an
opponent a chance to go wrong, vs [eg] sacrificing back almost all of a
large advantage in order to reach a K&P ending which is a guaranteed win
vs an easily won position in which the opponent has fiddling chances.
It can be hard to determine what is "perfect play" in such cases. This
is a concept which is ill-understood, as yet, by the computers.

Andf not to indulge, but...

[Technical note to any mathematicians reading: yes, I'm aware that not
all infinite ordinals are limit ordinals but introducing the idea of
games of length omega+1 in the current discussion will just confuse
everyone.]

Not *everyone*! But it's perhaps worth noting that there are
perfectly playable games with infinite [in various senses] values, and
["of course"] with infinitesimal values. Some of these are relevant
to chess [eg there are K&P endings most easily understood in terms
of infinitesimal, but strictly positive, games].

But neither answer, answerable, Andy?

Phil

--
Andy Walker, School of MathSci., Univ. of Nott'm, UK.

Dr.A.N.Walker wrote :

It can be hard to determine what is "perfect play" in such cases.
This
is a concept which is ill-understood, as yet, by the computers.

Thanks Dr. for the above point....if it is not possible to determine
"perfect play", how can it be possible to programme computers to play
the perfect game ? Will it be right to say that all lines leading to a
"sure win" can be treated as perfect play? Whether a player exchanges
pieces to arrive at a won end game, or goes for a middle game win,
both should be treated as "perfect play".

Even a master such as myself.....

ROFL!!

Innes, you senile jackass, how can you keep telling lies like this when
everyone knows that you are nowhere near being a master. You never were one.
And you're no longer worth the 2044 rating you used to have 12 years ago.

"Chess One" wrote in message
news:PSoDh.4165$_O1.691@trndny04...

"help bot" wrote in message
ups.com...

At present, I have *finally* achieved a position requiring
a deep think. Two pawns ahead, I need to select the
right follow-up or my attack will falter. This is in fact, the
very first time I have seen fit to set up a chessboard and
men. All my games at GetClub and all my games at
RedHotPawn have been played rather offhandedly, up
'till now. (Even so, I am considered a "star" at GetClub.)

Perhaps you could recruit IM Innes in this endeavor?
He has the latest, greatest chess program ever: Rybka,
which undoubtedly can improve on my actual moves
about 90% of the time.

Even a master such as myself can improve upon a 1300-beater such as
Kennedy,

Is this retard who goes by the name "help bitch" really 1300? I already knew
the guy had a very low IQ based on the content of his posts, but this is
hillarious!

Innes, you lying old geezer sac of ****. Is there a single person that
doesn't already know you're a worthless, know-nothing loser? You're a
typical sad old fart that makes up lies to try to impress people.

I'm much stronger at the game of chess than you were at your peak. As it is
now I would beat you easily 10 out of 10 games, (with no draws). I'm a cfc
rated EXPERT player who has played rated events as recent as a couple of
months ago. You're a burned out, never has been, who's ALL TIME BEST rating
is barely over 2000. But that was 12 years ago. You're probably not worth
more than 1600-1700 now. Unless of course you're cheating with a program as
you do on chessworld.net.

My rating on the playchess server is 2268 right now. It various between
2200-2300 most of the time. It ocassionaly has been lower, when I play when
I'm tired, etc.

Go away Innes. You've already faded to a point where nobody even notices
you.

JMR