[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.