Chess One wrote:
"David Richerby" wrote in message
...
Ray Johnstone wrote:
wrote:
Is the initial position in chess a mutual Zugswang?

We will probably never know. See:
http://members.iinet.net.au/~ray/Chessgames.htm

Just because chess is likely impossible to brute-force doesn't mean we
can never know the outcome of theoretical best play. For example, it
is known that the game of `chomp' is a theoretical win for the first
player but nobody knows how to force the win except in very simple
cases.

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

Yeah, this is always an interesting debate, but its not even known
if /theoretically/ if it is white or black who wins, or the game is
a draw. To make such a claim the basis of it needs to be discussed,
and strangely, must deal with this factor:- [psychology]

No, Phil, psychology is completely irrelevant to the question of
whether chess is a theoretical win for one of the players or a draw.
The question is entirely mathematical.


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? What does it mean?
Mathematical game theory doesn't deal with `potential' `::' or
`action'. It deals with sequences of moves leading to wins or losses.


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.


Although chess is ostensibly finite, if you take the way it is
played /the modus/ as the rules applicable to that part of the game,
then the rules do change as the game progresses [there are no pawn
promotions in the opening, eg]

That's not a change in the rules!!! The rules are fixed throughout
the game; it's just that some of them can't apply. You can tell that
they're fixed by checking FIDE's website after each move you make.


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 alternate moves and, if some condition is reached, the
game is over and player 1 has won; player 2 wins only if the game
continues forever.

(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.)


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.


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.


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.


or can it be shown to be unprovable?

No because it is not unprovable.


Dave.

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