# Longest Possible Chess game

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Anonymous

May 25, 2005 7:01:30 PM

Archived from groups: alt.philosophy,sci.physics,rec.games.chess.computer,sci.math (More info?)

(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&g...;

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>

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

(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&g...;

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>

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

More about : longest chess game

Anonymous

May 25, 2005 7:01:31 PM

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.

---

Replace you know what by j to email

Anonymous

May 25, 2005 7:01:31 PM

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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Anonymous

May 25, 2005 9:03:31 PM

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...

http://myweb.cableone.net/theyowans/chess_training.htm

http://gameknot.com/stats.pl?zargoth123

---

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Anonymous

May 25, 2005 9:12:52 PM

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.

Anonymous

May 26, 2005 1:14:16 AM

"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?

Anonymous

May 26, 2005 1:14:17 AM

Don H wrote:

>

>

> # What are the fewest moves to win a game?

>

Fool's mate, I think.

Bob Kolker

>

Anonymous

May 26, 2005 1:37:53 AM

"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.

Anonymous

May 26, 2005 1:40:21 AM

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/>

Anonymous

May 26, 2005 1:40:22 AM

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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Anonymous

May 26, 2005 1:40:23 AM

>>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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Anonymous

May 26, 2005 1:44:15 AM

"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.

Anonymous

May 26, 2005 3:32:43 AM

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

Anonymous

May 26, 2005 3:32:44 AM

Content-Transfer-Encoding: 8Bit

Claus-JÃ¼rgen 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?

Anonymous

May 26, 2005 6:12:55 AM

"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&g...;

>

> 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/

Anonymous

May 26, 2005 6:16:28 AM

"Guy Macon" <http://www.guymacon.com/> wrote in message

news:1199vepntknapc9@corp.supernews.com...

>

> Content-Transfer-Encoding: 8Bit

>

>

> Claus-JÃ¼rgen 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

--

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/

Anonymous

May 26, 2005 12:28:15 PM

On Wed, 25 May 2005, [ISO-8859-1] Claus-JÃ¼rgen 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

Anonymous

May 26, 2005 12:54:59 PM

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)

Anonymous

May 26, 2005 5:34:05 PM

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

Anonymous

May 26, 2005 7:49:44 PM

Don H wrote:

> "Claus-JÃ¼rgen Heigl" <unea@rz.uni-karlsruhe.de> wrote in message

> news 72qpj$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

Anonymous

May 26, 2005 8:45:06 PM

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.

Anonymous

May 27, 2005 1:18:29 AM

"Claus-JÃ¼rgen Heigl" <unea@rz.uni-karlsruhe.de> wrote in message

news 72qpj$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.

Anonymous

May 27, 2005 5:24:48 AM

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.)

Anonymous

May 27, 2005 8:42:08 PM

<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

salt and completely transparent!

Anonymous

May 27, 2005 8:42:09 PM

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.

Anonymous

May 27, 2005 8:42:10 PM

On Fri, 27 May 2005 16:17:51 +0000, Guy Macon

<http://www.guymacon.com/> wrote:

>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.

Well, normally. My daughter plays in scholastic tournaments. She

plays in a section for 3rd grade and under. The rule is game/30 but

they don't use clocks. If it is getting near the end of the hour, the

TD or assistant TD comes over with a clock. The TD may split the

remaining time for the players. But many of them don't know how to

use a clock. In one of my daughter's games this year, she got to the

ending K+2N vs K+P - one of those long, complicated wins that can

require more than 50 moves. (The assist. TD was there when it got

reduced to that from K+R+2N vs K+R+P.) Of course, my daughter doesn't

know how to win K+2N vs K+P. She (wisely) gave up a knight for the

pawn, and then the assist. TD declared K+N vs. K a draw (insufficient

mating material). I think it is OK for the TD to interfere in this

situation.

---

Replace you know what by j to email

Anonymous

May 27, 2005 9:51:49 PM

Jud McCranie wrote:

>

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

>

>>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.

>

>Well, normally. My daughter plays in scholastic tournaments. She

>plays in a section for 3rd grade and under. The rule is game/30 but

>they don't use clocks. If it is getting near the end of the hour, the

>TD or assistant TD comes over with a clock. The TD may split the

>remaining time for the players. But many of them don't know how to

>use a clock. In one of my daughter's games this year, she got to the

>ending K+2N vs K+P - one of those long, complicated wins that can

>require more than 50 moves. (The assist. TD was there when it got

>reduced to that from K+R+2N vs K+R+P.) Of course, my daughter doesn't

>know how to win K+2N vs K+P. She (wisely) gave up a knight for the

>pawn, and then the assist. TD declared K+N vs. K a draw (insufficient

>mating material). I think it is OK for the TD to interfere in this

>situation.

Of course it's OK. They can set whatever rules they like. They

were, however, not playing by FIDE rules and thus any results would

not be reflected in a FIDE rating. (I doubt that anyone there was

rated, and if they were it would likely have been with USCF, not

FIDE.)

Anonymous

May 27, 2005 9:51:50 PM

On Fri, 27 May 2005 17:51:49 +0000, Guy Macon

<http://www.guymacon.com/> wrote:

>Of course it's OK. They can set whatever rules they like. They

>were, however, not playing by FIDE rules and thus any results would

>not be reflected in a FIDE rating. (I doubt that anyone there was

>rated, and if they were it would likely have been with USCF, not

>FIDE.)

It was a USCF rated tournament.

---

Replace you know what by j to email

Anonymous

May 28, 2005 4:16:39 AM

Proginoskes wrote:

> anzaurres1@hotmail.com wrote:

> > Proginoskes wrote:

> > > Er, why must all elements of M begin with a Knight move?

> >

> > Suppose S is some element of M which doesn't begin with a

> > Knight move.

> >

> > Keep in mind that S is some sequence of moves.

> >

> > Let R be played as follows:

> >

> > 1. Nc3 Nc6

> > 2. Nb1 Nb8

> >

> > and then perform all the moves from S.

> >

> > Clearly R is also a winnning sequence. But R is 2 moves

> > longer than S.

>

> You also need to check for drawing possibilities. But if there is no

> draw in playing out S, then there is no draw in playing out R, because

> the 3rd move of R is a pawn move, and there is no draw before that.

Good point. The eventual irreversible pawn move is what makes my

argument valid. Actually, this pawn move will come much later than 3rd

move. First, there will be a whole bunch of knights moving back and

forth so that to repeat each postion exactly twice. There are 2^4

psitions with the knights in different "back and forth" posiitons. Each

position will be repeated twice. Except the for the original, which can

stand only one further repetition. Thus, in theory, there should be

2^4*2 - 1 = 31 half-moves of knights back and forth.

Can you by any chance find at least one such sequence of such 31

half-moves? I am too lazy today...

Next there will be some black pawn move. Next there will be at least 31

knight back and forth moves combined now with possible black bishop

and/or queen moves.

Then there will be another pawn move, folowed by incessant

back-and-forth mocves by more and more pieces... And so on. Pretty much

one "meaningful" move followed by hundreds of back-and-forth moves....

But!! There is the 50-move rule. Almost forgot! That will reduce the

number of back-and-forth moves in a hurry.... I mean, you need to

capture something every 50 moves....

Hmmmmmmm.... Interesting.....

So, every 50 moves, at least one peice must disappear or a pawn must

move forward. There are 32 pieces, counting the kings. But whenever a

game is over due to a checkmate or a draw, there will be at least 2

pieces still on the board, So, that means ther will be no more than 30

piece captures.

There are a total of 16 pawns each with 7 moves to make. Total of 16x7

= 112 moves. 30 + 112 is 140.

So,the total game length can't be longer than, say, 50x142 = 7100 or

so. That's not too bad..... :-)

This of course applies not only to winning games but to ALL games,

including draws.

I hope my stream of concience makes sense.

> > Thus S is not a sequence of winning moves of maximum length.

> > Contradiction. QED

>

> Okay, I believe it.

Thanks for providing a missing link to my proof.

Anonymous

May 28, 2005 4:27:16 AM

Actually, everything that I have said below applies to drawn games too.

So the theorems and calculations are universal.

I wonder if my thinking cam also produce a sequence of moves that

indeed comes close ot the theoretical upper bound... It should...

So, there will be pawn or capture moves every 50 moves. In-between

there will be 49 pairs of meanigless back-and-forth moves.

But pawns can't jump over each other. That'll reduce the possible

number of pawn moves quite a bit...

Unless somebody completes my train of thought in the meantime, I'll try

to return to it tomorrow..

How does this compare with other people's calculations?

This 50 move rule makes the problem tractible.... I think...

anzaurr...@hotmail.com wrote:

> Proginoskes wrote:

> > anzaurres1@hotmail.com wrote:

> > > Proginoskes wrote:

> > > > Er, why must all elements of M begin with a Knight move?

> > >

> > > Suppose S is some element of M which doesn't begin with a

> > > Knight move.

> > >

> > > Keep in mind that S is some sequence of moves.

> > >

> > > Let R be played as follows:

> > >

> > > 1. Nc3 Nc6

> > > 2. Nb1 Nb8

> > >

> > > and then perform all the moves from S.

> > >

> > > Clearly R is also a winnning sequence. But R is 2 moves

> > > longer than S.

> >

> > You also need to check for drawing possibilities. But if there is no

> > draw in playing out S, then there is no draw in playing out R, because

> > the 3rd move of R is a pawn move, and there is no draw before that.

>

> Good point. The eventual irreversible pawn move is what makes my

> argument valid. Actually, this pawn move will come much later than 3rd

> move. First, there will be a whole bunch of knights moving back and

> forth so that to repeat each postion exactly twice. There are 2^4

> psitions with the knights in different "back and forth" posiitons. Each

> position will be repeated twice. Except the for the original, which can

> stand only one further repetition. Thus, in theory, there should be

> 2^4*2 - 1 = 31 half-moves of knights back and forth.

>

> Can you by any chance find at least one such sequence of such 31

> half-moves? I am too lazy today...

>

> Next there will be some black pawn move. Next there will be at least 31

> knight back and forth moves combined now with possible black bishop

> and/or queen moves.

>

> Then there will be another pawn move, folowed by incessant

> back-and-forth mocves by more and more pieces... And so on. Pretty much

> one "meaningful" move followed by hundreds of back-and-forth moves....

>

> But!! There is the 50-move rule. Almost forgot! That will reduce the

> number of back-and-forth moves in a hurry.... I mean, you need to

> capture something every 50 moves....

>

> Hmmmmmmm.... Interesting.....

>

> So, every 50 moves, at least one peice must disappear or a pawn must

> move forward. There are 32 pieces, counting the kings. But whenever a

> game is over due to a checkmate or a draw, there will be at least 2

> pieces still on the board, So, that means ther will be no more than 30

> piece captures.

>

> There are a total of 16 pawns each with 7 moves to make. Total of 16x7

> = 112 moves. 30 + 112 is 140.

> So,the total game length can't be longer than, say, 50x142 = 7100 or

> so. That's not too bad..... :-)

>

> This of course applies not only to winning games but to ALL games,

> including draws.

>

> I hope my stream of concience makes sense.

>

> > > Thus S is not a sequence of winning moves of maximum length.

> > > Contradiction. QED

> >

> > Okay, I believe it.

>

> Thanks for providing a missing link to my proof.

Anonymous

May 28, 2005 12:18:26 PM

anzaurres1@hotmail.com wrote:

> ...

> I don't know. Can't follow your logic. Why should the longest sequence

> of moves necessarily involve having a last pawn on the board or having

> a king a queen checkmate.

It could as well be a rook, but a bishop or a knight would cause the

game to end in a dead position, so the last 50 moves could not be used.

As far as I can see, promoting every single pawn would allow to move up

to 6*8 times a pawn, and we'd get 7 promoted pieces to be captured and

the original queen, rooks, bishop and knights being captured.

As a first approximation right the same for both sides, allowing as much

as 50 * 2 * (6*8 + 15) = 6300 moves.

I'd guess it is impossible to reach this maximum number of moves, but it

should be possile to find a game where one side reaches this maximum

number of moves, so truth lies somewhere between 3150 and 6300 moves.

> ...

Anonymous

May 28, 2005 12:25:01 PM

AE wrote:

> ...

> It could as well be a rook, but a bishop or a knight would cause the

> game to end in a dead position, so the last 50 moves could not be used.

>

> As far as I can see, promoting every single pawn would allow to move up

> to 6*8 times a pawn, and we'd get 7 promoted pieces to be captured and

> the original queen, rooks, bishop and knights being captured.

>

> As a first approximation right the same for both sides, allowing as much

> as 50 * 2 * (6*8 + 15) = 6300 moves.

2 errors:

1) one queen or rook is not taken, because this would end the game

prematurely. On the other hand the last move could be a checkmate, so

the 3150 moves each are correct.

2) Since we don't know which rook or queen survives, the last promoted

pawn could be one of the pieces to be captured, so it doesn't matter

whether any of the promoted pawns is a queen or a rook.

> ...

Anonymous

May 28, 2005 1:07:05 PM

Guy Macon wrote:

> AE wrote:

> [in response to someone else:]

> >As a first approximation right the same for both

> >sides, allowing as much as 50 * 2 * (6*8 + 15) =

> >6300 moves.

> >

> >I'd guess it is impossible to reach this maximum

> >number of moves, but it should be possile to find

> >a game where one side reaches this maximum number

> >of moves, so truth lies somewhere between 3150 and

> >6300 moves.

Yes. This is something that X and Y (the authors of "The Longest Game",

a paper from a journal like the Journal of Recreational Mathematics)

take into consideration, that when a pawn captures, you cut down the

total number of moves by 50. But you're only shortening it by 8 * 50 =

400 moves.

> (When you write "moves", are you refering to what

> chessplayers call a move (white piece moves then

> black peice moves)?

Yes, a move is two plies.

> That is the meaning that is refered to in the "50

> move rule." Moving just a white piece or just a

> black piece is called a "ply". I find the

> calculations to be much easier to do when working

> with plies - no fractions needed.)

>

> Assuming that both players avoid allowing the other

> side to claim a draw according to the 50 move rule

> (if they don't and nobody claims the draw the game

> is infinite and this discussion becomes boring);

Note: (Once again, I'm going from memory here.) There are some

positions for which more than 100 plies are allowed before a draw can

be declared. I THINK that they involve several pieces, like K+B+R vs.

K+R, and that the number of allowed plies is not much larger than 200.

So these exceptions to the 50-move rule aren't actually relevant.

> 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.

Also mentioned in X's and Y's article.

> 1 of those sequences is only 99 plies long so that

> black can start taking his turn moving pawns or making

> captures.

This is also mentioned in X's and Y's article.

> Assuming FIDE rules, that gives us (100*(30+96-8))-1)

> =11799 plies (5899.5 moves) as the maximum number of

> moves until the game is over.

>

> I can prove by example that this maximum number of

> moves can be reached in actual play.

--- Christopher Heckman

Anonymous

May 28, 2005 5:02:28 PM

Guy, I think your analysis is either totally correct or close to it.

Guy Macon wrote:

> (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&g...;

>

> 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>

>

> ---------------------------------------------------------

Anonymous

May 28, 2005 7:38:23 PM

AE wrote:

>As far as I can see, promoting every single pawn would allow to move up

>to 6*8 times a pawn, and we'd get 7 promoted pieces to be captured and

>the original queen, rooks, bishop and knights being captured.

Figuring out how to get them past each other without losing any of

them is an interesting puzzle, but it can be done; you have to use

some of the original queen, rooks, bishop and knights being captured

to also shift the pawn doing the capturing sideways.

>As a first approximation right the same for both sides, allowing as much

>as 50 * 2 * (6*8 + 15) = 6300 moves.

>

>I'd guess it is impossible to reach this maximum number of moves, but it

>should be possile to find a game where one side reaches this maximum

>number of moves, so truth lies somewhere between 3150 and 6300 moves.

I need to sit down and work out the numbers after I go offline,

but on the face of it it seems from the above that my original

calculation might have missed something. Here is that calculation;

if anyone sees an error, please let me know

(When you write "moves", are you refering to what chessplayers call a

move (white piece moves then black peice moves)? That is the meaning

that is refered to in the "50 move rule." Moving just a white piece

or just a black piece is called a "ply". I find the calculations to

be much easier to do when working with plies - no fractions needed.)

Assuming that both players avoid allowing the other side to claim

a draw according to the 50 move rule (if they don't and nobody claims

the draw the game is infinite and this discussion becomes boring);

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 long so that black can start

taking his turn moving pawns or making captures.

Assuming FIDE rules, that gives us (100*(30+96-8))-1)=11799 plies

(5899.5 moves) as the maximum number of moves until the game is over.

I can prove by example that this maximum number of moves can be

reached in actual play.

Anonymous

May 28, 2005 7:59:56 PM

anzaurres1@hotmail.com wrote:

>But!! There is the 50-move rule. Almost forgot! That will reduce the

>number of back-and-forth moves in a hurry.... I mean, you need to

>capture something every 50 moves....

>

>Hmmmmmmm.... Interesting.....

>

>So, every 50 moves, at least one peice must disappear or a pawn must

>move forward. There are 32 pieces, counting the kings. But whenever a

>game is over due to a checkmate or a draw, there will be at least 2

>pieces still on the board, So, that means ther will be no more than 30

>piece captures.

>

>There are a total of 16 pawns each with 7 moves to make. Total of 16x7

>= 112 moves. 30 + 112 is 140.

>So,the total game length can't be longer than, say, 50x142 = 7100 or

>so. That's not too bad..... :-)

How do those pawns get past each other? After 8 of the pawns move

forward 4 squares each, no pawn can move.

(I find it to be easier to calculate of you use plies. In the text

above, "50 move rule" refers to a black piece moving and a white piece

moving (2 plies, one move), but "with 7 moves to make" refers to one

piece moving (1 ply, 1/2 of a move) It is a lot less confusing to

use a a 100 ply rule and count plies instead of moves.)

Anonymous

May 28, 2005 8:46:36 PM

anzaurres1@hotmail.com wrote:

>But pawns can't jump over each other. That'll reduce the possible

>number of pawn moves quite a bit...

by making 8 of the pawn moves captures, they can all pass each other.

Anonymous

May 28, 2005 9:14:58 PM

Proginoskes wrote:

>Note: (Once again, I'm going from memory here.) There are some

>positions for which more than 100 plies are allowed before a draw can

>be declared. I THINK that they involve several pieces, like K+B+R vs.

>K+R, and that the number of allowed plies is not much larger than 200.

>So these exceptions to the 50-move rule aren't actually relevant.

In the FIDE Laws of Chess, published in 1984 and 1988, the 50-move

rule was extended to 75 moves for the following positions:

King + Rook + Bishop against King + Rook;

King + 2 Knights against King + pawn;

King + Queen + pawn one square from promotion against King + Queen;

King + Queen against King + 2 Knights;

King + Queen against King + 2 Bishops;

King + 2 Bishops against King + Knight

In 1992 during the FIDE Congress in Manila the Rules Committee

suggested establishing one rule for all endings: 50 moves, and

the General Assembly of FIDE approved the change. In 1996 the

Congress in Yerevan revisited the decision and kept the 1992

rules. There are currently no exceptions to the 50-move rule.

Source: _An Arbiter's Notebook_,

by International Arbiter Geurt Gijssen

The Archives of _An Arbiter's Notebook_ are really quite

interesting. You can find them here:

http://www.chesscafe.com/archives/archives.htm#An%20Arb...'s%20Notebook

--

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

cbrown

May 29, 2005 6:05:40 PM

Guy Macon wrote:

> (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.

>

We can at least put the following very rough upper bound on this

problem:

There are 32 pieces; 64 squares; so if all pieces are on the board, and

we uniquely identify each piece, there are C(64,32) possible board

positions. Then, since the 8 pawns for each side are indistingusihable,

and the pairs of bishops, knights, and rooks are indistinguishable, we

can divide out these possibilities to get

C(64,32)/((8!^2)*2^6)

for the number of distinct board positions where all 32 pieces are on

the board. Of course, this includes many illegal board configurations;

both bishops can be on the same color for example; but this is just the

rough upper bound.

If we assume that each successive calculation for 31 pieces, 30 pieces,

etc. is roughly the same order of magnitude, then an upper bound would

be

32*C(64,32)/((8!^2)*2^6) = C(64,32)/((8!)^2*2)

which is on the order of 10^44. Assuming that we encode the optimal

"next move" as 11 bits (5 bits to identify which piece is to be moved,

and 6 bits to indicate the space to which it is to be moved), then we

are at about order 10^45 bits of information.

Big? For back of the envelope estimation, at 10^23 atoms per 12 grams

of carbon, and assuming we can encode 1 bit per atom, we'd need around

10^20 kg of carbon to encode this information. Given that the earth's

mass is around 10^24 kg and has a radius of around 6000km, that gives

me a comparable-density sphere of solid carbon (very roughly) 200 km in

radius. Not exactly your table-top version of the game.

Reminds me of a short joke about the first "perfect" computer chess

machine; the first game it plays as black; white moves pawn to Q4,

computer calculates furiously, then responds "Black resigns". :-)

Cheers - Chas

<snip>

Anonymous

May 29, 2005 9:43:54 PM

cbrown@cbrownsystems.com wrote:

> [...]

> We can at least put the following very rough upper bound

> on this problem:

>

> There are 32 pieces; 64 squares; so if all pieces are on

> the board, and we uniquely identify each piece, there are

> C(64,32) possible board positions. Then, since the 8 pawns

> for each side are indistingusihable, and the pairs of

> bishops, knights, and rooks are indistinguishable, we can

> divide out these possibilities to get

>

> C(64,32)/((8!^2)*2^6)

>

> for the number of distinct board positions where all 32

> pieces are on the board. Of course, this includes many

> illegal board configurations; both bishops can be on the

> same color for example; but this is just the rough upper

> bound.

No it isn't; you're off by 32!.

When you're choosing the squares for the pieces, you're choosing

squares for the black king and white king (for instance). The order in

which you choose these squares IS important, because choosing them the

other way around results in a different position. The rest of your

analysis is right, so you get an answer of

P(64,32)/((8!^2)*2^6).

> If we assume that each successive calculation for 31 pieces,

> 30 pieces, etc. is roughly the same order of magnitude, then

> an upper bound would be

>

> 32*C(64,32)/((8!^2)*2^6) = C(64,32)/((8!)^2*2)

Once the above mistake is fixed, this becomes

P(64,32)/((8!)^2*2^2).

> which is on the order of 10^44.

10^79.

> Assuming that we encode the optimal "next move" as 11 bits

> (5 bits to identify which piece is to be moved, and 6 bits

> to indicate the space to which it is to be moved), then we

> are at about order 10^45 bits of information.

10^80

> Big? For back of the envelope estimation, at 10^23 atoms

> per 12 grams of carbon, and assuming we can encode 1 bit

> per atom, we'd need around 10^20 kg of carbon

10^55 kg of carbon

> to encode this information. Given that the earth's mass

> is around 10^24 kg and has a radius of around 6000km,

> that gives me a comparable-density sphere of solid carbon

> (very roughly) 200 km in radius.

6 * 10^14 km (600 trillion km).

> Not exactly your table-top version of the game.

Re-doing the calculation and reflecting on THAT answer reminds me of a

saying: "Theoretical comptuer scientists never work with anything that

can fit on one planet."

> Reminds me of a short joke about the first "perfect"

> computer chess machine; the first game it plays as

> black; white moves pawn to Q4, computer calculates

> furiously, then responds "Black resigns". :-)

"Oh poo, you win AGAIN!" -- Fatbot, "Mars University", Futurama.

(Actually, the other robot announces "Mate in 143 moves" right before

this.)

--- Christopher Heckman

Anonymous

May 29, 2005 9:57:16 PM

Proginoskes wrote:

> cbrown@cbrownsystems.com wrote:

> > [...]

> > We can at least put the following very rough upper bound

> > on this problem:

> >

> > There are 32 pieces; 64 squares; so if all pieces are on

> > the board, and we uniquely identify each piece, there are

> > C(64,32) possible board positions. Then, since the 8 pawns

> > for each side are indistingusihable, and the pairs of

> > bishops, knights, and rooks are indistinguishable, we can

> > divide out these possibilities to get

> >

> > C(64,32)/((8!^2)*2^6)

> >

> > for the number of distinct board positions where all 32

> > pieces are on the board. Of course, this includes many

> > illegal board configurations; both bishops can be on the

> > same color for example; but this is just the rough upper

> > bound.

>

> No it isn't; you're off by 32!.

>

> When you're choosing the squares for the pieces, you're

> choosing squares for the black king and white king (for

> instance). The order in which you choose these squares

> IS important, because choosing them the other way around

> results in a different position. The rest of your analysis

> is right, so you get an answer of

>

> P(64,32)/((8!^2)*2^6).

>

> > If we assume that each successive calculation for 31 pieces,

> > 30 pieces, etc. is roughly the same order of magnitude, then

> > an upper bound would be

> >

> > 32*C(64,32)/((8!^2)*2^6) = C(64,32)/((8!)^2*2)

>

> Once the above mistake is fixed, this becomes

> P(64,32)/((8!)^2*2^2).

>

> > which is on the order of 10^44.

>

> 10^79.

>

> > Assuming that we encode the optimal "next move" as 11 bits

> > (5 bits to identify which piece is to be moved, and 6 bits

> > to indicate the space to which it is to be moved), then we

> > are at about order 10^45 bits of information.

>

> 10^80

>

> > Big? For back of the envelope estimation, at 10^23 atoms

> > per 12 grams of carbon, and assuming we can encode 1 bit

> > per atom, we'd need around 10^20 kg of carbon

>

> 10^55 kg of carbon

>

> > to encode this information. Given that the earth's mass

> > is around 10^24 kg and has a radius of around 6000km,

> > that gives me a comparable-density sphere of solid carbon

> > (very roughly) 200 km in radius.

>

> 6 * 10^14 km (600 trillion km).

Nonono. 1.292 * 10^14, a mere 129 trillion km.

> > Not exactly your table-top version of the game.

>

> Re-doing the calculation and reflecting on THAT answer

> reminds me of a saying: "Theoretical comptuer scientists

> never work with anything that can fit on one planet."

>

> > Reminds me of a short joke about the first "perfect"

> > computer chess machine; the first game it plays as

> > black; white moves pawn to Q4, computer calculates

> > furiously, then responds "Black resigns". :-)

>

> "Oh poo, you win AGAIN!" -- Fatbot, "Mars University",

> Futurama.

>

> (Actually, the other robot announces "Mate in 143 moves"

> right before this.)

>

> --- Christopher Heckman

cbrown

May 30, 2005 12:27:47 AM

Proginoskes wrote:

> cbrown@cbrownsystems.com wrote:

> > [...]

> > We can at least put the following very rough upper bound

> > on this problem:

> >

> > There are 32 pieces; 64 squares; so if all pieces are on

> > the board, and we uniquely identify each piece, there are

> > C(64,32) possible board positions. Then, since the 8 pawns

> > for each side are indistingusihable, and the pairs of

> > bishops, knights, and rooks are indistinguishable, we can

> > divide out these possibilities to get

> >

> > C(64,32)/((8!^2)*2^6)

> >

> > for the number of distinct board positions where all 32

> > pieces are on the board. Of course, this includes many

> > illegal board configurations; both bishops can be on the

> > same color for example; but this is just the rough upper

> > bound.

>

> No it isn't; you're off by 32!.

>

You're absolutely right; I noticed this while I was thinking about

Guy's comments... doh!

> When you're choosing the squares for the pieces, you're choosing

> squares for the black king and white king (for instance). The order in

> which you choose these squares IS important, because choosing them the

> other way around results in a different position. The rest of your

> analysis is right, so you get an answer of

>

> P(64,32)/((8!^2)*2^6).

>

> > If we assume that each successive calculation for 31 pieces,

> > 30 pieces, etc. is roughly the same order of magnitude, then

> > an upper bound would be

> >

> > 32*C(64,32)/((8!^2)*2^6) = C(64,32)/((8!)^2*2)

>

> Once the above mistake is fixed, this becomes

> P(64,32)/((8!)^2*2^2).

>

> > which is on the order of 10^44.

>

> 10^79.

>

Bah - you're quibbling about a mere 35 orders of magnitude? :-)

> > Assuming that we encode the optimal "next move" as 11 bits

> > (5 bits to identify which piece is to be moved, and 6 bits

> > to indicate the space to which it is to be moved), then we

> > are at about order 10^45 bits of information.

>

> 10^80

>

> > Big? For back of the envelope estimation, at 10^23 atoms

> > per 12 grams of carbon, and assuming we can encode 1 bit

> > per atom, we'd need around 10^20 kg of carbon

>

> 10^55 kg of carbon

>

> > to encode this information. Given that the earth's mass

> > is around 10^24 kg and has a radius of around 6000km,

> > that gives me a comparable-density sphere of solid carbon

> > (very roughly) 200 km in radius.

>

> 6 * 10^14 km (600 trillion km).

>

.... or about 120 light years for a clock signal to propagate across the

whole sphere? Those are going to be /long/ games, unless we switch to

something like neutronium...

> > Not exactly your table-top version of the game.

>

> Re-doing the calculation and reflecting on THAT answer reminds me of a

> saying: "Theoretical comptuer scientists never work with anything that

> can fit on one planet."

>

> > Reminds me of a short joke about the first "perfect"

> > computer chess machine; the first game it plays as

> > black; white moves pawn to Q4, computer calculates

> > furiously, then responds "Black resigns". :-)

>

> "Oh poo, you win AGAIN!" -- Fatbot, "Mars University", Futurama.

>

> (Actually, the other robot announces "Mate in 143 moves" right before

> this.)

>

> --- Christopher Heckman

Cheers - Chas

Anonymous

May 30, 2005 1:28:11 AM

Charles. Brown wrote:

> Reminds me of a short joke about the first

> "perfect" computer chess machine; the first

> game it plays as black; white moves pawn

> to Q4, computer calculates furiously, then

> responds "Black resigns". :-)

Right. With best play, there are only 2 possibilities.

Either white has a forced win or the game is a draw.

Anonymous

May 30, 2005 1:28:12 AM

On Sun, 29 May 2005 at 21:28 GMT, N. Silver wrote:

> Charles. Brown wrote:

>

>> Reminds me of a short joke about the first

>> "perfect" computer chess machine; the first

>> game it plays as black; white moves pawn

>> to Q4, computer calculates furiously, then

>> responds "Black resigns". :-)

>

> Right. With best play, there are only 2 possibilities.

> Either white has a forced win or the game is a draw.

A third possibility is that White is in zugzwang at the start of

the game.

--

Chris F.A. Johnson <http://cfaj.freeshell.org>

==================================================================

Shell Scripting Recipes: A Problem-Solution Approach, 2005, Apress

<http://www.torfree.net/~chris/books/cfaj/ssr.html>

Anonymous

May 30, 2005 2:05:02 AM

cbrown@cbrownsystems.com wrote:

>

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

>

>> 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.

>

>We can at least put the following very rough upper bound on this

>problem:

>

>There are 32 pieces; 64 squares; so if all pieces are on the

>board, and we uniquely identify each piece, there are C(64,32)

>possible board positions. Then, since the 8 pawns for each side

>are indistinguishable, >and the pairs of bishops, knights, and

>rooks are indistinguishable, we can divide out these possibilities

>to get

>

>C(64,32)/((8!^2)*2^6)

>

>for the number of distinct board positions where all 32 pieces

>are on the board. Of course, this includes many illegal board

>configurations; both bishops can be on the same color for example;

>but this is just the rough upper bound.

>

>If we assume that each successive calculation for 31 pieces,

>30 pieces, etc. is roughly the same order of magnitude, then

>an upper bound would be

>

>32*C(64,32)/((8!^2)*2^6) = C(64,32)/((8!)^2*2)

>

>which is on the order of 10^44. Assuming that we encode the optimal

>"next move" as 11 bits (5 bits to identify which piece is to be moved,

>and 6 bits to indicate the space to which it is to be moved), then we

>are at about order 10^45 bits of information.

>

>Big? For back of the envelope estimation, at 10^23 atoms per 12 grams

>of carbon, and assuming we can encode 1 bit per atom, we'd need around

>10^20 kg of carbon to encode this information. Given that the earth's

>mass is around 10^24 kg and has a radius of around 6000km, that gives

>me a comparable-density sphere of solid carbon (very roughly) 200 km in

>radius. Not exactly your table-top version of the game.

The tabletop version is made of neutronium. The handheld is a

black hole. <grin>

>Reminds me of a short joke about the first "perfect" computer chess

>machine; the first game it plays as black; white moves pawn to Q4,

>computer calculates furiously, then responds "Black resigns". :-)

I don't think that the 8 pawns for each side are indistinguishable.

They could move to the last rank and promote to different pieces,

so you might have, say, 7 queens or 8 bishops on each side.

I think you also have to store not only the position, but whether

white/black can still castle (2 bits), how many plies into the 50

move rule you are (7 bits), whether each pawn has en passant ability

(8 bits).

So unless I am mistaken, the upper bound is somewhat higher.

It's an interesting math puzzle, isn't it?

I am trying to decide whether you have to store info about past

positions so as to avoid blundering into a repetition of position

draw while winning or to seek a repetition of position draw while

losing. Does the nature of following a list of perfect moves for

each position mean that you never end up in the same position twice?

I think it does. Then again, storing all past positions that have

actually been reached in the current game wouldn't take much space.

Or do you have to store all past positions for every position in

the tablebase? That would take a lot of space.

--

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

Anonymous

May 30, 2005 2:38:56 AM

N. Silver wrote:

>Charles. Brown wrote:

>

>> Reminds me of a short joke about the first

>> "perfect" computer chess machine; the first

>> game it plays as black; white moves pawn

>> to Q4, computer calculates furiously, then

>> responds "Black resigns". :-)

>

>Right. With best play, there are only 2 possibilities.

>Either white has a forced win or the game is a draw.

I believe that you are incorrect. There are various games that

have the attribute that if the second to play has a forced win

then the first to play can get into that forced win position

first, but Chess is not one of those games. It could be a win

for black. Not likely, but certainly possible.

None

May 30, 2005 2:38:57 AM

Guy Macon wrote:

> N. Silver wrote:

>

>

>>Charles. Brown wrote:

>>

>>

>>>Reminds me of a short joke about the first

>>>"perfect" computer chess machine; the first

>>>game it plays as black; white moves pawn

>>>to Q4, computer calculates furiously, then

>>>responds "Black resigns". :-)

>>

>>Right. With best play, there are only 2 possibilities.

>>Either white has a forced win or the game is a draw.

>

>

> I believe that you are incorrect. There are various games that

> have the attribute that if the second to play has a forced win

> then the first to play can get into that forced win position

> first, but Chess is not one of those games. It could be a win

> for black. Not likely, but certainly possible.

>

>

Ernst Zermelo, a German mathematician, wrote a paper on chess in 1913

that is regarded as the first published contribution to game theory.

Zermeloâ€™s theorem is stated below.

A corollary exists that states for chess one of three possible outcomes

are possible:

1. White has a strategy which always wins.

2. White has a strategy that always draws, but not necessarily a winning

strategy as in 1.

3. Black has a strategy that always wins.

Basically this amounts to the statement that zero sum games with perfect

information have optimal strategies.

Mondo

Anonymous

May 30, 2005 2:50:30 AM

Guy Macon wrote:

>> Right. With best play, there are only 2 possibilities.

>> Either white has a forced win or the game is a draw.

>

> I believe that you are incorrect. There are various games that

> have the attribute that if the second to play has a forced win

> then the first to play can get into that forced win position

> first, but Chess is not one of those games. It could be a win

> for black. Not likely, but certainly possible.

If black has a forced win, white's first move can be one of

the four knight moves that allow white to mimic black's

winning sequence.

Anonymous

May 30, 2005 2:55:04 AM

Guy Macon wrote:

>> Right. With best play, there are only 2 possibilities.

>> Either white has a forced win or the game is a draw.

>

> I believe that you are incorrect. There are various games that

> have the attribute that if the second to play has a forced win

> then the first to play can get into that forced win position

> first, but Chess is not one of those games. It could be a win

> for black. Not likely, but certainly possible.

If black has a forced win, white's first move can be one of

the four knight moves or one of the 16 pawn moves that allow

white to mirror black's winning sequence.

cbrown

May 30, 2005 6:35:47 AM

Guy Macon wrote:

> cbrown@cbrownsystems.com wrote:

> >

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

> >

> >> 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.

> >

> >We can at least put the following very rough upper bound on this

> >problem:

> >

> >There are 32 pieces; 64 squares; so if all pieces are on the

> >board, and we uniquely identify each piece, there are C(64,32)

> >possible board positions. Then, since the 8 pawns for each side

> >are indistinguishable, >and the pairs of bishops, knights, and

> >rooks are indistinguishable, we can divide out these possibilities

> >to get

> >

> >C(64,32)/((8!^2)*2^6)

> >

> >for the number of distinct board positions where all 32 pieces

> >are on the board. Of course, this includes many illegal board

> >configurations; both bishops can be on the same color for example;

> >but this is just the rough upper bound.

> >

> >If we assume that each successive calculation for 31 pieces,

> >30 pieces, etc. is roughly the same order of magnitude, then

> >an upper bound would be

> >

> >32*C(64,32)/((8!^2)*2^6) = C(64,32)/((8!)^2*2)

> >

> >which is on the order of 10^44. Assuming that we encode the optimal

> >"next move" as 11 bits (5 bits to identify which piece is to be moved,

> >and 6 bits to indicate the space to which it is to be moved), then we

> >are at about order 10^45 bits of information.

> >

> >Big? For back of the envelope estimation, at 10^23 atoms per 12 grams

> >of carbon, and assuming we can encode 1 bit per atom, we'd need around

> >10^20 kg of carbon to encode this information. Given that the earth's

> >mass is around 10^24 kg and has a radius of around 6000km, that gives

> >me a comparable-density sphere of solid carbon (very roughly) 200 km in

> >radius. Not exactly your table-top version of the game.

>

> The tabletop version is made of neutronium. The handheld is a

> black hole. <grin>

>

Before I address some of your complications below, here's a much better

estimate, at least for the case of "32 pieces on the board".

Since all pieces are on the board, no captures have occured; in

particular, no pawn has performed a capture. Therefore, all pawns are

on their original columns.

In that case, each pair of opposing pawns cannot pass each other; and

for each of the 8 pairs of pawns, there are 5+4+3+2+1= 15 possible

relative positions.

If we assume that the remianing 16 pieces are then ditributed amongst

the unoccupied 48 spaces, and again dividing for pairs of rooks,

knights, and bishops, we get (using C. Heckman's notation):

(15^8)*P(48,16)/2^6

which is "only" about 10^35 positions. So by the above logic, with

roughly 10 bits per entry, we get a sphere of solid carbon only a mere

/20 meters/ in radius - of course, this only counts the first "layer"

of moves, before any captures. Now /that/ you can hide in your pocket -

assuming you have really, really droopy pants.

On the other hand, if say, the eight white pawns have managed to get

promoted without any loss of black pawns (I think this is at least

possible), then for each possible legal combinations of R's,B's, N's

and Q's, to have something like

6^8*P(48, 24)/(something not particularly huge)

which would total on the order of 10^37 - 10^40

which would take a sphere 1500 km in radius.

I'll hold off on the full analysis of all piece allocations for now;

but a 1500 km sphere is a lot more feasible than a solid sphere 120

lights across!

> >Reminds me of a short joke about the first "perfect" computer chess

> >machine; the first game it plays as black; white moves pawn to Q4,

> >computer calculates furiously, then responds "Black resigns". :-)

>

> I don't think that the 8 pawns for each side are indistinguishable.

> They could move to the last rank and promote to different pieces,

> so you might have, say, 7 queens or 8 bishops on each side.

>

That's only possible if pieces have been taken (because the opposing

pawns must "doesy-doe" in some fashion).

If all pawns have been promoted then we have at most 24 pieces on the

board.

> I think you also have to store not only the position, but whether

> white/black can still castle (2 bits), how many plies into the 50

> move rule you are (7 bits), whether each pawn has en passant ability

> (8 bits).

>

That only triples the amount of information we need to store - right

now, I think we're still in the land of "pi is approximately 1". :-)

> So unless I am mistaken, the upper bound is somewhat higher.

> It's an interesting math puzzle, isn't it?

>

> I am trying to decide whether you have to store info about past

> positions so as to avoid blundering into a repetition of position

> draw while winning or to seek a repetition of position draw while

> losing.

My first thought is to wonder why it wouldn't be sufficient to have a

single bit - set if this is the fiftieth move with no captures, clear

otherwise.

> Does the nature of following a list of perfect moves for

> each position mean that you never end up in the same position twice?

> I think it does. Then again, storing all past positions that have

> actually been reached in the current game wouldn't take much space.

> Or do you have to store all past positions for every position in

> the tablebase? That would take a lot of space.

>

I you are right that the longest game is under 10000 moves, then at

this level of estimation, it's not that much space.

Cheers - Chas

>

> --

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

- 1 / 2
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