Any brainy people to verify this chess/math question?

Hello.

I was visiting a place called How Stuff Works, and while looking up what they had to say about chess computers, they state (in the article at the link below) that in the game of chess, there are far more possible chess moves than there are atoms in the entire universe!!

They say there are roughly ten to the 75th power of atoms in the universe, and roughly 10 to the one-hundred-and-20th power number of chess moves. Question: Can this really be true?? (I would be very doubtful if there are more possible chess moves than there are atoms in a single drop of water, never mind the world's oceans and all the rest.)

Thanks in advance for your replies, if any.

Here's the link:

stuffo.howstuffworks.com...

I'm not that brainy but I looked at the site, and it looks at trees of all possible moves of every piece, so I guess it's possible. The number of the atoms in the universe seems right compared to what I've found elsewhere on the web.

[edit on 1/19/2005 by djohnsto77]

That's probably right. There are too many chess moves for anyone to learn. Even people usually specialize in a couple differnt strategies. There are too many different moves for someone to learn them all. Of course we as humans rule out many of these decisions based on the consequences and every move you make eliminates millions of possibilities in the future. I'd almost believe that there were an infinite amount of moves possible.

I've been playing chess off and on for most of my life and the statement of saying that there are more moves than atoms in the universe is absolutely preposterous!

The number of moves is quite high but not that high. Not nowhere near!

Not even a miniscule of a fraction!

Where HSW got it wrong is that they multiplied 20 possible moves for white and 20 possible moves for black from the get go and come up with 400 possible moves in just the first 2 moves! I'm sorry but that's wrong

There should have been only 40 at most after both white and black makes their initial moves!



[edit on 19/1/05 by Intelearthling]

Where HSW got it wrong is that they multiplied 20 possible moves for white and 20 possible moves for black from the get go and come up with 400 possible moves in just the first 2 moves! I'm sorry but that's wrong

There should have been only 40 at most after both white and black makes their initial moves!

Ummmm, I'm sorry, but *you* are *wrong*.

Example:

White moves left most pawn forward 1 square.
Black has 20 possible responses.

White moves left msot pawn forward 2 squares.
Black has 20 possible responses.

White move second-left-most pawn forward 1 square.
Black has 20 possible responses.
...
...

You get the idea.. While white has 20 opening moves, black has 20 moves that can counter EACH ONE.. total possible move combinations in the first turn: 400 (20x20) unique combinations of moves.

Regards,

Osiris

PS: The reason this is important isn't for the first two moves.. it's when you try and evaluate all the possibilities 10+ levels deep, you must consider (if you're a computer) every possibility and establish which of your moves leads to the least damaging possible outcome, given EVERY conceivable response from your opponent.

[edit on 19-1-2005 by otlg27]

Originally posted by otlg27
You get the idea.. While white has 20 opening moves, black has 20 moves that can counter EACH ONE.. total possible move combinations in the first turn: 400 (20x20) unique combinations of moves.

PS: The reason this is important isn't for the first two moves.. it's when you try and evaluate all the possibilities 10+ levels deep, you must consider (if you're a computer) every possibility and establish which of your moves leads to the least damaging possible outcome, given EVERY conceivable response from your opponent.
[edit on 19-1-2005 by otlg27]

Bingo. Computers have a significant disadvantage unless they have a great deal of computing power and plenty of time to think, especially in speed chess.
Humans have the advantage of recognizing patterns and common scenarios- we can take a short glance at how things are taking shape and steer the game in the direction of other successful games which we might remember.

Even humans can be way too methodical for speed chess though. For speed chess I've found that paying attention to scenarios or even common strategies/scenarios can get a mediocre player in big trouble.

I'm a mediocre player, so I don't think about chess. I keep details minimal and rely on generalized battlefield concepts. Desginate primary units and supporting units, feint to one side or show weakness there, then smash into the opposite flank with a sacrifical attack to get primary units into his rear. Only works in strict speed chess and against people without tons of experience- but it works great in that case.

I highly doubt there are more moves in chess than there are atoms in the universe... This si so unlikely, how can we possibly know whats out there?

Statistically speaking, that is. People need to keep in mind that the number of "Possible moves" in a chess match is not determinant and that it is exponential. The number of atoms (Not subatomic particles) is relatively static and is determinant and also exponential.

I wonder if they are counting atoms only of visible matter which overall makes up only a fraction of total matter in the Universe. What about Dark Matter particles?

...that they were referring only to those atoms whose mass creates visible matter. It is impossible to determine the amount of dark and/or anti-matter... although some hypothesize that these numbers are directly connected to the amount of visible matter.

I'm not sure I'll get this right because it's complicated but let's forsake the rules of chess and just talk about possible arrangements.

There are 64 squares occupied by 32 pieces. Starting with one piece in a given location, you must then allow for the placing of every other piece in every other square. It looks like this 32x64x31x63x30x62 etc etc.
In other words, multiply ever number between 1 and 32 (inclusive) together, then multiply that by ever number between 32 (inclusive) and 64.
I'm pretty sure that's how many possible arrangements of pieces on a chess board there are, without respect to restrictions imposed by rules of movement or captures. Captured pieces actually create additional scenarios.
To account for all possible piece exclusions I am not sure but I think you'd just about have to square the answer of the previous equation.

We're talking about the number of possible moves during a game. Moving pawn b1 to c1 and them moving pawn b2 to c2 is different than moving pawn b2 to c2 and them moving pawn b1 to c1. Now if you think about the fact that there are 8 pawns and they can each move one or 2 spaces, and you can change the order that they move in, thats a total of 16! possible moves in just the first 8 turns. But actually we've forgotten about the other side so we have a total of 32! for the first 8 turns. If I've lost you that's 1*2*3*4*......*32 = 2.6313083693369353016721801216e+35 possible moves in the first 8 turns

We haven't even factored in that the nights could have moved on one of the first 8 turns, or that the bishops could have moved.(or the queen, or rook...) This could get really big...really fast.

[ This could get really big...really fast.

Sure, but as big as an ocean and all of its atoms??

Would you be willing to bet your life on it? *s*

.
infinite moves? yes.

if you have two players and they each just move a piece back and forth every other turn that is an infinite number of moves, on that alone. Anyone know of any numbers bigger than infinity?

In general though the actual number of moves of any game are far less than that. [lets hope so anyway]

[In theory] If you have 5 pieces on the board, bishop, king, rook, knight, queen, say the queen can move into 20 different squares, king 3, rook 8, bishop 12, knight 6, so in this single turn we have 20+3+8+12+6=49 possible moves as a rough average. Then the opponent has his own 49+- on his move. So if know one ever checkmates or takes a piece this becomes 49*49*49*49*49*49 = 13,841,287,201 in just 6 moves. 49^20 = 6,366,805,760,909,027,985,741,435,139,224,000 in 20 moves.
49^infinity = infinity.

Note: this is probably a poor estimate of the number of moves, but i haven't played chess in decades.
.

Originally posted by TheManInTheShadows
[ This could get really big...really fast.

Sure, but as big as an ocean and all of its atoms??

Would you be willing to bet your life on it? *s*


My life, probably not - but a million bucks? Sure. No one knows the exact mass of the univers (and dark matter is not made of atoms, so that doesn't screw things up that bad), and no one can compute the total number of chess moves either (kind of gives you an idea how many there are, eh?), but it looks as though there are FAR more chess moves than atoms. If we changed the bet to include the "known universe" I would bet my life in a heartbeat.

A good web page to take a look at:

www.madsci.org...

how could they possibly calculate the number of atoms in the universe. This is a total fabrication of the truth. We have no idea how large the Universe truly is, or if it is infinite! That doesn't include the basic lack of knowledge of space itself. The Chess board is soo incredibly small, there is absolutely no way that this is true.

("Set of all unique chess games.") > ("Atoms in the known universe.")

I would bet my life, soul, first born child, and first born's soul on this.

Originally posted by Ryanp5555
how could they possibly calculate the number of atoms in the universe. This is a total fabrication of the truth. We have no idea how large the Universe truly is, or if it is infinite! That doesn't include the basic lack of knowledge of space itself. The Chess board is soo incredibly small, there is absolutely no way that this is true.

Did you by any chance read any of the posts or links provided?

We do have a very good idea of how big the universe is that we can see, approx 10 billion light years in diamter. This would create a volume (if the universe is spherical) of 4.4 x 10^77 m^3. If we assume the universe is as dense as solid sodium (which is pretty dense when looking at atoms/m^3 - approximately 2.5 x 10^28 atoms/m^3), that would put the total number of atoms in the universe around 1 x 10^106 - a very large number

However, the number of possible chess moves is at lest 10^120. This doesn't look like that much more, but it is far more. This leaves a ton of room to find more space in the universe, literally billions and trillions times more than what we know about.

Here are some links I used to find conversion/density/size information

www.sengpielaudio.com...
www.webelements.com...
stuffo.howstuffworks.com...
imagine.gsfc.nasa.gov...

Originally posted by Ryanp5555
The Chess board is soo incredibly small, there is absolutely no way that this is true.

Reminds me of a story I heard once.

A peasant learned of an attempt to assassinate the king and quickly told what he had learned to the kings trusted guard. Later, after it was found out to be true and the plot was foiled, the king summoned the poor peasant before him.

"As a reward for your great service you can have anything you wish for." The peasant thought about it and said "Do you have a chess board?" "Why yes", replied the king. The peasant then said, "I would like one grain of rice for the first square of the board, two grains for the second, four grains for the third and so on doubled for each of the 64 squares on a chess board."

The king laughed and summoned his servants to fulfill this simple request. Soon however the king realized he had been outsmarted and that there was not enough rice in all the kingdom to fulfill this request. "You have saved my life and I can't even fulfill your simple request." The poor peasant was then made the kings top adviser as a reward for his great wisdom and faithfulness.

Exactly how much rice was needed to fulfill this request? Approximately 18 billion, billion grains of rice. If you could find a bag that would hold a billion grains of rice, you would need 18 billion of them to store the amount needed. So don't let the small size of the chess board fool you. There are more possibilities than you can imagine, and honestly an infinite amount of moves.


[edit on 21-1-2005 by dbates]

Originally posted by slank
.
infinite moves? yes.

if you have two players and they each just move a piece back and forth every other turn that is an infinite number of moves, on that alone. Anyone know of any numbers bigger than infinity?

Although a chessgame could hypothetically be infinite if both sides aggreed to help make it so, each move back and forth does not create a unique board situation and therefore can arguably be excluded from the count.