God might know - so we could pray for guidance.
And the devil is well known to play chess (usually with DEATH and while playing the fiddle) so for some perfectly triffling and incorporeal payment I expect he would whisper the answer to you.
WHAT HAPPENS IN THE CHURCH STAYS IN TE CHURCH
this was the best my online calculator could handle so this is my solution to the number of positions in chess
1022134645914424867528704000 times 1026043200 times 4680030820902586690712371200
" Enjoy Chess Many Possibilities " - Samanthnaidu
The upper bound that I can calculate is 5.58×10⁵² positions.
The number of both king positions on the board is (4×60)+(24×58)+(36×55) = 3,612.
The number of ways to place 15 white pieces into the remaining 62 squares is less than C(62, 15)×6¹⁵.
The number of ways to place 15 black pieces into the remaining 47 squares is less than C(47, 15)×6¹⁵.
So we have upper bound 3,612 × (C(62, 15)×6¹⁵) × (C(47, 15)×6¹⁵) or about 5.58×10⁵² positions. This number includes pawn promotions and many illegal positions.
For a more detailed proof, check out this blog.
https://www.chess.com/blog/jomsup/math-proves-upper-bound-for-the-number-of-chess-positions
I read this, but it includes only legal positions:
Possible Positions: 10^43 to 10^50
Also this:
Possible games (move sequences): around 10^120
Possible games, yes. Positions, no.
There is a difference.
The number of Possible distinct and not distinct games is INFINITE
Possible games, yes. Positions, no.
There is a difference.
The number of Possible distinct and not distinct games is INFINITE
Nope
I don't believe that it is impossible to know. It "just" a matter of calculations. But..., and this is the big but, it is tremendously difficult to know and not all that interesting. So why would a mathematician devote a ton of time to answering a question that isn't interesting? They won't. That's not really on the path to tenure at a top university.
I don't believe that it is impossible to know. It "just" a matter of calculations. But..., and this is the big but, it is tremendously difficult to know and not all that interesting. So why would a mathematician devote a ton of time to answering a question that isn't interesting? They won't. That's not really on the path to tenure at a top university.
Mathematicians. Top universities. Devote time and resources to the question.
https://wismuth.com/chess/statistics-positions.html
https://people.math.harvard.edu/~elkies/FS23j.04/sources.html
See the link above your post. Francoise Labelle's PhD work at UC Berkeley was math and computer science.
It's true that he did not generate an exact number. But, his numbers give us a reasonably good estimate. The other link is to a Harvard mathematician who is building on Labelle's work.
Possible games, yes. Positions, no.
There is a difference.
The number of Possible distinct and not distinct games is INFINITE
Nope
yes, you will just start to repeat already played games INFINITE AMOUNT OF TIMES
ALSO IF YOU ARE NOT PLAYING FOR A WIN YOU CAN MOVE PIECES AROUND INDEFINATELY
ALSO IF YOU ARE NOT PLAYING FOR A WIN YOU CAN MOVE PIECES AROUND INDEFINATELY
I would disagree, as the game cannot go on indefinitely due to the 50 move rule. I think the longest recorded computer generated game was something like 6,000 moves or something like that.
There's at least 4