I need a math genius to explain how many Chess positions there are.
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More than there are atoms in the universe
DoYouLikeCurry wrote:
More than there are atoms in the universe
Possible games, yes. Positions, no.
There is a difference.
.
:(
Not simple due to the fact that you have to take in complexities of each move, checkmates, and checks into account. There are probably over a 100 trillion possible combinations.
Alrighty, there are only 2 chess positions..... winning ones and drawn ones. U might think there r 3 & that I forgot to add it but it's part of the winning position. I hope this helps.
It's 10¹²⁰
Shannons number
Kyobir wrote:
It's 10¹²⁰
Move sequences, not positions.
The only number in chess greater than the number of possible positions is the number of excuses players make when they lose. Truly, this number is so enormous that even the best mathematicians have not yet managed to calculate it. 😎
The hard part is eliminating all the unreachable positions. The rest is trivial. You set upper and lower bounds by defining known reachable and known unreachable positions. With effort you could refine those bounds until you got bored. Without having proven it, I'd say that the computational complexity of finding an exact number is the same as that for solving Chess.
Тнеге аге а lот оf тнем. Gгеатег тнаи (ог еqцаl) то 1.
Eniamar a écrit :
There's a better page on wikipedia that explains it a bit better, however:
http://en.wikipedia.org/wiki/Chess#Mathematics_and_computers
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.
It's actually not about intelligence, it's just not within our capacity to find a more accurate value...
Spr_chess_intermediate wrote:
Eniamar a écrit :
There's a better page on wikipedia that explains it a bit better, however:
http://en.wikipedia.org/wiki/Chess#Mathematics_and_computers
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.
It's actually not about intelligence, it's just not within our capacity to find a more accurate value...
I'm convinced that with funding for a few years of research, those numbers could be refined but it would be a soul destroying task because there would be nothing meaningful to come from it. When numbers are that large we content ourselves with high degrees of inaccuracy.
Tromp counted exactly 8726713169886222032347729969256422370854716254 positions, of which 4.82 * 10^44 are legal, of which the vast majority is not sensible as the 3 samples show.
https://github.com/tromp/ChessPositionRanking
A better estimate is Gourion's 3*10^37 without promotions to pieces not previously captured.
https://arxiv.org/pdf/2112.09386.pdf
@thgxc Good content. Thanks.
At least 7.
But it has to be a playable position you can’t say rook takes pawn with no compensation is a possible position because it would never be played. How would they estimate that number?
It is estimated there are between 10111 and 10123 positions (including illegal moves) in Chess. (If you rule out illegal moves that number drops dramatically to 1040 moves. Which is still a lot!). "There are even more possible variations of chess games than there are atoms in the observable universe." Thank you google
It is a mathematical question. Most chess positions have never appeared in a game.