are there more moves in go than atoms in the universe
Since each location on the board can be either empty, black, or white, there are a total of 3 possible board positions on a square board with length n; however only part of them are legal. Tromp and Farnebäck derived a recursive formula for legal positions L ( m , n ) (\displaystyle L(m,n)) of a rectangle board with length m and n. The exact number of L ( 19 , 19 ) (\displaystyle L(19,19)) is obtained in 2016. They also find an asymptotic formula L ≈ A B m + n C m n (\displaystyle L\approx AB^(m+n)C^(mn)) , where A ≈ 0.8506399258457145 (\displaystyle A\approx 0.8506399258457145) , B ≈ 0.96553505933837387 (\displaystyle B\approx 0.96553505933837387) and C ≈ 2.975734192043357249381 (\displaystyle C\approx 2.975734192043357249381) . It has been estimated that the observable universe contains around 10 atoms, far fewer than the number of possible legal positions of regular board size (m=n=19). As the board gets larger, the percentage of the positions that are legal decreases.
Go and mathematics