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


There's a better page on wikipedia that explains it a bit better, however:

So between 10^43 and 10^50 positions, given that nobody else is smart enough to figure out how to account for all the special cases and arrive at an exact number.


Picked this up on a blog-


The number of distinct chess positions after White’s first move is 20 (16 pawn moves and 4 knight moves).  There are 400 distinct chess positions after two moves (first move for White, followed by first move for Black).  There are 5,362 distinct chess positions or 8,902 total positions after three moves (White’s second move).  There are 71,852 distinct chess positions or 197,742 total positions after four moves (two moves for White and two moves for Black).  There are 809,896 distinct positions or 4, 897,256 total positions after 5 moves.  There are 9,132,484 distinct positions or 120,921,506 total positions after 6 moves (three moves for White and three moves for Black).  The total number of chess positions after 7 moves is 3,284,294,545.  The total number of chess positions is about 2x10 to the 46 power. If you understand this and like math tell us the answer.


You don't need a math genius, because the answer is simple: A lot.


The number you gave is Shannon's number. If you intuitively arrived at that, you don't need a genius as you are quite intellectual yourself. An exact number can't be arrived at because it is very difficult with all the special cases and such, but just a few powers higher than what you predicted is the accepted value. 


These previous discussions may shed some light on it ...











I have no clue, I heard something about if every atom in the universe was coming up with 1000 positions per second, it would take millions or billions (I dont remember) of years.


It came up in one of teacher_1's topics.


Pawn promotions make things even more complicated.


Including pawn promotions, bughouse, crazyhouse, and suicide/losers (since you can lose your king here without losing, giving a bunch more!), the number easily exceeds the amount of atoms in the known universe.

Pretty awesome, right?


Around  10120 moves, give or take a few. 


Mr Einamar

The counting of possible moves in chess is not a matter of knowing mathematics. . It is matter of "down to earth" feasibility. Any ten /twelve years kid knowing arithmetic and logarithms. . . not to mention the almighty portable calculators. . . can easily do it.

As you write, you seem surprised of not finding a mathemathian (who knows what he is talking about ) that could give you a conclusive answer about the matter.

Well, the best of them will always come with the answer. . . "iit is about so many moves. . ." it approximates so many moves. . ." etc.

Why? Because you have not given him the right and conclusive conditions to meet.

---what about the "en passant" moves?

---on crownning a pawn , , , does it ( per se) have to be a Queen? Why not a Bishop, or a Knight?

---and this, rather these, crowned pieces how many moves will execute?

I will stop here. But allow me another point

Most probably that person doing the counting will use a calculator (otherwise he might be considered a rare human specimen with a rotten mind). . . . . .does the natural (repeat "natural") number representing the final count fit in the width of the display window. . . or has the calculator to approximate the cipher. . . with the truncation which it might imply?


No Science will give you a right answer, it will give you the right approximate answer.


"Most probably that person doing the counting will use a calculator"

I don't understand why is a calculator necessary to 'count' movies.

Well, the answer to this question is very simple:

There are "sooooo" many possible positions in chess and it gets complex as the game moves forward. The number which I gave above, describes the approximate number of possible moves in a chess game. Even though it looks small, that number is insanely HUGE.

amalmurali47 wrote:

 Even though it looks small, that number is insanely HUGE.

No kidding, it's larger than the number of particles in the universe. If you were to try and write that many dots down, there wouldn't be enough matter to make the pens. And even if you had enough pens to write it out, the paper and pens would be so condensed that it would form a giant black hole.

So yeah, large number.


Why would anyone NEED to know?


God might know - so we could pray for guidance.

And the devil is well known to play chess (usually with DEATH and while playing the fiddle) so for some perfectly triffling and incorporeal payment I expect he would whisper the answer to you.


Thats it!...I've sold my soul..


I hope you got change out of that fiver  ...:o)


"Billions and billions" - Sagan


I got a pound ruby..But spent it on a bag o' crisps.


Well. we have settle down the chess move count, ...but, now, how does the cockroach sit down?