According to AI: With "no captures or promotions" it turns the full game tree to ≈10^120 possible games. However, even with this pruning, the number of unique, legal, non-capturing positions quickly becomes computationally intractable to count ...
But I guess if you are only talking about one of these two different game links given than there must be a way to discover how many legal moves each move could have done, from best to worst possibilities the tree would be large.
https://www.chessgames.com/perl/chessgame?gid=1268705
https://lichess.org/broadcast/iii-kingston-invitational-2024/round-7-adjourned/LmSWG74j/yUcQ4p4p
As I wrote it in the study, I believe that some of the positions are actually not reachable.
Nonetheless, nice idea and post, thanks!
@Coinduction said in #22:
> As I wrote it in the study, I believe that some of the positions are actually not reachable.
>
> Nonetheless, nice idea and post, thanks!
Your believe has been refuted, I created a proofgame for position 1. The key idea is that the last moves were Qxc1+ Bb1 and now it's White's move and White has 218 moves. Besides, I did not claim that all of the positions found by the Gurobi solver were reachable - people found a reachable position with 218 moves 60 years ago - I proved that there can't be a reachable one with 219 moves :) Nontheless, if I'm not missing anything, they all seem pretty reachable?
Bug bounty: I offer 5 dollars/euros, sent via PayPal and name mentioning at the end of the article to the first person to PM me with a solid argument about why (I don't think this is the case) any of the 12 positions would not be reachable :)
> chess engine developers, you can finally stop worrying. 256 moves will be enough.
Thanks!
an interesting and well-written article, ty
@Tobs40
Can you make a complete definition of what a reachable position is?
And was your claim that the given position was not reachable by a path that would be longer than 218?
I can try to figure it out from the Q&A. But having it declared at the beginning and not assumed would help my slow mind (slow in some ways, fast in others). I scanned the artcile and I could not find a declarative definition.
I might have missed something. This is not about the approach of big space from which to reason; that is almost a principle of non-constructive mathematics (not sure there). This remineds me of analog sound synthesizer problem, for musicians. Adding pure sine wawes, versus filtering from some white noise. An analogy of approaches. But the idea is that the bigger space must contain the critters we search.
So I am curious about compact definitions of the critters, the space, and the question mostly.
or where to find them.
Here is an attempt not at that, but at understanding, which I am not certain of. hence the questions above.
A reachable position. A position such that there exist a legal path to it. It would need a construction proof, right?
Now you question: The space of all legal paths that read a position, or that specific position, for which we know there is already on path, all the paths have to be shorter than 219 moves? Something is missing in the definition of mine.
for cooperative is also legal. and fold repeats. It can't be best play can it? or the shortest path can't be longer than 218?
I am not talking about your proof mechanism but the whole problem definition which I seem to not get. yet.
This is a very, very strange post, with all those pictures of clearly impossible and illegal positions.
Fantastic post.
To get a Gorubi licence do I need an academic email?
Did you try finding the position with the most moves but allowing extra pieces (ie. the most with the position being unreachable).
@dboing I think you misunderstand the post. The claim is that white can have a maximum of 218 moves in any reachable position. The number of moves to reach that position isn't discussed.
@krovsky The positions all seem reachable to me, why don't you think they are?