David Richerby wrote:
wrote:
Although this is a degenerate example, it is correct: the number of
possible chess *games* is infinite [...] A draw can be claimed by
repetition or the 50 move rule under this scenario, but that is an
option, not a requirement, as I understand the rules (otherwise my
example is incorrect).

You are absolutely correct that the number of possible chess games is
infinite because draws by repetition or the fifty-move rule have to be
claimed and are not automatic.

In order to generate a non-trivial problem, one supposes that either
player will claim a draw as soon as he has the opportunity. One then
asks how many of these `interesting' games there are.


Dave.


so, it's more important for the answer to be interesting than for it to
be correct?



--
Kenneth Sloan
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/

On Wed, 28 Nov 2007 11:30:35 -0600 in ,
Kenneth Sloan wrote:

so, it's more important for the answer to be interesting than for it to
be correct?

Well, as we've shown, the actual number of games is infinite, so it's
probably more interesting for the answer to be 'interesting' rather than
correct. (Or something like that)

Stephan
--
Stephan Bird MChem(Hons) AMRSC
Currently in Caernarfon, Wales

On Wed, 28 Nov 2007 07:50:55 -0800 (PST), "
wrote:

Although this is a degenerate example, it is correct: the number of
possible chess *games* is infinite, as is easily demonstrated by one
of many possible examples. Consider the sequence

1. Nf3 Nf6
2. Ng1 Ng8

Now repeat this sequence any arbitrary number of times. Though the
number of positions generated is just a few, the number of *games*
possible is as many as you wish, even though the games are not exactly
thrillers.

A draw can be claimed by repetition or the 50 move rule under this
scenario, but that is an option, not a requirement, as I understand
the rules (otherwise my example is incorrect).
That is why I wrote:
A "game" must here be defined as a legal sequence of moves ending in
mate, stalemate or a draw by obligatory imposition of the three-fold
repetition and fifty-move laws so that the result is beyond dispute.


www.iinet.com.au/~ray

Kenneth Sloan wrote:
David Richerby wrote:
In order to generate a non-trivial problem, one supposes that
either player will claim a draw as soon as he has the opportunity.
One then asks how many of these `interesting' games there are.

so, it's more important for the answer to be interesting than for it
to be correct?

It's not incorrect as long as you state the problem you're solving
correctly: `the number of possible chess games, assuming that both
players will claim a draw as soon as they have that option, is N.'


Dave.

--
David Richerby Adult Peanut (TM): it's like a roasted
www.chiark.greenend.org.uk/~davidr/ nut that you won't want the children
to see!

Ray Johnstone wrote:
A "game" must here be defined as a legal sequence of moves ending in
mate, stalemate or a draw by obligatory imposition of the three-fold
repetition and fifty-move laws so that the result is beyond dispute.

Giving the players the option of not claiming possible draws does not
put the result into dispute. Under the actual laws of chess, these
are all legal games, where `**' means any one of `Black resigns 1-0',
`White resigns 0-1' and `Draw agreed 1/2-1/2':

**
1.Nf3 **
1.Nf3 Nf6 **
1.Nf3 Nf6 2.Ng1 **
1.Nf3 Nf6 2.Ng1 Ng8 **
1.Nf3 Nf6 2.Ng1 Ng8 3.Nf3 **
1.Nf3 Nf6 2.Ng1 Ng8 3.Nf3 Nf6 **
1.Nf3 Nf6 2.Ng1 Ng8 3.Nf3 Nf6 4.Ng1 **
1.Nf3 Nf6 2.Ng1 Ng8 3.Nf3 Nf6 4.Ng1 Ng8 **
1.Nf3 Nf6 2.Ng1 Ng8 3.Nf3 Nf6 4.Ng1 Ng8 5.Nf3 **
1.Nf3 Nf6 2.Ng1 Ng8 3.Nf3 Nf6 4.Ng1 Ng8 5.Nf3 Nf6 **
1.Nf3 Nf6 2.Ng1 Ng8 3.Nf3 Nf6 4.Ng1 Ng8 5.Nf3 Nf6 6.Ng1 **
1.Nf3 Nf6 2.Ng1 Ng8 3.Nf3 Nf6 4.Ng1 Ng8 5.Nf3 Nf6 6.Ng1 {Black announces
his intention to play 6... Ng8. Draw by repetition} 1/2-1/2
1.Nf3 Nf6 2.Ng1 Ng8 3.Nf3 Nf6 4.Ng1 Ng8 5.Nf3 Nf6 6.Ng1 Ng8 **
1.Nf3 Nf6 2.Ng1 Ng8 3.Nf3 Nf6 4.Ng1 Ng8 5.Nf3 Nf6 6.Ng1 Ng8 {White
claims a draw by repetition} 1/2-/12
1.Nf3 Nf6 2.Ng1 Ng8 3.Nf3 Nf6 4.Ng1 Ng8 5.Nf3 Nf6 6.Ng1 Ng8 {White
announces his intention to play 7.Nf3. Draw by repetition} 1/2-1/2

and so on. It's just that there are infinitely many of them, so the
question is trivial and boring without the supposition that draws will
be claimed when available.


Dave.

--
David Richerby Mentholated Dish (TM): it's like
www.chiark.greenend.org.uk/~davidr/ a fine ceramic dish but it's
invigorating!