Maximum possible game is 6750 moves, ending on a draw by 50 move rule, by my calculations:
49 moves then a pawn push and so on until all pawns have promoted, but the pawns can only get past each other if every other pawn captures, so essentially half the pawns get 7 moves and half of them get 6 moves.
(49+1)*(7+6)*8 = 5200
All the promoted pawns getting captured allows for further moves; 49 moves then a capture:
(49+1)*16 = 800
All the other pieces getting captured:
(49+1)*14 = 700
then 50 moves after last capture:
5200+800+700+50 = 6750.
Or possibly maximum game is 6700 if you consider any game with only two kings left to be drawn by lack of material.
Originally posted by doodinthemoodPerhaps even more interesting is the number of different chess positions. No one has ever solved this problem.
Maximum possible game is 6750 moves, ending on a draw by 50 move rule, by my calculations:
49 moves then a pawn push and so on until all pawns have promoted, but the pawns can only get past each other if every other pawn captures, so essentially half the pawns get 7 moves and half of them get 6 moves.
(49+1)*(7+6)*8 = 5200
All the promoted pawns ...[text shortened]... game is 6700 if you consider any game with only two kings left to be drawn by lack of material.
I read somewhere the accepted number is about 10^43 positions for the first 40 moves.
Originally posted by doodinthemoodWow... my maths is awful so i have no clue if this is correct but it looks good :o
Maximum possible game is 6750 moves, ending on a draw by 50 move rule, by my calculations:
49 moves then a pawn push and so on until all pawns have promoted, but the pawns can only get past each other if every other pawn captures, so essentially half the pawns get 7 moves and half of them get 6 moves.
(49+1)*(7+6)*8 = 5200
All the promoted pawns ...[text shortened]... game is 6700 if you consider any game with only two kings left to be drawn by lack of material.
Originally posted by PedroMSurely the number of different chess positions isn't so hard to calculate that no one has ever done it?
Perhaps even more interesting is the number of different chess positions. No one has ever solved this problem.
I read somewhere the accepted number is about 10^43 positions for the first 40 moves.
An upper bound is easily found by calculating all the different ways that 32 peices can sit on 64 squares (discounting the repititions from having 2 rooks, 2 bishops etc...)
After that the problem is eliminating positions that are not 'chess' positions--ie. one of the kings is in check, or there are pawns on the first rank.
Someone with a basic background in IP (integer programming--a branch of mathematical optimisation) should be able to write a (reasonably) simple code to remove these obvious false positions.
Then we are left with trying to remove other, but not so obvious, illegal positions, such as all pieces being in their starting positions, apart from a white rook on a4, or a position that can only be achieved by some series of illegal moves.
But surely someone has found a way to deal with these problems?
Originally posted by doodinthemoodwouldn't you run into trouble with the three move repitition rule?
Maximum possible game is 6750 moves, ending on a draw by 50 move rule, by my calculations:
49 moves then a pawn push and so on until all pawns have promoted, but the pawns can only get past each other if every other pawn captures, so essentially half the pawns get 7 moves and half of them get 6 moves.
(49+1)*(7+6)*8 = 5200
All the promoted pawns ...[text shortened]... game is 6700 if you consider any game with only two kings left to be drawn by lack of material.
Originally posted by doodinthemood5,899 moves.
Maximum possible game is 6750 moves, ending on a draw by 50 move rule, by my calculations:
49 moves then a pawn push and so on until all pawns have promoted, but the pawns can only get past each other if every other pawn captures, so essentially half the pawns get 7 moves and half of them get 6 moves.
(49+1)*(7+6)*8 = 5200
All the promoted pawns ...[text shortened]... game is 6700 if you consider any game with only two kings left to be drawn by lack of material.
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Originally posted by droflaceIt has been solved, but your method is flawed (if you don't mind me saying - not being confrontational !! 🙂 ).
Surely the number of different chess positions isn't so hard to calculate that no one has ever done it?
An upper bound is easily found by calculating all the different ways that 32 peices can sit on 64 squares (discounting the repititions from having 2 rooks, 2 bishops etc...)
After that the problem is eliminating positions that are not 'chess' positi ...[text shortened]... e series of illegal moves.
But surely someone has found a way to deal with these problems?
Simply calculating the number of different positions that 32 pieces can sit on 64 squares would only count a drop in the ocean of the number of variations possible. For a computer to calculate this, the number of specific 'end positions' is vastly outweighed by the number of move-orders that could create such a position.
A computer can assess the first move by one of 16 pawn moves, and 4 knight moves (20 possible first moves for white). This can be countered by one of 20 possible replies for white (20x20 = 400 possibilities). Now imagine every sequence of positions in 40 moves!
In a 40 move games, there are 1x10 to the power 115 (can't write that with my keyboard, but it's 1 followed by 115 zeros) possible legal variations that could occur. This does not include illegal moves, but critically it includes positions that repeat themselves (knight moving forwards and backwards and forwards....). One single board position reached after 20 moves could have occured via many millions of sequences - each a unique move order by white then black. This may only count as one chess position in your calculation - a fraction of the total complexity of moves a computer would have to calculate to reach it.
Indeed it would have taken Deeper Blue longer than the age of the Universe to calcuate them all, at 200 million calculations per second. 🙂
Originally posted by PolicestateMy friend Policestate,
It has been solved, but your method is flawed (if you don't mind me saying - not being confrontational !! 🙂 ).
Simply calculating the number of different positions that 32 pieces can sit on 64 squares would only count a drop in the ocean of the number of variations possible. For a computer to calculate this, the number of specific 'end positions' is va ...[text shortened]... an the age of the Universe to calcuate them all, at 200 million calculations per second. 🙂
Not being confrontational 🙂, I believe you are mixing up 2 different concepts. 10^115 or 10^120 is the game tree complexity, which is not the same as the number of chess positions (10^43). See details here:
http://en.wikipedia.org/wiki/Shannon_number
It takes a little while to understand the difference, but I guess the conclusion is that you can have variations for different moves that actually end up in the same position. A computer would have to calculate all those 10^120 variations to solve the game of chess, but many of the positions found could have been reached via several different moves or move orders. As you said "One single board position reached after 20 moves could have occured via many millions of sequences - each a unique move order by white then black"
Therefore the number of positions is much less than the number of possible variations. Don't know if this makes sense to you, but this is the way I understand it 😀
>The maximum number of moves in a game is unlimited because the 50-move draw rule and the 3-fold repetition rule must be claimed, If no claim is made, the game can go on forever.
"As I said in an earler post, it is possible on RHP to earn the 100,000-move spinning star in just one game where both players just repeat their moves until 100,000 moves have been made. Idiots they would be, but it is possible.
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Originally posted by AttilaTheHornI have seen games here go on for 100's of moves after it was reduced to king vs king. Seems kinda pointless to me.
>The maximum number of moves in a game is unlimited because the 50-move draw rule and the 3-fold repetition rule must be claimed, If no claim is made, the game can go on forever.
"As I said in an earler post, it is possible on RHP to earn the 100,000-move spinning star in just one game where both players just repeat their moves until 100,000 moves have been made. Idiots they would be, but it is possible.
Edit: Maybe not so pointless. There is a chance that one player will eventually run out of time.