What about combination of moves? There could be 800 in just one combination of moves, but wouldn't there be different combinations, and thus different games? One game shows one combination, another game shows another. Wouldn't that raise it?
Chess Moves V Atoms
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Hmm, okay, just thought I would throw that out there just incase.
Um, Teamwillow is way off. Alxndr was right that there could be more than 800 in just one set of moves (one by black and one by white).
http://en.wikipedia.org/wiki/Shannon_number
If 8x8 = 50 as teamwillow proposes than anything is possible.
simpledimple wrote:
If 8x8 = 50 as teamwillow proposes than anything is possible.
LOL, true story.
They mean the observable universe. It's estimated to have about 10^80 atoms. Checkers has 500,000,000,000,000,000,000 possible moves. They think chess has at least 40 more zeros than checkers.
Teamwillow, I think your slightly! missing the point. On the first move there are 20 possibilities for white then 20 for black theres 400 possibilities after just two moves .....
This is how a computer looks at chess. It thinks about it in a world of "all possible moves," and it makes a big treefor all of those moves, like this:
 |
In this tree, there are 20 possible moves for white. There are 20 * 20 = 400 possible moves for black, depending on what white does. Then there are 400 * 20 = 8,000 for white. Then there are 8,000 * 20 = 160,000 for black, and so on. If you were to fully develop the entire tree for all possible chess moves, the total number of board positions is about 1,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000
But still finite, Right ?
Still finite, true. But if what woodshover is saying is true, the comparison is to the observable universe, which is also finite.
Teamwillow wrote:
ok here's an example:
There are approximately 10 million stars in the milky way galaxy.
There are approximately 50 squares on a chess board.
There are exactly 16 pieces of chess pieces.
50 squares x 16 pieces = 800 possible moves. Now, take the original number, 10 million, and compare it to our outcome, 800. Not quite the same is it? Therefore there are way moer atoms than chess moves.
You are incorrect. There is 64 squares and 32 pieces. If there are 3 pieces on the board there is 64 places the white king could go. That leaves 63 places the black king could go. 64*63 so far.
Now to add the first piece. There are 10 different pieces. So it is 64*63*62*10.
Now to account for pawn restrictions. There are 2 colors of pawns that can't go on 16 of the squares. I do not know if one has to take into account if the kings are on the 1st or 8th rank or how to do that.
That would 64*63*62*10-2*16 = 2499808 different positions with only 3 pieces. 2.5 million positions. With 4 pieces it is 64*63*62*10*61*10-2*16-2*16 = 1524902336. That is 1.5 billion. It goes up very fast.
moduspawnens wrote:
I,ve Heard mention on many occations that there are as many or more possible chess moves/positions as there are atoms in the universe. For the sake of this thread lets agree with the Standard Model postulate that the Universe is infinite, surley the amout of chess positions though enormous is finite and as such has to be less ?
The universe is infinite but there is a limited amount of stuff in it. If I has a 4 liter container with water in it, there does not have to be 4 liters of water in it for both things to be true. There could be just a little drop in the bottom.
Anchovey wrote:
Still finite, true. But if what woodshover is saying is true, the comparison is to the observable universe, which is also finite.
Mmm, Ok then It should be expressed as the observable, even so this figure is constantly changing with technology, the amount of chess moves do not.
Hi all,
Suppose any field on a chess board can, in principle, harbour any of 13 different pieces (white king, white pawn, black king and so on, including no piece), the total number of possible positions would be 13^64. In itself this is way less than the 10^80 atoms in the universe, and it includes boards with 64 kings, boards with no pieces at all, an awful lot of boards with more than 32 pieces on it and so on, reducing the real number of possible positions still.
Teamwillow wrote:
mrguy888 wrote:
Teamwillow wrote:
ok here's an example:
There are approximately 10 million stars in the milky way galaxy.
There are approximately 50 squares on a chess board.
There are exactly 16 pieces of chess pieces.
50 squares x 16 pieces = 800 possible moves. Now, take the original number, 10 million, and compare it to our outcome, 800. Not quite the same is it? Therefore there are way moer atoms than chess moves.
You are incorrect. There is 64 squares and 32 pieces. If there are 3 pieces on the board there is 64 places the white king could go. That leaves 63 places the black king could go. 64*63 so far.
Now to add the first piece. There are 10 different pieces. So it is 64*63*62*10.
Now to account for pawn restrictions. There are 2 colors of pawns that can't go on 16 of the squares. I do not know if one has to take into account if the kings are on the 1st or 8th rank or how to do that.
That would 64*63*62*10-2*16 = 2499808 different positions with only 3 pieces. 2.5 million positions. With 4 pieces it is 64*63*62*10*61*10-2*16-2*16 = 1524902336. That is 1.5 billion. It goes up very fast.
You could not be more wrong. 64 squares x 32 pieces x move combos (40x2) (its 40x2 cuz 40 move average times 1 move per person) = 163,840. You're way off, check ur math
I can't tell if you are a troll or an idiot. Either way I doubt I will be able to explain math to you. It is not as simple as taking a few relevent numbers, a few irrelevent numbers, and adding math signs in between.
http://en.wikipedia.org/wiki/Permutations is the wikipedia page on some or all of the math I was doing. I did not read the page beyond checking to see if it is the right one. And no, I did not learn math from wikipedia.
Teamwillow wrote:
In an argument, generally whoever starts namecalling (troll/idiot) is losing the argument. Thank you for notifying me that you're incapable of a proper rebuttal and are resorting to namecalling.
What is there to rebut? You do not even say what you are calculating. You just called be wrong, multiplied a few seemingly random things together, and claimed that I was wrong because your number was different from my number.
All I could assume from that is that you are simply aiming for an arguement or are clueless when it comes to math. So I said that and provided an articles that backs up what I did as the correct math in this scenario. What else is there to say?
My favorite part; a decent mathematician/programmer could probably figure out some real numbers in the effort people put into this argument. Unfortunately, I have yet to see such a person in any of these threads.
Teamwillow wrote:
You could not be more wrong. 64 squares x 32 pieces x move combos (40x2) (its 40x2 cuz 40 move average times 1 move per person) = 163,840. You're way off, check ur math
Actually, The first part of your calculations (64 squares x 32 pieces) are a little too large. Those would be correct if each piece could move to every square (though the number of pieces would diminish as the game goes on). I think the actual number of moves per turn is about 37.
Where your number gets too low is the x move combos. Instead of multiplying by the number of half-moves (turns), you have to take it to the power of the number of half moves. So, accepting that the average game is 40 moves long, the number of possible games would be
37^(40*2) not 37*(40*2)
and 37^(40*2)~2.858*10^125 in scientific notation, or
2.85800000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000
give or take a few zeroes, in case I miscounted.
If you are finding the number of posible positions, then it would be
64*63*62*61*60*59.....34*33*2 (or 2*(64!/32!)) minus illegal positions, since the first piece can go in any of the 64 squares, the second piece can go anywhere exept where the first can go, etc., and then you have to multiply by 2, because the position is different if the other color has the move.
That comes to ~4.822*10^53 positions before you take out the illegal ones, so the true number would be a few orders of magnitude lower than that.
apteryx was correct! The math is 64*63*62*61*60*59*58*57*56...34*33*32-illegal positions as he said
Drikhen wrote:
apteryx was correct! The math is 64*63*62*61*60*59*58*57*56...34*33*32-illegal positions as he said
Also, you must multiply by the amount of different peices that can go in each square. After the two kings the third peice can be a white queen who can go in the empty spots. The piece could also be a black rook, which pretty much doubles the places that the third peice can go. Also, it could be a black knight ect.
mrguy888 wrote:
Drikhen wrote:
apteryx was correct! The math is 64*63*62*61*60*59*58*57*56...34*33*32-illegal positions as he said
Also, you must multiply by the amount of different peices that can go in each square. After the two kings the third peice can be a white queen who can go in the empty spots. The piece could also be a black rook, which pretty much doubles the places that the third peice can go. Also, it could be a black knight ect.
I don't think the order that the pieces are placed matters... Only the square which they go in.
e.g chess isn't a different game if the first pice you put on the board when setting it up is the White Queen, the Black Rook, or the Black Knight.
I,ve Heard mention on many occations that there are as many or more possible chess moves/positions as there are atoms in the universe. For the sake of this thread lets agree with the Standard Model postulate that the Universe is infinite, surley the amout of chess positions though enormous is finite and as such has to be less ?