How many different chess positions are there?

No, I was saying that there are 10E12 chess position.

The number is greater than the number of atoms in the universe, or something like that. 

At least that's the number of different possible games. The number of possible positions is far less, of course. 

Cherub_Enjel wrote:

The number is greater than the number of atoms in the universe, or something like that. 

At least that's the number of different possible games. The number of possible positions is far less, of course. 

Please explain why the number of possible positions is far less than the number of possible games? What am I missing here ?

Claude Shannon already did the math, 10 to the power of 120 (10^120). Just search Shannon number in google

Well, each position can be reached through many possible continuations. 

As a starting example, if 5 moves of a game are played, each white moving a different pawn for each move, then in the one final position, there are already 5! = 120 ways of reaching that position (games). This number grows of course, as more moves are played. 

Not following the logic. Problem lies in definition and difference of the terms position and game. They can easily be thought of as the same. There must be as many possible positions as there are games as each position is unigue. I get that the same position can be reached by different move orders, thus 5 games can reach the same postion. But, getting there each position is unique and counted individually.

Suppose that there were as many (or more) legal positions as there were games. But for a position to be legal, by definition, there must be a game that leads to it. 

So that means there are as many games as there are positions. 

But we've also shown that there are positions that can be reached with more than one game. 

I consider a legal position to be any position that can be reached through a legal combination of moves. A game is a combination of moves ending in a result - resignation is possible, of course. 

Cherub. by your last statement you seem to agree, there are as many games as there are legal positions. Let me remind you of your original claim "the number of possible positions is far less "

So, TLDR, give me any legal position, and there's a game (at least one, and possibly more) leading to that.

That game may involve many positions, but each of those positions are also legal, and apply the same logic to each of those positions. 

Yeah, correct. I am arguing against there being as many legal positions as there are games. 

Take a look at this, by the way: https://en.wikipedia.org/wiki/Shannon_number

The number of games possible is estimated to be on the order of 10^120, while the number of possible positions is estimated to be around 10^52. 

These are estimates, because no one can calculate the real number. 

Read it. So according to Shannon, there are twice as many possible games as positions. There is a factor given, that of "sensible" games. There is fault in the logic concluding twice as many games. It can't be argued with however. A premise is based upon a presumed, beggining princible. Defining what constitutes the difference between a game and the positions occurring can be interpreted differently.

40 games with only 80 unique positions? ??

The whole question is quite pointless imo. Shannon came up with,"numbers" to emphasize that chess can never be "solved". The numbers are to high even for computers. However "sensible" games are a different parameter.

Knights can open the game, jump around to all open squares and return to starting point. Each side moves a pawn and the Knights start their hopping all over again and return. Move another pawn or 1st pawn and the Knights begin again. All rediculas of course, with the numbers quickly becoming astronomical.

One could just as easily count the positions in the same way games are being counted.

Note that it's not "twice" as much. If there are 10^100 games and 10^50 positions, it's actually 10^50 times as much, which is a much bigger factor.

Of course chess probably can't be solved, but it's very conceivable that it can be "effectively" solved, like checkers is. 

Yep, my error by saying twice as many. Shannon is playing "tricks" with the numbers. Easy to do. Mathamatical equations can be used to "prove" anything. All someone needs do is state a premise, the math can be found to support it as long as it conforms to the original hypothesis.

The numbers get greatly eschewed. Legal positions can occur exactly the same twice, only on the 3rd is the game ended. How is this factored in? Is this one trick to account for more games than position?

If we could figure out how many chess positions aren't there ?....then that may be a good start.

Gotta be more illegal positions than legal.

There are more solutions to the Knight's tour than grains of sand.

An interesting puzzle is the N by N Queens Problem. It asks how to place 8 Queens on a chess board so that none of them threaten any other in one move.

The eight queens puzzle has 92 distinct solutions. If solutions that differ only by the symmetry operations of rotation and reflection of the board are counted as one, the puzzle has 12 solutions. These are called fundamental solutions;

Yeah, check this out:

https://www.quora.com/Are-there-more-possible-legal-moves-in-chess-than-there-are-atoms-in-the-universe