How many different chess positions are there?
If I gave you the exact number, would you believe me?
How many different chess positions are there?
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Aug 6, 2012
0
#123
There is a greater variety of pizzas than there are chess positions. (I have discovered a wonderful proof for this, but the margin is not big enough for me to write it.)
Ok Nudistneill here is the story---
The validity of the myth is unknown. However, it is known that a game similar to chess was found in Persia called Chaturunga or Chatreng. The game consists of a chessboard with 64 squares (8x8) identical to todays´s chess board.
The origin of chess is a controversial topic and can not be accurately placed, even though a great majority favors India. The oldest documented records of chess have been found in Persia (Iran) India, and China.
There have been some "Albion fanatics" that say the game was invened in the Court of King Arthur. And, because Islam introduced the game to Europe, others say the game was invented by the Arabs. (That is why many associate chess men with "cavalliers" and cruzaders.)
Well, anyhow, this is the real mathematical fact about it. . .
A long time ago the Indian Rajah Balhait asked Sissa, the Brahman of the court to create a game that should demonstrate the values of such qualities as prudence, diligence, foresight and knowledge, and in this way oppose the fatalist teaching of "nard" (today backgammon) in which chance (dice) decided the oucome.
Sissa brought an eight by eight squares board with men similar to those used today in chess---foot soldiers, chariots, elephants, horses led by the king and his vizier (In those days the Indus used protective boxes mounted on elephants to carry archmen = today in the game, rooks)
The Rajah was so impressed and delighted with the game that said to Sissa "Ask any reward you desired. . . it will be yours"
Sissa said:
"Give me a reward in grains of rice upon the chessboard. On the first square a grain, on the second two, on the third four, on the fourth square double of that, and so on. . ."
So the King ordered it to be done. But before they reached the thirtieth square they ran out of rice. . .
That is a secuence
1, 2, 4, 8, 16, 32, 64, 128. . .
The sum total would be: ( 2 to the 64th power, less less one unit)
Or in plain English
18,446,744,073,709,551,615 grains.. .
which somebody (who?) said would cover the Earth up to 9 inches....
It is really easy to calculate an upper bound.
there are 6 different pieces (king, queen, rook, knight, bishop, pawn)
2 different colors of each. so 12 pieces (then add the empty space) so 13.
Now if we pretend that we could have a bord where all 64 squares could be anything (a board full of 64 black kings, or 20 black king with 44 white pawns, or 22 black bishops with 22 white bishops and 20 empty spaces... etc)
In other words, every one of the 13 objects could be repeated on any of the 64 spaces
it would just be: 13^64
wich gives 1.96053476e+71 positions.
Obviously it would be less then that, since you can only have 2 kings... there will always be 32+ spaces that are empty... etc. This just gives us an upper bound.
So i don't know how someone could say "there are 10^120 positions"... well... this is only considering 2 identical positions that were reached by different paths as 'the same'... if you count them as 'different', then you could easily.
Songofdeath wrote:
It is really easy to calculate an upper bound.
there are 6 different pieces (king, queen, rook, knight, bishop, pawn)
2 different colors of each. so 12 pieces (then add the empty space) so 13.
Now if we pretend that we could have a bord where all 64 squares could be anything (a board full of 64 black kings, or 20 black king with 44 white pawns, or 22 black bishops with 22 white bishops and 20 empty spaces... etc)
In other words, every one of the 13 objects could be repeated on any of the 64 spaces
it would just be: 13^64
wich gives 1.96053476e+71 positions.
Obviously it would be less then that, since you can only have 2 kings... there will always be 32+ spaces that are empty... etc. This just gives us an upper bound.
So i don't know how someone could say "there are 10^120 positions"... well... this is only considering 2 identical positions that were reached by different paths as 'the same'... if you count them as 'different', then you could easily.
Actually, it would be 64^13, think
Oct 19, 2012
0
#129
At least 9,000
I am about to start an acadimic research about chess and I need this kind of information. If you find an answer for it please let me know ... ..
limitless chess positions - because there are sometimes move 10 the same move 20 or will go back to its original positions. move 10 and 20 the same positions but it can count 2 positions so, it is more than the atoms of the universe...
nobody can answer this including super computer this is the mistery of chess!
Well, it's a mystery of chess anyway.
unforyuneatly it is vertually impossible to tell
If the answer is called Np, it can be proved (mathematically / algorithmically) that
Np < 2^113
which is roughly 1.04 x 10^34.
The demonstration (in french, by me) is in this article http://m3m.homelinux.org/wikiPG/index.php/Nombre_de_positions_légales_au_jeu_d'échecs
The demonstration is based on the Huffman coding approach.
If anyone wants to comment or criticise the demonstration mentionned in the previous message, feel free to contact pg@matscape.com ...
gonzepge wrote:
If the answer is called Np, it can be proved (mathematically / algorithmically) that
Np < 2^113
which is roughly 1.04 x 10^34.
The demonstration (in french, by me) is in this article http://m3m.homelinux.org/wikiPG/index.php/Nombre_de_positions_légales_au_jeu_d'échecs
The demonstration is based on the Huffman coding approach.
I don't need to know french to know that calculation is flawed.
Both sides have 8 queens, one king, and one more piece. Your representation gives >113 bits.
As far as I remember, I got the smallest board representation to around 160 bits.
In the total volume of oceans there are 4.45*10^46 water molecules:
Given the estimates presented in this thread it should be possible to store a complete tablebase of chess including all legal positions on 4.45*10^46 bits ( this is an other way of saying that the complete solution of chess can be stored on that many bits ). So if we were somehow able to store 1 bit of information in 1 water molecule than we would need to use all the water molecules in the total volume of oceans on Earth to store all legal chess positions.
id like to hear this explanation, because the do you mean the invention of the original chess game or the chess game that exists today?