I need a math genius to explain how many Chess positions there are.

it's not halloween, but there are some frisky gravediggers on tonite!

in the first 4 moves of chess there are just over 9 million different positions the board could look like in the first 10 moves there are over 1 trillion

I could calculate exact number of positions. I need sponsor to finance it for the period DURATION AROUND MIN 1 OR MAYBE 2 YEARS, DOING ONLY THAT.

10 ^ 0 == 1
10 ^ 1 == 10
10 ^ 2 == 100
10 ^ 3 == 1,000
10 ^ 4 == 10,000
10 ^ 5 == 100,000

...

10 ^ 50 == 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

... But, you get the idea...

Here is an article that has the calculation:

http://bit.ly/1dOj8e0

At a guess I'd say 17.

Well remember castling, so 21.

Good point, forgot about that.

      I asked Carl Sagen. He said there are BILLIONS AND BILLIONS of choices.

Go to chess openings on chess.com

There are no more than 10^46 legal chess positions. This has been proven by mathematicians.

There are 10^46 water molecules in Earth's oceans.

As a consequence the number of legal chess positions is certainly less than the number of water molecules in Earth's oceans.

The number of legal games is much higher taking into account that the maximum possible length of a chess game can be 11797 halfmoves under the 50 move rule and there are on average 35 legal moves in a chess position.

The number of legal games is irrelevant when it comes to solving chess because the limiting factor is the number of legal positions.

That is why chess is special, unlimited possibilities.

ninoak wrote:

watcha wrote:

There are no more than 10^46 legal chess positions. This has been proven by mathematicians.

There are 10^46 water molecules in Earth's oceans.

As a consequence the number of legal chess positions is certainly less than the number of water molecules in Earth's oceans.

The number of legal games is much higher taking into account that the maximum possible length of a chess game can be 11797 halfmoves under the 50 move rule and there are on average 35 legal moves in a chess position.

The number of legal games is irrelevant when it comes to solving chess because the limiting factor is the number of legal positions.

I think that the number of different positions shall increase when we consider that the pawn might become any figure when reached 8th raw. It would be interessting to consider total number of posible positions after at least one pawn has reache 8th raw!:))

Pawn promotion has been taken into account.

10^46 takes into account all legal promotions.

I have calculated with a program the number of possible legal armies of chessmen, together with their contribution to the number of positions ( the sum total is a little bit more than 10^46, because I used a rough method ):

My Chess Position Ranking project at https://github.com/tromp/ChessPositionRanking

obtains an estimate of the number of legal chess positions of 4.5e44.

Further improving the accuracy of this estimate, by determining legality of each of 10000 randomly picked positions, is an ongoing effort, that everyone is invited to help with.

#36
That is right. However, the vast majority of these 4e44 positions is not sensible with multiple excess promotions. The number of sensible and legal positions possible with one set of chess pieces without having to borrow promotion pieces from other sets is 1e39.

2e+47

Ask François Labelle

http://wismuth.com/chess/statistics-positions.html

ask ken tompson, a math genius who developed the first chess tablebases. he probably has an email. he's not a celebrity, so he may answer u.