<s>[INST] An artist gives points randomly based on the probability distribution $p\colon \mathbb{N} \to \mathbb{R}$, $p\left( n \right) = \frac{n}{2^{n+1}}$. So, if she decides to give $5$ points, it's $\frac{5}{2^{5+1}}$; if she decides to give $1$ point, it's $\frac{1}{2^{1+1}}$. Also, she asks a model to draw one dot for each point that she gives. Then, she gives herself $n$ points and asks the model to draw $m$ extra dots, so that $n + m = 100$ and it is uncertain which dots the model drew.

Which $m$ causes the most uncertainty in terms of expected Shannon entropy?[/INST]