Guy Macon's Longest Possible Game Of Chess Calculation

Main

Date: 18 Oct 2006 09:02:08
From: Guy Macon
Subject: Guy Macon's Longest Possible Game Of Chess Calculation

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

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

Here is my calculation for the longest possible chess game
before one of the players can claim a draw[1] under FIDE[2]
rules. Corrections, comments welcome.

To calculate the longest possible chess game before one of the
players can claim a draw under FIDE rules:

Start with 32 chess pieces.

Move 100 plies[3], 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 98 plies long so that black can
start taking his turn moving pawns and making captures.

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

(Note to the non-chessplayer: a "ply" is a black piece changing
position or a white piece changing position. Chessplayers call
ten black piece moving and ten white pieces moving "ten
moves"/"twenty plies." Non-chess-players often call the same
sequence "twenty moves.")

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

Here is one way of reaching the maximum number of moves
calculated above in an actual chess game. Assume that
each ply described has 99 (or in one case 98) "wasted"
plies between the plies/moves described.

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 black's queen and bishops, leaving 8 pawns,
2 knights, 2 rooks, and 1 King.

The white pawns on A,C,E,G capture the knights rooks,
passing and freeing the black pawns that were 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 98 ply sequence...)
The black king captures something and continues to capture 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
exactly (and no more than) 11799 plies.

Comments/corrections are welcome.

Guy Macon
www.guymacon.com

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

NOTES:

[1] If nobody claims a draw the players can continue to push
pieces back and forth forever and the game is infinitely long -
and boring to calculate. See
<http://www.fide.com/official/handbook.asp?level=EE101 >

[2] I was unable to repeat this calculation under USCF rules
because the USCG rules contain ambiguities.

[3] This is the limit under current FIDE rules. See
<http://www.fide.com/official/handbook.asp?level=EE1 >

In the versions of 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

BTW, The Archives of _An Arbiter's Notebook_ are really quite
interesting. You can find them here:

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

--
Guy Macon

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

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

Date: 20 Oct 2006 15:44:21
From: Deedlit
Subject: Re: Guy Macon's Longest Possible Game Of Chess Calculation

Kenneth Sloan wrote:
> Deedlit wrote:
> > On ply 11,683, white can capture and end the game, or he can claim a
> > draw. I'm assuming that in both cases, the length of the game will be
> > considered 11,683 plies.
> >
>
> That can't be right. One of these two choices must be 1 ply
> longer than the other...
>

For the draw, you call the referee over, announce your attention to
make a (noncapturing) move, and claim a draw by the 50-move rule. I
assumed that the scoresheet would include the required last move.

>
>
> --
> Kenneth Sloan [email protected]
> Computer and Information Sciences +1-205-932-2213
> University of Alabama at Birmingham FAX +1-205-934-5473
> Birmingham, AL 35294-1170 http://www.cis.uab.edu/sloan/

Date: 19 Oct 2006 06:54:57
From: Deedlit
Subject: Re: Guy Macon's Longest Possible Game Of Chess Calculation

On ply 11,683, white can capture and end the game, or he can claim a
draw. I'm assuming that in both cases, the length of the game will be
considered 11,683 plies.

Guy Macon wrote:
> Deedlit wrote:
> >
> >Well, the draw is claimed on ply 118 * 99 + 1.
>
> Would that be the point where there are only two kings?
> If so, the game is drawn whether claimed or not. It's the
> 50-move-rule draw that must be claimed.
>
> --
> Guy Macon <http://www.guymacon.com/>

Date: 19 Oct 2006 15:29:41
From: Kenneth Sloan
Subject: Re: Guy Macon's Longest Possible Game Of Chess Calculation

Deedlit wrote:
> On ply 11,683, white can capture and end the game, or he can claim a
> draw. I'm assuming that in both cases, the length of the game will be
> considered 11,683 plies.
>

That can't be right. One of these two choices must be 1 ply
longer than the other...

--
Kenneth Sloan [email protected]
Computer and Information Sciences +1-205-932-2213
University of Alabama at Birmingham FAX +1-205-934-5473
Birmingham, AL 35294-1170 http://www.cis.uab.edu/sloan/

Date: 19 Oct 2006 12:10:26
From: Guy Macon
Subject: Re: Guy Macon's Longest Possible Game Of Chess Calculation

Deedlit wrote:
>
>Well, the draw is claimed on ply 118 * 99 + 1.

Would that be the point where there are only two kings?
If so, the game is drawn whether claimed or not. It's the
50-move-rule draw that must be claimed.

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

Date: 18 Oct 2006 23:02:18
From: Proginoskes
Subject: Re: Guy Macon's Longest Possible Game Of Chess Calculation

[email protected] wrote:
> PendulousAppendages wrote:
>
> >Nice ! WOuld anyone be up for writing a client for one of the free
> >chess servers? Can it be rigged pass the scrutiny of the 'program
> >spotter' and still kik arrs?
>
> What does your question have to do with calculating the longest
> possible game of chess?

Evidently you don't speak Australian Geek.

--- Christopher Heckman

Date: 18 Oct 2006 22:26:33
From: Deedlit
Subject: Re: Guy Macon's Longest Possible Game Of Chess Calculation

Well, the draw is claimed on ply 118 * 99 + 1.

Date: 18 Oct 2006 22:12:47
From: Deedlit
Subject: Re: Guy Macon's Longest Possible Game Of Chess Calculation

I see... my calculation is based on the longest game in which no one
can declare a draw, while sticking to a listed sequence of moves. In
this case, there have to be at least 3 changes of who's pushing
pawns/capturing, resulting in 11,800 - 3 plies. (Note that the last
interval doesn't have to be 98 plies, so there's no need to subtract
one like you did in your example.)

Under your interpretation, 118 * 99 looks correct.

Date: 18 Oct 2006 14:48:05
From: Deedlit
Subject: Re: Guy Macon's Longest Possible Game Of Chess Calculation

11799 is not possible. Hint: after each of the 99-ply intervals,
whose move is it?

The maximum is actually 11797. (It's actually a bit tricky to
accomplish this.)

Date: 19 Oct 2006 03:13:59
From: Guy Macon
Subject: Re: Guy Macon's Longest Possible Game Of Chess Calculation

Deedlit wrote:

>11799 is not possible. Hint: after each of the 99-ply intervals,
>whose move is it?

Interesting! Let's look at it one ply at a time.

First, the rules:

Article 5: The completion of the game

5.1 The game may be drawn if each player has made at least the last
50 consecutive moves without the movement of any pawn and without
any capture. (See Article 9.3)

Article 9: The drawn game

9.3 The game is drawn, upon a correct claim by the player
having the move, if

1. he writes his move on his scoresheet, and declares to
the arbiter his intention to make this move which shall
result in the last 50 moves having been made by each player
without the movement of any pawn and without any capture, or

2. the last 50 consecutive moves have been made by each
player without the movement of any pawn and without any
capture.

Now the ply-by-ply:

("Count" is the count of consecutive moves that player has
made without the movement of any pawn and without any capture)

Ply 1: White moves a pawn or makes a capture. Black/white count = 0
Ply 2: Black makes a non-pawn non-capture move. Black's count = 1
Ply 3: White makes a non-pawn non-capture move. White's count = 1
Ply 4: Black makes a non-pawn non-capture move. Black's count = 2
Ply 5: White makes a non-pawn non-capture move. White's count = 2
Ply 6: Black makes a non-pawn non-capture move. Black's count = 3
Ply 7: White makes a non-pawn non-capture move. White's count = 3

....

Ply 94: Black makes a non-pawn non-capture move. Black's count = 47
Ply 95: White makes a non-pawn non-capture move. White's count = 47
Ply 96: Black makes a non-pawn non-capture move. Black's count = 48
Ply 97: White makes a non-pawn non-capture move. White's count = 48
Ply 98: Black makes a non-pawn non-capture move. Black's count = 49
Ply 99: White makes a non-pawn non-capture move. White's count = 49

Can either player claim a draw at this point? No.

Now what would happen if black made a non-pawn, non-capture move.
Black's count would be 50, White's count would be 49, ply would be 100.

Can either player claim a draw at this point?

Black can't. The rules say "upon a correct claim by the
player having the move" and black doesn't have the move.

White *can*. The rules say that white can declare to
the arbiter his intention to make this move which shall
result in the last 50 moves having been made by each player
without the movement of any pawn and without any capture.

So, to avoid ether layer being able to claim a draw, black
must move a pawn or make a capture

So we get:

Ply 1: White moves a pawn or makes a capture. Black/white count = 0
Ply 2: Black makes a non-pawn non-capture move. Black's count = 1
Ply 3: White makes a non-pawn non-capture move. White's count = 1
Ply 4: Black makes a non-pawn non-capture move. Black's count = 2
Ply 5: White makes a non-pawn non-capture move. White's count = 2
Ply 6: Black makes a non-pawn non-capture move. Black's count = 3
Ply 7: White makes a non-pawn non-capture move. White's count = 3

....

Ply 94: Black makes a non-pawn non-capture move. Black's count = 47
Ply 95: White makes a non-pawn non-capture move. White's count = 47
Ply 96: Black makes a non-pawn non-capture move. Black's count = 48
Ply 97: White makes a non-pawn non-capture move. White's count = 48
Ply 98: Black makes a non-pawn non-capture move. Black's count = 49
Ply 99: White makes a non-pawn non-capture move. White's count = 49
New ply 1: Black moves a pawn or makes a capture. Black/white count = 0

So it looks like the formula is not, as I wrote,
((100*(30+96-8))-1) but is rather (99*(30+96-8))=11682.

>The maximum is actually 11797. (It's actually a bit tricky to
>accomplish this.)

Could you show me how you calculated this number?

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

Date: 18 Oct 2006 14:49:52
From: Kenneth Sloan
Subject: Re: Guy Macon's Longest Possible Game Of Chess Calculation

Could you please provide an Executive Sumy, detailing
how your computation differs from the last 100 postings
on this topic over the past 10 years? Do you get a different
answer? If so, why is your answer right, and their answer wrong?

You *did* read what has been done before, didn't you?

Guy Macon wrote:
>
> ---------------------------------------------------------
>
> LONGEST POSSIBLE CHESS GAME CALCULATION:
> By Guy Macon <http://www.guymacon.com/>
>
> Here is my calculation for the longest possible chess game
> before one of the players can claim a draw[1] under FIDE[2]
> rules. Corrections, comments welcome.
>
> To calculate the longest possible chess game before one of the
> players can claim a draw under FIDE rules:
>
> Start with 32 chess pieces.
>
> Move 100 plies[3], 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 98 plies long so that black can
> start taking his turn moving pawns and making captures.
>
> Assuming FIDE rules, that comes to a total of
> ((100*(30+96-8))-1)=11799 plies until the game is over.
>
> (Note to the non-chessplayer: a "ply" is a black piece changing
> position or a white piece changing position. Chessplayers call
> ten black piece moving and ten white pieces moving "ten
> moves"/"twenty plies." Non-chess-players often call the same
> sequence "twenty moves.")
>
> - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
>
> Here is one way of reaching the maximum number of moves
> calculated above in an actual chess game. Assume that
> each ply described has 99 (or in one case 98) "wasted"
> plies between the plies/moves described.
>
> 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 black's queen and bishops, leaving 8 pawns,
> 2 knights, 2 rooks, and 1 King.
>
> The white pawns on A,C,E,G capture the knights rooks,
> passing and freeing the black pawns that were 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 98 ply sequence...)
> The black king captures something and continues to capture 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
> exactly (and no more than) 11799 plies.
>
> Comments/corrections are welcome.
>
> Guy Macon
> www.guymacon.com
>
> - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
>
> NOTES:
>
> [1] If nobody claims a draw the players can continue to push
> pieces back and forth forever and the game is infinitely long -
> and boring to calculate. See
> <http://www.fide.com/official/handbook.asp?level=EE101>
>
> [2] I was unable to repeat this calculation under USCF rules
> because the USCG rules contain ambiguities.
>
> [3] This is the limit under current FIDE rules. See
> <http://www.fide.com/official/handbook.asp?level=EE1>
>
> In the versions of 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
>
> BTW, The Archives of _An Arbiter's Notebook_ are really quite
> interesting. You can find them here:
>
> <http://www.chesscafe.com/archives/archives.htm#An%20Arbiter's%20Notebook>
>
> --
> Guy Macon
>
> <http://www.guymacon.com/>
>
> ---------------------------------------------------------
>
>

--
Kenneth Sloan [email protected]
Computer and Information Sciences +1-205-932-2213
University of Alabama at Birmingham FAX +1-205-934-5473
Birmingham, AL 35294-1170 http://www.cis.uab.edu/sloan/

Date: 19 Oct 2006 03:20:15
From: Guy Macon
Subject: Re: Guy Macon's Longest Possible Game Of Chess Calculation

Kenneth Sloan wrote:

>Could you please provide an Executive Sumy, detailing
>how your computation differs from the last 100 postings
>on this topic over the past 10 years?

No. Do your own homework.

>Do you get a different answer?

I haven't seen anyone get it right, and my own calculation
may have errors, which is why I posted it for review and
corrections.

>If so, why is your answer right, and their answer wrong?

Individually comment on every other person who ever did
this calculation? No. Do your own homework.

If you name one persn who you believe got it right,
I will be happy to analyse that one calculation.

>You *did* read what has been done before, didn't you?

Yes. Did you?

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

Date: 18 Oct 2006 22:43:52
From: Kenneth Sloan
Subject: Re: Guy Macon's Longest Possible Game Of Chess Calculation

Date: 18 Oct 2006 22:42:23
From: Kenneth Sloan
Subject: Re: Guy Macon's Longest Possible Game Of Chess Calculation

Guy Macon wrote:
> Kenneth Sloan wrote:
>
>> Could you please provide an Executive Sumy, detailing
>> how your computation differs from the last 100 postings
>> on this topic over the past 10 years?
>
> No. Do your own homework.
>
>> Do you get a different answer?
>
> I haven't seen anyone get it right, and my own calculation
> may have errors, which is why I posted it for review and
> corrections.
>
>> If so, why is your answer right, and their answer wrong?
>
> Individually comment on every other person who ever did
> this calculation? No. Do your own homework.
>
> If you name one persn who you believe got it right,
> I will be happy to analyse that one calculation.
>
>> You *did* read what has been done before, didn't you?
>
> Yes. Did you?
>
Most of them - but I won't bother to read yours.

I stopped doing homework a long time ago. Now I assign
homework. And, I find it much more efficient to pay
attention to people making claims when they take the
trouble to put their work in context. In my experience,
those who *don't* put their own work in context are
highly likely to be lazy....and this particular topic
is not one where laziness pays off.

Some people like to stand on the shoulders of the giants
who have come before them....others prefer to step on
their toes.

--
Kenneth Sloan [email protected]
Computer and Information Sciences +1-205-932-2213
University of Alabama at Birmingham FAX +1-205-934-5473
Birmingham, AL 35294-1170 http://www.cis.uab.edu/sloan/

Date: 18 Oct 2006 03:32:51
From: PendulousAppendages
Subject: Re: Guy Macon's Longest Possible Game Of Chess Calculation

Nice ! WOuld anyone be up for writing a client for one of the free
chess servers? Can it be rigged pass the scrutiny of the 'program
spotter' and still kik arrs?
Guy Macon wrote:
> ---------------------------------------------------------
>
> LONGEST POSSIBLE CHESS GAME CALCULATION:
> By Guy Macon <http://www.guymacon.com/>
>
> Here is my calculation for the longest possible chess game
> before one of the players can claim a draw[1] under FIDE[2]
> rules. Corrections, comments welcome.
>
> To calculate the longest possible chess game before one of the
> players can claim a draw under FIDE rules:
>
> Start with 32 chess pieces.
>
> Move 100 plies[3], 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 98 plies long so that black can
> start taking his turn moving pawns and making captures.
>
> Assuming FIDE rules, that comes to a total of
> ((100*(30+96-8))-1)=11799 plies until the game is over.
>
> (Note to the non-chessplayer: a "ply" is a black piece changing
> position or a white piece changing position. Chessplayers call
> ten black piece moving and ten white pieces moving "ten
> moves"/"twenty plies." Non-chess-players often call the same
> sequence "twenty moves.")
>
> - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
>
> Here is one way of reaching the maximum number of moves
> calculated above in an actual chess game. Assume that
> each ply described has 99 (or in one case 98) "wasted"
> plies between the plies/moves described.
>
> 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 black's queen and bishops, leaving 8 pawns,
> 2 knights, 2 rooks, and 1 King.
>
> The white pawns on A,C,E,G capture the knights rooks,
> passing and freeing the black pawns that were 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 98 ply sequence...)
> The black king captures something and continues to capture 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
> exactly (and no more than) 11799 plies.
>
> Comments/corrections are welcome.
>
> Guy Macon
> www.guymacon.com
>
> - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
>
> NOTES:
>
> [1] If nobody claims a draw the players can continue to push
> pieces back and forth forever and the game is infinitely long -
> and boring to calculate. See
> <http://www.fide.com/official/handbook.asp?level=EE101>
>
> [2] I was unable to repeat this calculation under USCF rules
> because the USCG rules contain ambiguities.
>
> [3] This is the limit under current FIDE rules. See
> <http://www.fide.com/official/handbook.asp?level=EE1>
>
> In the versions of 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
>
> BTW, The Archives of _An Arbiter's Notebook_ are really quite
> interesting. You can find them here:
>
> <http://www.chesscafe.com/archives/archives.htm#An%20Arbiter's%20Notebook>
>
> --
> Guy Macon
>
> <http://www.guymacon.com/>
>
> ---------------------------------------------------------

Date: 18 Oct 2006 11:54:43
From:
Subject: Re: Guy Macon's Longest Possible Game Of Chess Calculation

PendulousAppendages wrote:

>Nice ! WOuld anyone be up for writing a client for one of the free
>chess servers? Can it be rigged pass the scrutiny of the 'program
>spotter' and still kik arrs?

What does your question have to do with calculating the longest
possible game of chess?