# Tag Info

The Geometric Distribution comes in handy. Consider the case in which the very initial saving throw fails. Denote with $p$ the probability of a successful saving throw $n_i$ the number of turns in which the $i$-th saving throw fails. The expected value for the total damage can be written as  \begin{eqnarray*} \mathbb{E}[{\rm damage}] &=& \...
Let us assume that our victim has a probability $p$ of passing the DC 13 Constitution saving throw, and we will assume that $p$ is greater than 0 and less than 1 (that is, passing and failing the save are both possible). Let us also, for simplicity, measure damage in number of d6's (we can convert to actual damage at the end; 1d6 has a mean damage of 3.5)...