Longest Possible Chess game

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(This came out of an ongoing discussion about whether
playing chess shows intelligence, with a comparison of
Nalimov Tablebase lookups and the Chinese Room thought
experiment.)

Note to the non-chess-player: a "ply" is a black move or
a white move. Cheesplayers call ten black 'moves' and ten
white 'moves' ten moves/twenty plies. "FIDE" is the
international chess federation. A "3 man Nalimov
Tablebase" is a database of every possible position that
3 chesspieces (king, king, pawn, king,king, rook, etc.)
can be in along with instructions on how to play perfectly
(shortest possible path to a win or longest possible path
to a draw/loss) for each position.

Mike Murray wrote:
>
>Guy Macon <http://www.guymacon.com/> wrote:
>
>>Complete 3 man Nalimov Tablebase...80KB
>>Complete 3+4 man Nalimov Tablebase...30MB
>>Complete 3+4+5 man Nalimov Tablebase...7GB
>>Complete 3+4+5+6 man Nalimov Tablebase...1-2TB(est.)
>>Complete 3+4+5+6+7 man Nalimov Tablebase...200-600TB(est.)
>>Complete 3+4+5+6+7+8 man Nalimov Tablebase...40-180PB(est.)
>>...
>>Complete 3+4+5+[...]+30+31+32 man Nalimov Tablebase...????
>
>Yes, the trend is toward big, ain't it?

REALLY big. I have always wondered whether it is possible
to get even the roughest of estimates of how big; it's
certainly past my skills to calculate or even estimate it.

Alas, it appears that, despite my limited abilities, most
people who do chess calculations are a lot worse than I am.
There are a lot of different answers published to the far
easier question of how long the longest possible game of
chess is. Here is, I believe, the correct number:

---------------------------------------------------------

LONGEST POSSIBLE CHESS GAME CALCULATION:
By Guy Macon <http://www.guymacon.com>

Here is my calculation for the longest possible chess
game under FIDE rules. You may find the rules here:
<http://www.fide.com/official/handbook.asp?level=EE101>

Start with 32 chesspieces.

Move 100 plies, avoiding repeating positions.

On ply 100, move a pawn or make a capture.

Repeat N times until you make the last capture that leaves
2 kings. So how big is N?

There are 30 100-ply sequences ending with a capture.

There are 96 100-ply sequences ending with a pawn move.

8 of these sequences end with a pawn move that is also a capture.

1 of those sequences is only 99 plies to so that black can start
taking his turn making captures.

Assuming FIDE rules, that comes to a total of
(100*(30+96-8))-1)=11799 plies until the game is over.

- - - - - - - - - - - - - - -

Here is one way of reaching the maximum number of moves
in a chess game (see calculation above). Assume that
each ply described has 99 or 98 wasted plies between.

White advances his A,C,E,G pawns as far as they will go.

Black advances his B,D,F,H pawns as far as they will go.

White captures every black piece except 8 pawns, 2 knights,
1 bishop, one rook, and a King.

The white pawns on A,C,E,G capture the knights, bishops and rook,
passing and freeing the black pawns blocking them.

The now-unblocked black pawns move forward, promote, and move into
position to be taken by the white pawns on B,D,F,H, unblocking the
black pawns on B,D,F,H.

The now-unblocked black pawns move forward, promote, and are taken.

Black now only has a king. (Here is the lone 99 ply sequence) The
black king captures something, and the game continues a capture
by black on every 100th ply. When black captures the last white
piece, there are only the two kings left and the game is a draw
after 11799 plies.

Comments/corrections are welcome.

-Guy Macon <http://www.guymacon.com>

---------------------------------------------------------
 
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On Wed, 25 May 2005 15:01:30 +0000, Guy Macon
<http://www.guymacon.com/> wrote:

>Black now only has a king. (Here is the lone 99 ply sequence) The
>black king captures something, and the game continues a capture
>by black on every 100th ply. When black captures the last white
>piece, there are only the two kings left and the game is a draw
>after 11799 plies.
>
>Comments/corrections are welcome.

That looks about right. Keep in mind, though, that someone has to
claim a draw by the 50 move rule, it isn't automatic. Play continues
if no one claims a draw.

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Guy Macon wrote:
> [...]
> There are a lot of different answers published to the far
> easier question of how long the longest possible game of
> chess is. Here is, I believe, the correct number:
> [...] 11799 plies.

.... or 5850 moves. The number usually given is 6530. (Chernev, Curious
Chess Facts, The Black Knight Press, 1937.) A couple of mathematicians
published a paper called "The Longest Game", but I can't remember who
it was, or what the number was, and my printed-out copy of the article
is in Arizona. If you have access to MathSciNet (most universities do),
go to http://ams.rice.edu/mathscinet/search/ and search for the paper
with that title.

The length depends strongly on the rules which determine when a game is
drawn. The longest game by two grandmasters is around 269 moves.

--- Christopher Heckman
 
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On 25 May 2005 13:26:29 -0700, "Proginoskes"
<proginoskes@email.msn.com> wrote:

>
>
>Guy Macon wrote:
>> [...]
>> There are a lot of different answers published to the far
>> easier question of how long the longest possible game of
>> chess is. Here is, I believe, the correct number:
>> [...] 11799 plies.
>
>... or 5850 moves. The number usually given is 6530.

I've found references to 5949 moves:
http://www.chess-poster.com/english/notes_and_facts/did_you_know.htm
http://myweb.cableone.net/theyowans/chess_training.htm
http://gameknot.com/stats.pl?zargoth123

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Note that the game doesn't end just by virtue of there being 100 consecutive half-moves without a pawn move or capture; the rule is just that at that point a player is allowed to claim a draw if he wishes. The players can continue to push pieces for as long as they like.
 
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"Proginoskes" <proginoskes@email.msn.com> wrote in message
news:1117052789.143022.307790@g14g2000cwa.googlegroups.com...
>
>
> Guy Macon wrote:
> > [...]
> > There are a lot of different answers published to the far
> > easier question of how long the longest possible game of
> > chess is. Here is, I believe, the correct number:
> > [...] 11799 plies.
>
> ... or 5850 moves. The number usually given is 6530. (Chernev, Curious
> Chess Facts, The Black Knight Press, 1937.) A couple of mathematicians
> published a paper called "The Longest Game", but I can't remember who
> it was, or what the number was, and my printed-out copy of the article
> is in Arizona. If you have access to MathSciNet (most universities do),
> go to http://ams.rice.edu/mathscinet/search/ and search for the paper
> with that title.
>
> The length depends strongly on the rules which determine when a game is
> drawn. The longest game by two grandmasters is around 269 moves.
>
> --- Christopher Heckman

# What are the fewest moves to win a game?
 
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Don H wrote:
>
>
> # What are the fewest moves to win a game?
>

Fool's mate, I think.

Bob Kolker

>
 
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"Proginoskes" <proginoskes@email.msn.com> writes in article <1117052789.143022.307790@g14g2000cwa.googlegroups.com> dated 25 May 2005 13:26:29 -0700:
>The length depends strongly on the rules which determine when a game is
>drawn. The longest game by two grandmasters is around 269 moves.

Actually, both the 50-move and 3-repeat rules have loopholes. One player
must "claim" the draw; otherwise the game continues. So the length is
unbounded.

--Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.
 
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Proginoskes wrote:

>Guy Macon wrote:
>
>> There are a lot of different answers published to the far
>> easier question of how long the longest possible game of
>> chess is. Here is, I believe, the correct number:
>> [...] 11799 plies.
>
>... or 5850 moves. The number usually given is 6530. (Chernev, Curious
>Chess Facts, The Black Knight Press, 1937.)

Not being one of those kooks who think that They Alone Know The Truth
and the All Experts Are Wrong, it bothers me that my calculations came
up with a different answer than other folks got, but I have never seen
any of them say how they made the calculation.

> A couple of mathematicians
>published a paper called "The Longest Game", but I can't remember who
>it was, or what the number was, and my printed-out copy of the article
>is in Arizona. If you have access to MathSciNet (most universities do),
>go to http://ams.rice.edu/mathscinet/search/ and search for the paper
>with that title.

Available by subscription only. :(

I did a web search and found the title _The longest chess game:
Discovery of chess endgames that require 221 moves to capture a
piece and subsequently win_ by by Lewis Stiller (PhD thesis).
Is that it?

>The length depends strongly on the rules which determine when a game is
>drawn. The longest game by two grandmasters is around 269 moves.

I tried to calculate it with USCF (USA Chess federation) rules rather
than FIDE (International Chess Federation) rules, and concluded that
the USCF rules were ambiguous enough that I couldn't do the math.

Jud McCranie wrote:

>That looks about right. Keep in mind, though, that someone has to
>claim a draw by the 50 move rule, it isn't automatic. Play continues
>if no one claims a draw.

Excellent point. I will add the assumption that one or the other
player claims the draw, otherwise they can go on for a very long
time. Otherwise the player can just move the same piece back and
forth forever, never claiming the repetition of position draw or
the 50 move draw.

--
Guy Macon <http://www.guymacon.com/>
 
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On Wed, 25 May 2005 21:40:21 +0000, Guy Macon
<http://www.guymacon.com/> wrote:

>I did a web search and found the title _The longest chess game:
>Discovery of chess endgames that require 221 moves to capture a
>piece and subsequently win_ by by Lewis Stiller (PhD thesis).
>Is that it?

No, that's for a particular type of endgame, rook and bishop versus
two knights.

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>>I did a web search and found the title _The longest chess game:
>>Discovery of chess endgames that require 221 moves to capture a
>>piece and subsequently win_ by by Lewis Stiller (PhD thesis).
>>Is that it?
>
>No, that's for a particular type of endgame, rook and bishop versus
>two knights.

And, BTW, that is ignoring the 50-move rule. So it is for puzzles.

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"Don H" <donlhumphries@bigpond.com> writes in article <IU5le.991$BR4.227@news-server.bigpond.net.au> dated Wed, 25 May 2005 21:14:16 GMT:
># What are the fewest moves to win a game?

Again, there's a loophole in the rules. Either player may resign on his
move, so white can resign after 0 plies.

I think the shortest route to checkmate is 4 plies, with black checkmating
on his second move.

1. f3 e6
2. g4 Qh4++

--Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.
 
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Don H wrote:
>
> # What are the fewest moves to win a game?

Apart from things like 1. e4 resign the shortest mate is

1. g4 e5 2. f4 Qh4 mate.

Claus-Juergen
 
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Content-Transfer-Encoding: 8Bit


Claus-Jürgen Heigl wrote:
>
>Don H wrote:
>>
>> # What are the fewest moves to win a game?
>
>Apart from things like 1. e4 resign the shortest mate is
>
>1. g4 e5 2. f4 Qh4 mate.
>
>Claus-Juergen

What are the fewest moves to win a game of Go?
 
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"Guy Macon" <http://www.guymacon.com/> wrote in message
news:1199560is22ctbc@corp.supernews.com...
> LONGEST POSSIBLE CHESS GAME CALCULATION:
> By Guy Macon <http://www.guymacon.com>
>
> Here is my calculation for the longest possible chess
> game under FIDE rules. You may find the rules here:
> <http://www.fide.com/official/handbook.asp?level=EE101>
>
> Start with 32 chesspieces.
>
> Move 100 plies, avoiding repeating positions.
>
> On ply 100, move a pawn or make a capture.
>
> Repeat N times until you make the last capture that leaves
> 2 kings. So how big is N?
>
> There are 30 100-ply sequences ending with a capture.
>
> There are 96 100-ply sequences ending with a pawn move.
>
> 8 of these sequences end with a pawn move that is also a capture.
>
> 1 of those sequences is only 99 plies to so that black can start
> taking his turn making captures.
>
> Assuming FIDE rules, that comes to a total of
> (100*(30+96-8))-1)=11799 plies until the game is over.

Sorry, but you're completely wrong!
Refer to article 9 of the FIDE rules of chess. 9.3 describes the '50 move
rule':

" 9.3 The game is drawn, *****upon a correct claim***** by the player having
the move, if [...]"

Since neither player is required to claim the draw (and the same applies
with repeated positions), a game of chess is not limited to having a finite
number of moves. :)

Alun Harford

--
Include the word 'lemongrass' in any email you send to me, or you'll hit my
spam filter. If you're reading archives, I may have changed this word -
check http://www.alunharford.co.uk/
 
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"Guy Macon" <http://www.guymacon.com/> wrote in message
news:1199vepntknapc9@corp.supernews.com...
>
> Content-Transfer-Encoding: 8Bit
>
>
> Claus-Jürgen Heigl wrote:
> >
> >Don H wrote:
> >>
> >> # What are the fewest moves to win a game?
> >
> >Apart from things like 1. e4 resign the shortest mate is
> >
> >1. g4 e5 2. f4 Qh4 mate.
> >
> >Claus-Juergen
>
> What are the fewest moves to win a game of Go?


1. pass pass

white wins because of komi

--
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On Wed, 25 May 2005, [ISO-8859-1] Claus-Jürgen Heigl wrote:

> Don H wrote:
> > # What are the fewest moves to win a game?
>
> Apart from things like 1. e4 resign the shortest mate is
>
> 1. g4 e5 2. f4 Qh4 mate.

[1. White resigns] would be possible, but bizarre. However, [1. White
loses on time] happens when White doesn't make it to the board.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
 
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In article <1117052789.143022.307790@g14g2000cwa.googlegroups.com>,
"Proginoskes" <proginoskes@email.msn.com> wrote:

> Guy Macon wrote:
> > [...]
> > There are a lot of different answers published to the far
> > easier question of how long the longest possible game of
> > chess is. Here is, I believe, the correct number:
> > [...] 11799 plies.
>
> ... or 5850 moves. The number usually given is 6530. (Chernev, Curious
> Chess Facts, The Black Knight Press, 1937.) A couple of mathematicians
> published a paper called "The Longest Game", but I can't remember who
> it was, or what the number was, and my printed-out copy of the article
> is in Arizona. If you have access to MathSciNet (most universities do),
> go to http://ams.rice.edu/mathscinet/search/ and search for the paper
> with that title.

No papers found with longest game in the title.

No papers found with longest & game & chess anywhere.

About 40 papers with longest & game somewhere in title or review,
but just looking at the titles I don't think they're about chess.

There are 294 reviews that mention chess but I'm not going to look
through them all to see if I can find what you think you've seen.

--
Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email)
 
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Gerry Myerson wrote:
> In article <1117052789.143022.307790@g14g2000cwa.googlegroups.com>,
> "Proginoskes" <proginoskes@email.msn.com> wrote:
>
> > Guy Macon wrote:
> > > [...]
> > > There are a lot of different answers published to the far
> > > easier question of how long the longest possible game of
> > > chess is. Here is, I believe, the correct number:
> > > [...] 11799 plies.
> >
> > ... or 5850 moves. The number usually given is 6530.
> > (Chernev, Curious Chess Facts, The Black Knight Press,
> > 1937.) A couple of mathematicians published a paper
> > called "The Longest Game", but I can't remember who
> > it was, or what the number was, and my printed-out
> > copy of the article is in Arizona. If you have access
> > to MathSciNet (most universities do), go to
> > http://ams.rice.edu/mathscinet/search/ and search for
> > the paper with that title.
>
> No papers found with longest game in the title.
>
> No papers found with longest & game & chess anywhere.
>
> About 40 papers with longest & game somewhere in title
> or review, but just looking at the titles I don't think
> they're about chess.
>
> There are 294 reviews that mention chess but I'm not
> going to look through them all to see if I can find what
> you think you've seen.

It may have been in a journal like the Journal of Recreational
Mathematics, which isn't indexed at MathSciNet. I ran across the
article by accident, checking some references at MathWorld. (Why
couldn't this thread have come up 2 weeks earlier !?!??!) It's probably
within the last 25 years, so a glance at the table of contents should
be sufficient. Otherwise, I'll have to respond in a few months, when I
get back home ...

--- Christopher Heckman
 
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Don H wrote:
> "Claus-Jürgen Heigl" <unea@rz.uni-karlsruhe.de> wrote in message
> news:d72qpj$fft$1@news2.rz.uni-karlsruhe.de...
> > Don H wrote:
> > >
> > > # What are the fewest moves to win a game?
> >
> > Apart from things like 1. e4 resign the shortest
> > mate is
> >
> > 1. g4 e5 2. f4 Qh4 mate.
> >
> > Claus-Juergen
>
> # Thanks. I don't know much about chess, but have
> heard it called a game of pure skill (no "luck"
> involved; e.g. as in dealing a pack of cards).
> Presumably, this is because -
> (1) It has fixed rules, with no exceptions.
> (2) to any move, there are only a certain number of
> options available (disjunctives).
> (3) the two players take turns to move one piece.
> (4) result is check(mate), or stalemate (draw).
> (5) given above factors, all possible games can be
> determined.
> (6) from this, longest possible game can be found.
> (7) a computer is likely to beat a human, as it has
> greater memory capacity, and is ruthlessly logical.

You forgot --

(8) Both players have complete information, unlike in cards, where each
player is the only one that sees their hand.

--- Christopher Heckman
 
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Keith A. Lewis wrote:
> "Proginoskes" <proginoskes@email.msn.com> writes

> >The length depends strongly on the rules which determine when a game is
> >drawn. The longest game by two grandmasters is around 269 moves.

> Actually, both the 50-move and 3-repeat rules have loopholes.

There are no 50-move restrictions. Official chess games continue to
their natural end.

> 3-repeat rules have loopholes. One player
> must "claim" the draw;

Are you sure? In any case, a game between 2 players or computer
programs, who are smart enough to understand the basic rules of chess,
will not continue after, say, the fifth repetiotion.

> otherwise the game continues. So the length is
> unbounded.

Well, if both players are so insane that they can't notice that they
are going in circles, here is indeed a simple infinite game:

1 Kc3 Kc6
2 Kb1 Kb8

3 Kc3 Kc6
4 Kb1 Kb8

5 Kc3 Kc6
6 Kb1 Kb8

etc

But what's the point in this? Chess is a problem of search on a graph.
The nodes of this graph are all possible positions in a chess game. The
arcs point from one position to every other position, accessible from
that position in one "move".

When a human or a computer program plays a game of chess or analyses a
position, he/it will never consider the same position more than once.

Thus, what matters is the total number of possible DISTINCT positions,
which is finite. And the number of non-repeating sequences of
positions, which is also finite.
 
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"Claus-Jürgen Heigl" <unea@rz.uni-karlsruhe.de> wrote in message
news:d72qpj$fft$1@news2.rz.uni-karlsruhe.de...
> Don H wrote:
> >
> > # What are the fewest moves to win a game?
>
> Apart from things like 1. e4 resign the shortest mate is
>
> 1. g4 e5 2. f4 Qh4 mate.
>
> Claus-Juergen

# Thanks. I don't know much about chess, but have heard it called a game of
pure skill (no "luck" involved; e.g. as in dealing a pack of cards).
Presumably, this is because -
(1) It has fixed rules, with no exceptions.
(2) to any move, there are only a certain number of options available
(disjunctives).
(3) the two players take turns to move one piece.
(4) result is check(mate), or stalemate (draw).
(5) given above factors, all possible games can be determined.
(6) from this, longest possible game can be found.
(7) a computer is likely to beat a human, as it has greater memory capacity,
and is ruthlessly logical.
 
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Don H wrote:

># Thanks. I don't know much about chess, but have heard it called a game of
>pure skill (no "luck" involved; e.g. as in dealing a pack of cards).
> Presumably, this is because -
>(1) It has fixed rules, with no exceptions.
>(2) to any move, there are only a certain number of options available
>(disjunctives).
>(3) the two players take turns to move one piece.
>(4) result is check(mate), or stalemate (draw).
>(5) given above factors, all possible games can be determined.
>(6) from this, longest possible game can be found.
>(7) a computer is likely to beat a human, as it has greater memory capacity,
>and is ruthlessly logical.

Items 1-6 are all roughly true of Go, but computers aren't very
good at Go. The move tree gets way too big way too soon to make
searching for a win a workable option, and humans are (for now)
much better at the pattern matching needed to have a good evaluation
function.

I conclude from this that #7 does not follow from numbers #1-6.

(They are also true of checkers, and we have one common checker
opening solved - the computer plays perfectly - with more on the
way.)
 
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<anzaurres1@hotmail.com> wrote:
> Keith A. Lewis wrote:
>> "Proginoskes" <proginoskes@email.msn.com> writes
>>> The length depends strongly on the rules which determine when a game
>>> is drawn. The longest game by two grandmasters is around 269 moves.
>>
>> Actually, both the 50-move and 3-repeat rules have loopholes.
>
> There are no 50-move restrictions. Official chess games continue to
> their natural end.

The 50-move restriction is that a draw can be made if there have been no
captures or pawn moves in fifty consecutive moves (100 ply).


>> 3-repeat rules have loopholes. One player must "claim" the draw;
>
> Are you sure?

Yes. The official rules of chess are on the web at

http://www.fide.com/official/handbook.asp?level=EE101

Draws by repetition and the 50-move rule are covered by Articles 9.3 and
9.4, respectively.


> Well, if both players are so insane that they can't notice that they
> are going in circles, here is indeed a simple infinite game:
>
> 1 Kc3 Kc6 [etc]

It's a minor point but, in standard chess notation, `K' denotes the king.
Knights are `N' and used to be written `Kt'.


> Chess is a problem of search on a graph.

This is true of all games of perfect information.


Dave.

--
David Richerby Crystal Salted Book (TM): it's like
www.chiark.greenend.org.uk/~davidr/ a romantic novel but it's covered in
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David Richerby wrote:
>
><anzaurres1@hotmail.com> wrote:
>
>>> "Proginoskes" <proginoskes@email.msn.com> writes
>>>
>>> 3-repeat rules have loopholes. One player must "claim" the draw;
>>
>> Are you sure?
>
>Yes. The official rules of chess are on the web at
>
>http://www.fide.com/official/handbook.asp?level=EE101
>
>Draws by repetition and the 50-move rule are covered by Articles 9.3 and
>9.4, respectively.

Not only that, but it is forbidden for spectators or tournament
officials to interfere in any way, including pointing out that
a draw claim can be made.

Although I didn't make it clear at first, obviously my calculations
assume that the players claim a draw when it is legal to do so.
Otherwise the problem becomes uninteresting - the answer is that
it never stops. This is of no interest when discussing real-world
computer chess, of course; if the computer is behind it will claim
a draw when it gets a chance, and if the computer is ahead it will
avoid a position that allows the opponent to claim a draw.