Any brainy people to verify this chess/math question?

Originally posted by slank
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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?

Actually you cant just keep moving back and forth. I was playing a game with my friend online and we just kept moving the same pieces back and forth and the computer called it a tie after a while. I think its against the rules

Yes, more chess moves than all atoms in the universe, the board is designed around movements around the board which exponentialise. The game was possibly even made by extra- terrestrials as both civilizations who started very simular versions for there military like strategy games had very extra-terrestrial links.

There is a discussion on this here: www.madsci.org...

I personally think that as we do not know the size of the universe, we cannot say with any degree of certainty whether x is greater than the number of atoms in it. I have no idea how you would calculate the number of unique combinations in a game of chess.

considering i play chess all the time, and i am in the local city chess club, yea that's not that hard to believe. i have never ever played 2 games that are the same.

Originally posted by Croat56
Actually you cant just keep moving back and forth. I was playing a game with my friend online and we just kept moving the same pieces back and forth and the computer called it a tie after a while. I think its against the rules

If you go 50 moves without taking a piece it's a stalemate. This usually only comes up in the end of a poorly played game, when one side is down to just a king but the other side fails to solve for mate.

The question is poorly phrased and therefore invalid. 'Moves' means what, exactly? Two opponents can move their knights all around the board for a very long time. What's the point?

To define moves in relation to the other pieces on the board is the only way to approach numbers like those being discussed, but this still does not suffice.

By defining the beginning and end of the game, we can call the entire game a single 'chess-thread' from beginning to end. The question can then be phrased, "How many possible 'chess-threads' exist? This number would presumably reach very high due to the absurd games that do become POSSIBLE and yet are never actually played (where opponents 'queen' several pawns or perhaps upon queening they select different pieces like a rook or a knight). Let us say that there are 10^27 (ten to the 27th power) possible 'chess-threads'. This statement is more assailable/definable because this is the challenge that chess programmers face. Essentially it becomes a chore in which the ENTIRE PROGRESS of the game is tracked. Until recently, a full analysis of chess-threads was not possible, but they're getting much closer.

Chess moves mean nothing when there is no spatial context.

Originally posted by Croat56
Actually you cant just keep moving back and forth. I was playing a game with my friend online and we just kept moving the same pieces back and forth and the computer called it a tie after a while. I think its against the rules

Yes that is correct. There is a '50 move rule' commonly applied in chess to prevent this sort of thing from happening when either player is incapable of checkmating the other.

Osiris

dbates --

How can you say there are an infinate number of chess moves? There's a big difference between REALLY big and infinate.

Nox --

You're insane! I, in fact, would be willing to bet life in enternal hell that there are more atoms in a single 8-oz glass of water than legal movies in chess. And if they dragged me away saying they proved me wrong? I'd certainly kick and scream, but I'd also know in the back of my mind that the test was rigged!;-)

Indigo Child --

Thanks for the link! It's a great read!

Originally posted by TheManInTheShadows

You're insane! I, in fact, would be willing to bet life in enternal hell that there are more atoms in a single 8-oz glass of water than legal movies in chess. And if they dragged me away saying they proved me wrong? I'd certainly kick and scream, but I'd also know in the back of my mind that the test was rigged!;-)

Well, let's see (I'll go step by step) ..

8oz of Water = 236.58 mL (1 US FL OZ = 29.57 mL)
1mL H2O = 1 gram of H20
So we have 236.58 grams of H20
Molecular weight of H20 is 18 (16 for the Oxygen, 1 for each hydrogen). This means that in 18 grams of H20 there are 6x10^23 molecules (that's Avogadro's number, look up a mole in google)

236.58/18 = 13.14 * 6*10^23 = 7.88x10^24 H20 Molecules
1 H2O molecule = 3 atoms, so we have (approx.) 2.36*10^25 atoms.

As previous posters explained (I will repeat if you'd like) there are over 10^35 possible moves in only the first 8 rounds of a chess game (just for the pawns!). This is 10 Billion (10,000,000,000) times more moves (considering only a very small number of the possible moves) than there are atoms in a glass of water.

You may begin to prepare your sould for eternal damnation now...

Since this question of possible moves involves my avocation and sometime profession within chess, let me tell you the practical story and case. Right now computers play better chess than 99 per cent of the people. The only reason I can beat my Fritz 8 program is because I play it in analysis mode, reserving only a few takebacks. Playing the program straight I can draw because I play into a book game that is closed, and go for a win at the time that I recognize the possibility of it. I would be too hard pressed for time, to analyze everthing in a short game, so tactics of computers mostly crops into the picture.

Now in practice the range of permutations over the chess board is limited by what people consider good moves. There are many bad moves in chess, ignoring an opposing threat, pin, capture or even flank attack. These terms can be understood in elementary chess books. Computers limit their field of search also by pruning those nonsense moves, and looking ahead by its opening book. In a sense computers actually cheat, by making book moves, and get away with it! For the human player the tactics of chess are what you have to face, because if there are forced moves over the board, the computer will find them. You will have to think these things through, and in the brief times you want to spend sparring with the computer, again you can play analysis mode and rethink positions maybe two or three times in a game. That is a basis of improvement at the game, without setting up the pieces to the beginning and hoping to arrive at the same position. In your own mind in analysis mode you lose the game, and reset the game to the takeback of a move. To do otherwise and consider your game anew is THE game is to neglect your own self improvement.

Well welcome to the world of chess. By the way I have never written an introduction here, as I handled duties in the press room in London at the the 1993 Kasparov Nigel Short Times World Chess Championship. We called my position "data base manager," but there was much more to it.

Thank you for the opportunity here.

[edit on 21-1-2005 by SkipShipman]

Starwars51 and Skipshipman --

THANKS for laying ALL that great stuff out!!

I'll have to read 'em both a couple of more times so as to get the most out of all that info. Again, Thanks!!!

The number of chess moves is at most 218.

The number of chess positions is estimated to be between 10^43 and 10^50.

The number of chess games is infinite, as the 50-move rule and the draw by repetition of position don't apply if no player makes the claim.

The game tree complexity is about 10^123. That's the number of chess games you may have to consider to play perfect chess.

Source: en2.wikipedia.org...



10^78 to just under 10^81 atoms in the universe depending on assumptions of the number of galaxies and atoms in galaxies and dark matter and the like.

pages.prodigy.net...

[edit on 23-1-2005 by Vanguard]

I would agree that the number of possible moves in one game of chess exceeds the number of atoms in the visible universe.

I would not agree that the number of moves exceeds the atoms present in our universe - period.

There are a couple of reasons for my feelings, I'll just touch on them, nothing like my usual marathon posts.

The number of atoms in the universe increases exponentially when you consider the ramifications of quantum physics and the properties sometimes bestowed on ordinary atoms by quantum interference. If you consider other dimensions the numbers are similarly unequal, but tilt in favor of the other side (the universe wins).

The number of chess moves can never change, unless the rules change. And there are not an infinite number of them. The universe, on the other hand, appears to be renewing itself in some ways while deconstructing itself in other ways. The whole system being considered operates using many laws that remain a mystery. The properties of our galaxy are largely mathematical speculation. Even the depths of our oceans remain unexplored and defy quantification. What sort of hubris is it, that makes men think they can conceive of the universe as a whole?

I was taught how to play chess before I learned to dress myself, and I play a good unconventional game. I don't rely on opening patterns, and I don't try to identify opening patterns played by my opponents. I play alternately agressively and defensively, it tends to throw off human opponents, but not the computers. On a good day I calculate five or six moves ahead after the opening three, on a bad day I play strict grid control to appease my fuzzy brain. I'm no Fischer, and I don't hold any graduate degrees in mathematics, so take my comments with the grain of salt due.

Originally posted by otlg27
Ummmm, I'm sorry, but *you* are *wrong*.

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.

Yes, I see my mistake!

There are a combination of 400 different board settings in the first two moves alone.

My bad!

But still, more combinations than atoms in the universe? That's preposterous!

This might be a bit off topic, but i remember reading somewhere on here that there is going to be chess on here? I was probably hallucinating, but if this is true please point me towards a thread etc.

Originally posted by Nox
("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.

make that

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

And I would join you.

Simply put, I have many times ended a game in a stalemate, in which the game would literally go on for infinity. Since there are infinite sets of unique chess games, there is no possable way that there could be more atoms in the universe. If somehow we prove there to be an infinite amount of atoms, it would still only equal that of unique chess games.


EDIT:
Well, now that I have seen the 50 move rule, this kinda debunks my comment now doesn't it

[edit on 3-2-2005 by American Mad Man]

Even though there are my different possible moves is a game of chess, that doesn't mean that they will be useful in winning a game. Since you are looking for the best possible moves in a certain situation, the number of USEFUL moves is but a TINY TINY TINY fraction of all the moves in total, making chess a simple game in the end. Seeing those few better useful moves the your opponent is what makes a player good in a game of chess.

cant they just program the computer certain openings that result in open games and let its superior calculations do the rest?

All this speculation of mathmatics over a chess board and all the multitude of different equations over said board, very interesting....and people think they can still classify the universe??? read my second signature quote and get a grip..everyday from the smallest to the biggest science speculations are being reinvented and reclassified due to new information....anyone that states they KNOW for sure anything about the mass expanse we call the universe is sadly mistaken and mislead.

But as usual...thats just IMHO