Number of chess positions and molecules in the universe


Okay, there is a quote I read somewhere a long time ago about how the number of molecules in the universe (or earth, something along those lines) and how that number is equvalent or less than the number of different chess moves or positions. Does anyone know? If you do please post it.



Or possibly no.

Depends who you ask.

But really yes.


It's probably close to a googol.

    Think how many atoms are in a pencil - millions.   Think how many in a samurai sword - billions, maybe trillions.  Think how many in the earth - quardrillion to the guadrillion'th power.(10 x10 to the 30th power)   Then think how many atoms in all the planets and solar systems we can see with our powerful telescopes (the observable universe) - it's been estimated 10 x 10 to the 80th power.    A googol is 10 x10 to the 100th power. 


if we make a few assumptions then yes.
check this out:

edit: don't forget that we're talking bout the observable universe of course. the whole thing could be and probably is n times bigger


Althogh however varied the estimates, all are many orders of magnitude smaller than the number of atoms in the known universe. Since most of those are elemental hydrogen, I suspect this easily holds true for molecules as well.


Yes, but that includes all the stupid silly messing around games to, where each player just does the kind of moves to stretch out the game and make various variations of the game, instead of making logical beneficial moves.

Sort of like how you can have a whole bunch of monkeys typing on typewritters for infinity and they will eventually write the complete works of Shakespeare. (Unless they run out of ink... or starve...)

Take this for instance. Just completely pointless random moves, but that and every variation of every bit of that would count as possible games. (Even though you'd never see them played.)

There are 26,830 plausible games of naughts and crosses (excluding symetrically identical games). But against a smart player you'll probably only ever see 10 or 20 different games. (All resulting in a tie).

Oh and DavyWilliams, there would something like 50,000,000,000,000,000,000,000 atoms in a pencil. Molecules are much bigger though.


Well, there doesn't need to be a measure of quality of the positions that are included, because even with those positions included there's still no comparison.


Apparently you didn't read the article so let me summarise it by saying:
Estimated lower bound on the game-tree complexity of chess - 10 to the 120th power
Number of atoms in the observable Universe - 10 to the 81st power [estimate]
  => more chess moves than atoms in the observable universe


I thought there were sources though that indeed suggested that there were more chess positions than atoms in the universe.

If that turns out to be true (even though, of course, stupid positions are counted), it's still kind of a cute fact, don't you think? It's not easy to be bigger than a universe even if you cheat Smile


This source below says that there are between 10 to the 78th power and 10 to the 82nd power atoms in the known universe which is consistent with nrabbit's post. Any sources on the number of different chess moves to confirm 10 to the 120th power? And are chess moves and chess positions the same in terms of these comparisons?


Yes, sorry, I do have that backwards don't I. Where I said smaller I mean larger.


the number chess positions is much smaller.  Each square has 15 possibilities (empty, WKing,WQqueen,WRook,Wknight,WBishop,WPawn,BKing,BQqueen,Bknight,BBishop,and  BPawn)  with 64 squares, that would mean that the possibilities would equal 15 to the 64th power.   This number includes a lot of illegal positions (no kings, more than one king of a color, more than 8 pawns, ect.)  Thus clearly the number of positions is far less than the number of atoms.  Now the number of possible games might well be more than the number of atoms in the universe. I don't know, but it is clear that the number of positions is considerably less.


Happily, I know exactly how many atoms there are in the universe.  Unhappily, I'm not telling.


Kasparov made this quote in Bobby Fischer Against the World. I believe he also stated something along the lines of the possibility of chess moves are somewhere in the area of 9,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. He then continues saying that this is the like same amount of molecules that are in the galaxy, but this is a total presumption.


Then again, we're used to presumptions on the forums... Smile


Most sources that I can see (including the two on nrabbit's excellent link) estimate the game-tree complexity of chess like this: ~30-35 average legal moves, and average ~40 moves per game = around 10^120. I really doubt the accuracy of that method, though. For one thing, if we're looking at every possible game, including silly ones, the average game length should be way more than 40 moves.


it  can be  much  simpler  if  one  could  agree  the  answer is infinite to both  solutions in counting even mathematically

robertpetersen wrote:

it  can be  much  simpler  if  one  could  agree  the  answer is infinite to both  solutions in counting even mathematically

Well, we could agree on that, but we'd still be wrong.


or you could be right...


If you were trying to make a super long game, you could probably make it thousands of moves long or something, but due to the 50 move rule it should not be possible to have an infinitely long game as eventually you will run out of pawn moves/captures (or perhaps end up repeating the position too many times at some point).