The upper bound is 3.8521*10^37.
https://arxiv.org/pdf/2112.09386.pdf
I need a math genius to explain how many Chess positions there are.
Sort:
tygxc wrote:
The upper bound is 3.8521*10^37.
https://arxiv.org/pdf/2112.09386.pdf
*brain hurt sounds*
Maybe just go to the Computer Championships page and look at the number of examined tablebase positions in a completed game. [NOTE: Thought produced on equipment that sometimes processes error.] When I did that the biggest number I saw was about 45M.
The number of legal chess positions is approximately 4.8 x 10^44,
based on analyzing 1 million uniformly random chosen positions,
as explained at https://github.com/tromp/ChessPositionRanking
wow
thats crazy
There are 64 squares and 32 pieces the first one can go on 64 squares, the second on 63 and so on.So 64*63"62*61...*33.So there 64!/32! Positions at MAX.
This would be the Upper limit(containing illegal positions.
There are as many squares on a chess board as there are positions in the Kama Sutra. Now that's food for thought.
5.75861e+163?
It is interesting how such an ancient game–qith just medieval army statues–can be so interesting (and complicated)
The small subset of the number of moves and games that could be played which we, as humans, can actually explore means that Chess is essentially infinite.
Simple. Too many for you to memeorize
Ask ChatGPT
64^32 including illegal positions where the king is in check
"There are more chess moves than atoms in the universe"
The number of possible games is just a construct. It would be more interesting to know how many variations there are with a limit of 100 to 150 moves, since this will cover almost every game played. It should also just look at possibilities with promotions to queens.
François Labelle is pretty good at math. https://wismuth.com/chess/statistics-positions.html
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.
Alright…..fess up, who counted them all……even if your dead dude. Possess my screen so I know who counted every possible move.