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3

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}] &=& \...


7

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)...


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