Estimated # of unique chess games

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Avatar of savy_swede
glassworks wrote: I would imagine that only a small fraction of those games would be considered "logical". Meaning that if a stragety were to be invoked, and reasoning applied, the number would be cut drastically.

exactly why every possible game will not be played. If it played every possible move there are going to be games with a lot of hanging pieces

Avatar of ericmittens
Sharukin wrote: ivoryknight71 wrote:

I just came across something interesting in one of my chess books. The estimated total number of possible unique chess games is 10 to the 120th power: 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, 000, 000, 000, 000. In English, that is a thousand trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion.

 

For your information, physicists estimate the total number of electrons in the universe is "only" 10 to the 79th power. 


 That number is only a lower bound on the number of positions possible. The real total is likely much higher.


 That estimate is only up to move 40


Avatar of MCW
Surely it's possible to work out exactly how many possible games there are (excluding lego pieces Erik!) and we shouldn't have to rely on a 'lower bound'. Ok it would take a super duper computer to do it, but I would imagine it could be worked out to an exact figure because, large though the number is, it is still finite. We know that there are 400 possible combinations for the first move (20 possible first moves, 20 possible responses, 20 x 20 = 400) and I would have thought, therefore, that an accurate total figure could be achieved. Any thoughts?
Avatar of millerthesmurf
there will be more neutrinos tho
Avatar of BILL_5666
fleiman wrote:

What do you mean "the universe" ? The Universe is endless, so I guess the number

of electrons is also endless.


The universe may be larger and grander than we can comprehend, but it is finite.  I guess the same can be said about chess.

Avatar of trold
MCW wrote: Surely it's possible to work out exactly how many possible games there are (excluding lego pieces Erik!) and we shouldn't have to rely on a 'lower bound'. Ok it would take a super duper computer to do it, but I would imagine it could be worked out to an exact figure because, large though the number is, it is still finite. We know that there are 400 possible combinations for the first move (20 possible first moves, 20 possible responses, 20 x 20 = 400) and I would have thought, therefore, that an accurate total figure could be achieved. Any thoughts?

First, it should be made clear that there is a difference between number of possible positions (state space) and number of possible games (game tree).  The size of the state space has been estimated to be around 10^50 while the size of the game tree has been estimated to be around 10^120.  If we assume that someone clever could compute the latter number exactly by just examining the state space, we are looking at the following time frame.  With price of hardware dropping exponentially, it is always best to wait a few years.  Asume we want to get it computed in a year once we buy the hardware, and assume that some clever programmer can code to only use a single operation per state in the state space.  We would then need:

10^50 states / 10^9 states per GFLOP / seconds per year

    = 10^38 GFLOP of hardware

The current price of a GFLOP is $0.20, with the number roughly halving every six months.  We are thus looking at at least half a century before the hardware would become afordable to the combined wealth of the world.


Avatar of WhereDoesTheHorseGo
if your post is true, trold, holy [insert creative expletive here]!
Avatar of WhereDoesTheHorseGo
BILL_5666 wrote: fleiman wrote:

What do you mean "the universe" ? The Universe is endless, so I guess the number

of electrons is also endless.


The universe may be larger and grander than we can comprehend, but it is finite.  I guess the same can be said about chess.


 maybe the author meant the *known* universe?


Avatar of depthshaman
has to be known universe. People can only observe as far as light has traveled since the big bang. universe = 14 billion years old, so we can only see 14 billion light years. Beyond that scope there is no telling what may exist. Anyways, this universe may be finite, but I doubt the number of universes in existence is.
Avatar of Charlie91
Assuming the 14 billion is accurate, there's nothing beyond that.
Avatar of KillaBeez
ivoryknight71 wrote:

I just came across something interesting in one of my chess books. The estimated total number of possible unique chess games is 10 to the 120th power: 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, 000, 000, 000, 000. In English, that is a thousand trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion.

 

For your information, physicists estimate the total number of electrons in the universe is "only" 10 to the 79th po

You would not say that elongated number in that way.  It would be 100 quintillion googles.
Avatar of Manning
fleiman wrote: ivoryknight71 wrote:

I just came across something interesting in one of my chess books. The estimated total number of possible unique chess games is 10 to the 120th power: 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, 000, 000, 000, 000. In English, that is a thousand trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion.

 

For your information, physicists estimate the total number of electrons in the universe is "only" 10 to the 79th power. 


What do you mean "the universe" ? The Universe is endless, so I guess the number

of electrons is also endless.


Actaully the physicists of the world have had a stab at estimating the total mass of the universe, based on mathematical analysis of the Big Bang, Inflationary Theory, Planck's number and a whole bunch of other groovy stuff. 10^79 is the (ahem) "generally agreed" number, not that there is any meaningful way of proving it conclusively at present.

Avatar of Tommygun
I've just found another one
Avatar of WhereDoesTheHorseGo
KillaBeez wrote: ivoryknight71 wrote:

I just came across something interesting in one of my chess books. The estimated total number of possible unique chess games is 10 to the 120th power: 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, 000, 000, 000, 000. In English, that is a thousand trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion.

 

For your information, physicists estimate the total number of electrons in the universe is "only" 10 to the 79th po

You would not say that elongated number in that way.  It would be 100 quintillion googles.

(again) i was quoting the author. 

/golfclap for you, though.


Avatar of janus255
That number includes non-sense games though, like sacrifices your queen for no real reason. It could be cut down drastically by only considering games where players use reasonable strategies. That's how chess engines work: they don't look down every path as far as they can, when they come across a strategy that is "obviously" poor, they stop looking. So it's very possible that chess could be solved without going through every one of these games.
Avatar of BILL_5666
ivoryknight71 wrote: BILL_5666 wrote: fleiman wrote:

What do you mean "the universe" ? The Universe is endless, so I guess the number

of electrons is also endless.


The universe may be larger and grander than we can comprehend, but it is finite.  I guess the same can be said about chess.


 maybe the author meant the *known* universe?


I don't quite follow your logic.  Almost by definition the "known" universe is a subset of the universe, so if the universe is finite then the "known" universe is finite and probably smaller than the universe.  By extension the number of electrons is also finite.


Avatar of calvinhobbesliker
Am3692 wrote: The question is now, how many of those 10^120 games has been played? Has mankind yet to play them all?

Yes, because 10 to the 120th power is more than the number of electrons in the universe. Ches was invented in it's MODERN form only a couple hundred years ago. in that time it's is impossible because even if all 6 billion people played at the sme time, the number would decrease to 10 to the 111th power divided by 6, and that's if everyone is playing a computer, not each other.it thakes about 275,000 years to Count to a trillion, which is 10 to the 9th power. so you would take 275,000x10 to the 102nd power for a person to count  the number of games he or she has to play against a computer. And of course, it takes much longer to play a chess game than to say how many games you've played so far. Of course, people usually play against other people, which makes it harder to play all those possibilities. We probably won't find all of them before humans go extinct and another, smarter specis replaces us and invents a newer version of chess that's different from the old one.


Avatar of itaibn
Sharukin wrote: ivoryknight71 wrote:

I just came across something interesting in one of my chess books. The estimated total number of possible unique chess games is 10 to the 120th power: 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, 000, 000, 000, 000. In English, that is a thousand trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion.

 

For your information, physicists estimate the total number of electrons in the universe is "only" 10 to the 79th power. 


 That number is only a lower bound on the number of positions possible. The real total is likely much higher.


First of all, you probably meant "games possible". Second of all, this number is actually and estimate for chess's "game tree complexity" (which is smaller than the number of possible games), according to this wikipedia article.


Avatar of broze
Does the fact that there is a finite number of chess games imply that the game is solvable?
Avatar of Loomis
broze, yes, but it doesn't answer the question of the practical nature of the solution. How long does it take to determine the solution and how much information do you have to store to play the game according to the solution? The answers to these questions may very well be on the order of or greater than the age of the universe and the amount of information stored in it.