Why is it that Btrees most of the times have a degree that is odd? What happens if they are even?
One thing that distinguishes real-world B-trees from "lecture B-trees" is that real B-trees tend to have nodes and leaves where the size in bytes is fixed. So the "degree" of a B-tree is determined by the number of keys that will fit on a page.

So if the keys vary in size (e.g. strings), the "degree" of different nodes may be different. Roughly 50% of them will have even degree.