One minus Infinite 
How many possible games of chess are there?
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3 a win, lost and drawn game
thechessdreamer wrote:
There are only... 1023 grains of sand on Earth.
Oh, that's not much sand.
There are 20 possible moves for white to start the game, and 20 possible moves for black to then respond with. This means that there are 400 different possible chess positions after each player has moved just once. Even though there are not infinite possible games in chess, there is a mind breaking number of them.
Also, the maximum number of moves a game could last for would be about 5,500 moves. If one piece is captured every 50 moves, or a pawn is moved every 50 moves, then that adds up to 5,500 moves for each player. I may be a little bit off with the pawn moves, but even if the pawns never moved, the game could last for 1,500 moves. As long as no position is repeated too many times, of course.
Godfrey Hardy, a famous 20th century mathematician calculated the TOTAL no. of chess games possible: his estimate was 10^10^50. The 10^120 approximation is the rough estimate of the 30-40 move games in chess.
The number of games is enormous because chess has so many transpositions: any position can be reached by many many different move orders. The number of positions is much smaller.
The question is not well posed. You should have asked "How many reasonable games are there?". If we are eliminating "unreasonable" games (where players just move pieces without eating other pieces or withouth any intent of playing) than I think the number of possible games falls drastically.
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 4.8*10^44.
https://github.com/tromp/ChessPositionRanking but those positions have 3 or more rooks or bishops per side.
A better estimate is 3*10^37 reasonable positions.
https://arxiv.org/pdf/2112.09386.pdf
Of these about 10^17 are relevant.
marcorossi1968 wrote:
The question is not well posed. You should have asked "How many reasonable games are there?". If we are eliminating "unreasonable" games (where players just move pieces without eating other pieces or withouth any intent of playing) than I think the number of possible games falls drastically (my note: he asked for possible games because he wanted to know possible games, not because he wanted reasonable ones)k
marcorossi1968 wrote:
The question is not well posed. You should have asked "How many reasonable games are there?". If we are eliminating "unreasonable" games (where players just move pieces without eating other pieces or withouth any intent of playing) than I think the number of possible games falls drastically.
By the way he mentioned that he wasn’t only thinking about reasonable games in ghe thread
Too many to count for sure.
vickalan wrote:
thechessdreamer wrote:
Some have estimated it at around 10100,000. Out of those, 10120 games are "typical": about 40 moves long with an average of 30 choices per move.
There are only 1015 total hairs on all the human heads in the world, 1023 grains of sand on Earth, and about 1081 atoms in the universe.
Your exponent symbols didn't show up or you forgot to include them. By 10120 I assume you mean 10^120 (10 with 120 zeros). 1081 atoms in the universe is 10^81? The number of games in chess is more than 10100,000 but 10^100,000 sounds too high!
How is 10^100,000 too high? After all, a Chess game can go on for 5900 moves, so the possibilities are endless. I think 10^100,000 might be too low
Some have estimated it at around 10100,000. Out of those, 10120 games are "typical": about 40 moves long with an average of 30 choices per move.
There are only 1015 total hairs on all the human heads in the world, 1023 grains of sand on Earth, and about 1081 atoms in the universe.
Your exponent symbols didn't show up or you forgot to include them. By 10120 I assume you mean 10^120 (10 with 120 zeros). 1081 atoms in the universe is 10^81? The number of games in chess is more than 10100,000 but 10^100,000 sounds too high!