Shannon Entropy

I have absolutely no idea what this is or how to use it, but I would like to learn more… I stumbled into it trying to figure out how to calculate the entropy of passwords.

Entropy (information theory) - Wikipedia

Given a discrete random variable $X$, which may be any member $x$ within the set $\mathcal{X}$ and is distributed according to ${p: {\mathcal {X}}\to [0,1]}$, the entropy is

$$H(X) := -\sum_{x\in \mathcal {X}} p(x) \: \log \: p(x)$$

where $\sum$ denotes the sum over the variable’s possible values.

Changing the base of the logarithm varies by application. I am going to have to learn quite a bit to tackle this topic further.