Arghh...
Recommend that you use scientific notation. The two subjects you discuss, by their very nature, require estimates. Therefore, the large number of significant digits used is meaningless.
There are more chess positions than there are atoms in the universe.
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Oct 22, 2015
0
#3
Okay first of all its atoms in the visible universe, not the Universe(or what scientists called the Multiverse). Second the you should set the numbers equal to each other and find the smaller one's percentage ratio to the bigger one and then set that percentage ratio equal to one. Divide both estimates by x. The reason for this is simple: Both the universe and the chess numbers should algebraically come out to one,(There is 1 universe. There is 1 chessboard). By doing the above I think(?) you have just checked for the possibility by checking if the ratio is illogical in some way(If its below a certain barrier). Don't quote me on this cause I'm not sure, I never studied math really.
I thought it was electrons.
there are 10 to the power of 78 atoms in the observable universe.
That would be: 100000000000000000000000000000000000000000000000000000000000000000000000000000 atoms.
If I use the same font as you then it would be longer:
1000000000000000000000000000000000000000000000000000000000000000000000000000000000
And that's only the observable universe. You never mentioned whether it was the observable universe or not so the number could be a lot bigger!
There are an estimated number of atoms in the visible universe of around 10 to the power of 88. Thats huge but the number of chess positions has been predicted to be around 10 to the power of 120!!!.
For example after the 1st move in chess there are 400 combinatoins. 20 moves for white and 20 replys. Then after 2 moves there are approximately 5000 combos. After 7 moves the number is already 9,132,484+-10,921,506. The longest game of chess ver played was around 250 moves showing the amount of combos are vast.
In truth even the best super computers will be unable to calucate the exact amount but for sure there are more chess positions than atoms in the VISIBLE universe.
So 10 to the power of 88 is
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
However the amount of predicted chess postoins is way bigger.
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Thats 10 to the 120.
*Mind Blown* Jk.
Lol
Yeah its a pretty complex subject.
How much time of your life did you spend figuring that out? :D
Chess players dont have lives, we play chess! I already knew a lot of it and just a little research and bish bash bosh!
I like when people do stuff like this, but you used the the wrong equation.
To get an estimate for the number of total chess board positions, recall that the first piece can go on any of 64 squares, then the next piece on a total of 63 squares, then the next piece on any of 62 squares etc.) With 16 total pieces we get a rough estimate of 64!/48! which is a maximum of about 1.04 * 10^28 illegal positions. That's not very much. The math equation generally talks about the number of possible games rather than the number of possible positions and we can see why.
Even if 9999/10000 of those positions are illegal, that will only bring the number down to 10^24. So although it is not a good estimate, it does serve to show scale. The number of possible chess positions is not in the millions or in the googles. It's somewhere in the sextillions or millions of sextillions, which is more information than what we started with.
It is very very hard to come up with even a fermi estimate for the number of atoms in the universe. But we'll try.
Again, we want an estimate to just get an idea for the scale. Chances are the numbers won't be very close, so it will either be much larger than 10^28 or much smaller than 10^28. We just want to know if the atoms in the universe is on the scale of sextillions of over a googol or even bigger than that.
Well off the top of my head our galaxy has about 200,000 stars. Let's call it 100,000 stars. Well I don't know how many galaxies there in the universe. But I know off the top of my head that the observable universe has a radius of about 46 billion light years, and the andromeda galaxy is about 4 million light years away. As a rough estimate that means we have one galaxy for every 6.4 * 10^19 cubic light years. Let's say the universe has a radius of 5.0 * 10^10 light years instead of 4.6 * 10^10 light years. That would mean the universe has a total area of about 500 * 10^30 cubic light years or 5 * 10^32 cubic light years. That gives an estimate of about 10^13 total galaxies.
That gives a universal total of 10^18 stars with 100000 stars per galaxy. However, I heard that there are galaxies with as many as a billion stars (I hear a lot of things). So let's pin the average at somewhere between 10^5 and 10^9, so 10^7. Therefore, that bumps our universal estimate to about 10^20 stars.
Although this number could be off by millions in either direction, this gives us a good clue: The number of chess position is on the scale of the number of stars in the universe. This means it shouldn't even be close to the number of atoms in the universe.
The number of atoms in a star would only have to be a billion to match the number of illegal chess positions. I remember that avogadro's number has something to do with converting weight into atoms, and that is 6.022 * 10^23, so let's throw that into the equation. I also remember that the earth is something like 10^24 kg and the sun is something like 10^36 kg. So if we multiply those together we get that the total number of atoms in the stars of the universe is something on the scale of 10^79 and not on the scale of 10^28.
I remember also hearing that the smallest stars are about 1/1000th the size of our sun, but our sun is about 1/1000000000th the size of the biggest star. So we take the average again and assume the average star size is about 1000 times bigger than our sun. That bumps the number of atoms up to 10^82.
The point is that just by estimating, we have figured out that the number of chess positions isn't even close to the number of atoms in the universe, but it is probably pretty similar to the number of stars in the universe.
Some chess players have lives
There are symmetries which can lower the number of positions to be analysed. This is explained in a very interesting paper (in French) :
http://www.societe-informatique-de-france.fr/wp-content/uploads/2015/07/1024-no6-lemoine-viennot.pdf
They conclude the number to be not greater than 10^20
Oct 22, 2015
0
#16
Chess is infinite: there are 400 different positions after each player makes one move apiece. 72,084 positions after each player makes two moves apiece. More than 9 million unique positions from the third move. After the 4th move, more than 288+ billion different positions are possible. Many 40-move games on Level-1 can be achieved than the number of electrons in our universe. There are more game-trees of Chess than the number of galaxies (100+ billion), and more openings, defences, gambits, etc. than the number of quarks in our universe! --Chesmayne
qoute taken from http://www.chess-poster.com/english/notes_and_facts/did_you_know.htm
Great and infinite are two differents things.
I wonder how many positions there are when you eliminate the ones that even a beginner wouldn't make. Or redundant ones.
Great feedback from everyone! A few things to address. First you don’t have to use estimates if you have an exact formula which we have here with 12 multiplied by itself 64 times. What’s more is that to me it’s more important to come closer to finding an exact formula than to get a better estimate.
Next, the difference between observable universe and non-observable universe is too great to measure. In my opionion it is of very little significant value if we only calculate what we can see up to when we know “there is more than meets the eye! TRANSFORMERS!” Sorry, you know what I mean. (Aquarius550 and Megadroid - I believe I said universe which means that it’s the WHOLE universe not just the observable part. Remember addition by subtraction.)
Also, too after posting I also realized you have to double the number in two if you want to include White to move or Black to move.
The maximum number of zeroes after 97 is 66. This means that any number larger than this will mean there’s more to that than chess positions.
Also this post was in regards to the number of positions possible not number of different moves possible which obviously will be larger and even more complicated to analyse due to different positions being able to be reached by different move orders.
I love Xman’s post, a lot of information in there and what he said at the end “The point is that just be estimating, we have figured out that the number of chess positions isn’t even close to the number of atoms in the universe, but it is probably pretty similar to the number of stars in the universe.” is spot on. Thank’s Xman!
“There are more chess positions than there are atoms in the universe.”
While I don’t know if this is true or not, I was trying to come up with a math equation to see if it is “possible”. Now I am not a mathematician in any shape or form but I’m going to give this a go.
First we need to know how many atoms are in the universe. (Like scientists haven’t been wrong before! Sorry Socrates! The Earth goes around the sun guys!) Now being me, I’m only interested in hard numbers not estimates. They haven’t been able to figure out a formula for the exact number of LEGAL positions, they can only give an estimate.
Now there is only one way to know what the MAXIMUM number of positions are IGNORING the rules of chess. So this number will include illegal positions with pawns on the first and eighth rank and it will also include positions where the king is in check and other subtleties.
There are 64 squares of course. There are six different pieces that can be on any square. A pawn, knight, bishop, rook, queen and king. You have white and black. So that makes 12 total different pieces that can be on any given square. So if I’m remembering my 5th grade teacher, Ms Owens correctly, this would mean you want to multiple twelve by twelve sixty-four times. (Boy, that’s a lot of math).
I tried doing this with my calculator on the computer and realized after doing it 15 times you need a bigger calculator so I found this: .
And after some time I came up with this number:
97,368,504,802,272,205,153,595,678,239,454,304,952,368,475,046,930,119,079,817,985,916,928
To put this in perspective if you live to 100 and you start looking at these positions right after birth (stop sucking that bottle kid and get to it) you
would have to view 30,875,350,330,502,348,158,801,267,833,413,972,904,733,788,383,729,743,493,092 positions per second in order to see every position in your life.
Or
as of midnight last night the world population was 7,375,534,434 according to . If everyone currently looked at them for 100 years we all would need to view 4,186,184,825,898,454,772,070,998,080,220,470,285,819,261,946,073 per second
Or
according to there has a total number between 110 to 115 billion people to have ever been on planet earth (not including aliens). Figuring on the high end, if 115 billion people that was ever born on planet earth looked at them for 100 years all of us would need to view 268,481,307,221,759,549,206,967,546,377,512,807,867,250,333,771 per second
So now, I leave up to you scientists. Do atoms in the universe total more than 97,368,504,802,272,205,153,595,678,239,454,304,952,368,475,046,930,119,079,817,985,916,928? Only then it’s POSSIBLE. No estimates please. Only exact numbers!