ChessCounter

What is the least number of bits that can describe any reachable chess board? update: article says there are approximately 8.7x10^45 reachable chess positions and https://github.com/lechmazur/ChessCounter says this is an upper bound. (this would correspond to about 153 bits)

Your page only mentions > Upper bound estimate of possible legal chess position (counts en passant, castling, sides to move, allows underpromotions): 8.7E+45. But how exactly is this number determined? Is this a sampling based estimate? My 8726713169886222032347729969256422370854716254 is an exact upperbound on the number of so-called urpositions, and is not sampling based. In any case it will be easier to continue this discussion at https://github.com/lechmazur/ChessCounter/issues/1

Note that the number of possible legal positions will likely be largest with fewer than 24 pieces. For regular chess, I've calculated that there are most legal positions for 29 pieces: https://github.com/lechmazur/ChessCounter?tab=readme-ov-file...

You don't need to care about possible games, but game states, what's the best result and the move to achieve it in each. Another user computed an upper bound at 8.7E+45 positions: https://github.com/lechmazur/ChessCounter . I pointed out that our planet has about 1E+50 atoms. And we can further compress the database by perhaps two orders of magnitude if we don't store symmetric positions or positions close to mate. A Kardashev 2 civilization could play perfect chess.

No, it's not close to being solved. I made a new estimate recently at there are about 8.7E+45 unique positions: https://github.com/lechmazur/ChessCounter. You don't need to analyze all of them to generate the proof but it's still far beyond our computational and storage capacities to solve chess.

"Claude Shannon calculated that there are around 10^120 possible games of chess in his seminal paper Programming a Computer for Playing Chess in 1950." I've just finished a weekend project to calculate the number of legal chess positions and there are about 8.8E+45: https://github.com/lechmazur/ChessCounter. For people considering making a chess program, take a look at this message board http://talkchess.com/forum3/index.php. As the author mentions, python-chess is really nice. The project maintainers are very responsive - a bug I found was fixed within a day.