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Ah, wow, I read the article wrong all this time, thank you. I thought they meant "the maximum number of moves you can make to reach any chess position is 218", and I was wondering why the article made no sense to me.
The word 'available' inserted at the right spot would make all the difference in clarity here.
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There are no more than 218 ways to interpret this title
It'll take at most 218 comments on HN to figure out the meaning of the submission title
The black pawn on b2 is eating a lot of possible moves for the other pieces… It has only one legal move, take the Knight on c1. If that pawn wasn't there it would free that square for 4 white queens and a Knight. But of course the black king would already be in checkmate so these moves wouldn't really be available. Tempting to put that e5 Queen elsewhere so that it doesn't immediately checkmate and leave the b2 squar…
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)
The 8.7e45 "restricted" number in that repo rules out certain patterns of pawn promotions. It looks like the 5.68e50 "general" number is the true upper bound, allowing any promotions possible.
They dont really spell it out but they mean "from this position the player has 218 possible legal moves to choose from"
Ah, wow, I read the article wrong all this time, thank you. I thought they meant "the maximum number of moves you can make to reach any chess position is 218", and I was wondering why the article made no sense to me.
This is not so interesting then…
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…
> 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 the same 256-moves space. If you have an algorithm for generating the list of legal moves in a position that always generates them in the same order, you can just use the index at which the move is in the list. Of course that would come at the cost of…
Right, that's exactly what I'm saying, the algorithm that generates the list of legal moves would be an encoder (maps a move into an index), and the reverse would be a decoder (maps the index into a move).
You don't necessarily need to generate the list of legal moves, though. Consider a 16 bit encoding where the first 4 bits represent the piece moved, and the next 5 bits represent the direction, and the next 4 bits represent the distance and so on.
They dont really spell it out but they mean "from this position the player has 218 possible legal moves to choose from"
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
They dont really spell it out but they mean "from this position the player has 218 possible legal moves to choose from"
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).