Reduced Ordered Binary Decision Diagrams (ROBDD) are an efficient data structure for representing boolean functions of multiple variables $f(x_1,x_2,...,x_n)$. I would like to get an intuition for how efficient they are.
For instance, for data compression, we know that data with low entropy (some symbols appearing more often than other, many repetitions) can be compressed very well while completely random data cannot be compressed.
Is there an analogous intuition for estimating how efficiently ROBDDs can represent a given boolean formula?
For example, I have heard that multiplication of $n$-bit numbers cannot be represented efficiently, the minimum ROBDD size is exponential in $n$. Do you know of an intuitive argument that explains why this is the case?
Related question: intuition about efficiency of BDDs that calculate numbers (multiple terminal BDDs, etc.)