[harerazer]

While this post has a good amount of substance, I found it rather hard to understand due to small mistakes (or hidden assumptions, or something else?). All of which seem easily fixed/clarified, but these sorts of things are unnecessary friction for readers.

Edit: Thanks to Jasper for stating the big hidden assumption made by the author - that he is only considering the case of being blocked by enemy pieces, not one's own pieces. This is motivated by the fact that one can use the same side occupancy board to trivially remove all moves that are illegal due to self-blocking. This resolves many of the technical issues, although again, it should be be made explicit. The typos/silly errors and pedagogical mistakes remain.

Some examples:

- According to the first bitboard (and the convention stated in the OP), A2 has index 8, not 1.

- In the second bitboard, the rook on e4 should be able to move to e1,a4,e8,h4.

- max of 9 relevant occupancy bits for a bishop - how? A bishop on e4 for example would have to check b1,c2,d3,f5,g6,h7 and a8,b7,c6,d5,f3,g2,h1 for a total of 13 bits. Similar mistake for a the rook.

- The so called "original" masked occupancy bitboard was not mentioned previously

- That same bitboard has variables b1,b2,b3,b4,b5 on it, a notational collision with the squares b1-b5. - The variables b1-b5 are in the wrong place (presumably they were meant to be on c3,d4,e5,f6,g7 since the bishop is on b2, and again there is the question of why not h8 and the other missing squares).

- Magic number comes out of nowhere. What is it doing? Presumably the purpose is to extract the relevant positional bits to be the most significant ones while keeping the order, done through the multiplication + bitmasking, but this should be explicitly stated. We also have no idea how it is derived.

- What are the "collisions" actually collisions of? It would be nice to see an example of this.

[claytonwramsey]

Hi, I'm the original author! This is my first post. I might talk more about chess engines in my blog in the future...

Some background: I taught a class on chess engines this spring (at some point, I'll write up a postmortem on it, maybe). This post was originally derived from my lecture notes for the class, and was (if I remember correctly) the 5th lecture, so I could make more assumptions about the students being steeped in chess-engine lingo.

Josh Triplett is entirely correct here on the masking technique. There are two steps to sliding-piece move generation: first, creating the set of squares a piece can "see," and then the set that it can attack. Magic bitboards are used for generating the set of squares a piece can see.

In terms of where magic bitboards come from: there's not that much in terms of logical derivation. You just have to kind of squint and say, "yeah, I believe that'll work." Magic numbers are found by brute force trial-and-error.

Collisions are caused when the magic multiply doesn't actually yield a perfect bit extraction. Imagine if O * M >> 59 was instead some gross expression of all five bits. The magic number for B1 here is actually an exception - things are not usually so easy. However, if two different positions have the same attack set, and they get sent to the same index by a magic multiply, it doesn't matter that they collided because they map to the same value.

[JoshTriplett]

> - max of 9 relevant occupancy bits for a bishop - how? A bishop on e4 for example would have to check b1,c2,d3,f5,g6,h7 and a8,b7,c6,d5,f3,g2,h1 for a total of 13 bits. Similar mistake for a the rook.

If I'm understanding correctly: it's trivial to use a mask with the occupancy bitmap for white/black to eliminate moves atop your own pieces, and generate captures for moves atop your opponent's pieces. The sliding move handling needs to look up whether a piece is in the way of your destination. So, the sliding move handling doesn't need to handle spaces on the edge of the board, because they'll never be in the way of another square.

[harerazer]

This makes a lot of sense and gives context to the assumption that we only need to handle the case where an opponent's piece is in the way. Would be great if the author took the 2 sentences to explain this near the beginning of the article.

[Jasper_]

> - In the second bitboard, the rook on e4 should be able to move to e1,a4,e8,h4.

It's trying to find the set of legal moves. Or, rather, it's trying to find the set of illegal moves that it can exclude from the subset of possible moves. The only thing determining whether a move is legal is whether there's a piece in the way of that move, aka whether a piece is occupying a square, that's what the bitboard check is about. If E1 is occupied, the set of legal moves is the same as if it is unoccupied, so it is irrelevant to check the bitboard for E1. I agree the article could be clearer about this.

[harerazer]

I'm clearly misunderstanding something here. Assuming the rest of the board is empty, if e1 is occupied, the rook can't move to e1, whereas if it isn't occupied, the rook can move to e1, so there is at least one position in which we must check e1. What am I misunderstanding here?

[Jasper_]

Oh, I was assuming it was occupied by an enemy piece, and would capture it. You're right that if it was occupied by an allied piece, it's not a legal move.