Yet despite these numbers being so large, my IQ is larger.😎🤓
Possible positions after 40 moves
After 40 chess moves, assuming there were no peices taken, there can be 10^120 possible positions. However after 40 moves peices are likely taken with some peices stuck, so there is more realistically around 10^100 moves. Possible chess moves are statistics, like typing out 1TB in a .txt file in a laptop with 40GB.
The number of possible chess games lies between 10^29241 and 10^34082.
https://wismuth.com/chess/longest-game.html
The number of legal chess positions is 4.82 * 10^44
https://github.com/tromp/ChessPositionRanking
However, as the 3 diagrams show, the vast majority of those positions contain 3 or more rooks and/or bishops per side, which makes no sense.
A better estimate is thus 3 * 10^37 positions
https://arxiv.org/pdf/2112.09386.pdf
Of these 10^17 positions are relevant.