161–170 of 195 posts
This is pretty cool. Would have been neat to see some descriptive text about encoding to integer programming problem.
I considered but decided against the complexity, haha.
I added a Github link towards the bottom of the article though. Code might not be pretty though .__.
Earlier quoted context omitted.
Is that weird? I feel like it’s plausible though. Very rare to have chess games with more than 200 moves.
It’s also rare to have one with more than 50 moves. I’m curious if this class of observation will help establish a true bounds. Especially because we don’t have a definition of what it means - my instinct is to first do that, so “infinity” isn’t the obvious upper bound.
Not sure if I'm reading your comment correctly
The upper bound of moves is 8848.5 https://www.reddit.com/r/chess/comments/168qmk6/longest_poss...
... under the rule that after 75 moves without a capture or pawn advancement the game is drawn
I'm not sure but I think the original utility and motivation for this mathematical puzzle is how to represent possible legal moves when programming chess, and this would be evidence that an 8bit unsigned integer is sufficient for the worst case scenario, although you would need some complex kind of encoding mechanism to make the representation terse enough to represent the common moves along with 7 promoted queens in…
my motiviation was intellectual curiosity and some random Lichess reading about chess engine authors wondering whether 8 bit e.g. numbers 0 to 255 (or 1 to 256), will be enough for storing the number of legal moves. Which triggered my brain: "I HAVE THE KNOWLEDGE TO SOLVET HIS FOR HUMANITY :O". It's not at all relevant practically, as you have elaborated, and there probably is a more elegant proof that 256 can't be exceeded.
Earlier quoted context omitted.
Yes, very strange that the phrase "possible moves" never occurs in the article. The key word is "possible". The article consistently just uses the phrasing "have moves" but this is not an obvious way of phrasing things to the average person (although I think it's more common in chess lingo).
"moves" includes the idea of possible. "reachable" chess positions can only be the result of moves which are only those possible, and any follow-on moves would also only be those that are possible
Earlier quoted context omitted.
in chess lingo the most common is “legal moves”
in chess lingo, most common is "moves"; only in a weird circumstance (beginners?) would you need to say "legal". the "possible" qualifier would probably be used for an "english" reason rather than a "chess" reason, to suggest "future" moves as opposed to the moves already made to get to a position. it would be more likely for whatever reason to say "how many possible moves" than "how many future/hypothetical moves",…
Sure, but the article is written in English. :-)
Earlier quoted context omitted.
If you can start from any arbitrary different point, you can just start from the point you’re intending to reach, and don't need to break any other rules. As per FIDE rule 3.10.3 "A position is illegal when it cannot have been reached by any series of legal moves". The position isn't legal per FIDE rules. Beyond there being too many queens… black could not possibly have made the last move. For white to have any moves…
Legality is a long standing term of art used by chess problem creators. Essentially it means a position withtwo kings on the board, non touching, and not both in check. And no pawns on first or eighth ranks. It has nothing to do with whether the position is reachable from standard chess rules. Along came FIDE in 1999 with its standardized nomenclature but that doesn't invalidate the terminology used by chess problem…
I don't think I’ve ever heard it used like that, and in trying to find any example other than the page we’re commenting on, I’ve only found counterexamples.
Whether it’s wikipedia’s 'Glossary of Chess Problems' or OzProblems or 'Sam Loyd and his chess problems' from 1913, they’re all using 'legal' as synonymous with 'reachable'.
Hi all, a friend of mine pointed out that my article is being discussed in this forum. I am sorry for choosing a suboptimal title and I hope that it is unambiguous now. I am grateful for your feedback and kind words! If you have any questions, also in regard to proving similar chess facts, I'd be happy to help ^^ Best regards, Tobi
This is pretty cool. Would have been neat to see some descriptive text about encoding to integer programming problem.
Author here, I considered but decided against the complexity, haha. I added a Github link towards the bottom of the article though. Code might not be pretty though .__.
Thanks for the writeup.
They dont really spell it out but they mean "from this position the player has 218 possible legal moves to choose from"