## Permutations and board games

**Moderators:** gmalivuk, Moderators General, Prelates

### Permutations and board games

Specifically, chess. How would I go about calculating exactly how many permutations of piece positions there are in a game of chess?

### Re: Permutations and board games

Can you elaborate a little more? Do you mean how many legal board positions are there? How many different games there could be?

double epsilon = -.0000001;

### Re: Permutations and board games

Dason wrote:Can you elaborate a little more? Do you mean how many legal board positions are there? How many different games there could be?

As in legal board positions and positions that could only be achieved through legal board moves. Yup.

### Re: Permutations and board games

Wikipedia wrote:The number of legal positions in chess is estimated to be between 10^43 and 10^47 (a provable upper bound[84]), with a game-tree complexity of approximately 10^123. The game-tree complexity of chess was first calculated by Claude Shannon as 10^120, a number known as the Shannon number.[85] Typically an average position has thirty to forty possible moves, but there may be as few as zero (in the case of checkmate or stalemate) or as many as 218.[86]

Perhaps looking at some of the references will give you the answer?

Edit: fixed exponents.

Last edited by nash1429 on Sun Aug 29, 2010 2:20 am UTC, edited 1 time in total.

### Re: Permutations and board games

nash1429 wrote:Wikipedia wrote:The number of legal positions in chess is estimated to be between 1043 and 1047 (a provable upper bound[84]), with a game-tree complexity of approximately 10123. The game-tree complexity of chess was first calculated by Claude Shannon as 10120, a number known as the Shannon number.[85] Typically an average position has thirty to forty possible moves, but there may be as few as zero (in the case of checkmate or stalemate) or as many as 218.[86]

Perhaps looking at some of the references will give you the answer?

It should be made clear that "1043" in that quote actually means 10

^{43}.

- Indigo is a lie.

Which idiot decided that websites can't go within 4cm of the edge of the screen?

There should be a null word, for the question "Is anybody there?" and to see if microphones are on.

### Re: Permutations and board games

Thank you all.

### Who is online

Users browsing this forum: No registered users and 12 guests