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