Minimum expected cost through an unconventional graph with probabilities at which edges are selected
Once you know the expected success rate for room 3 (given a certain budget), you should be able to work out the expected success rate for room 2 (given a certain budget).

In other words, let $A[r,b]$ denote the probability of success when starting at room $r$ and starting with budget $b$, using the optimal strategy.  Given $A[r+1,\cdot]$, you can compute $A[r,\cdot]$ via a simple recurrence (consider all possible things you could buy, and the probability of beating room $r$, and how much that reduces your budget when starting at room $r+1$).  This immediately leads to a dynamic programming algorithm for your problem.

If charms persist from one room to the next, use $A[r,b,c]$ where $c$ is the set of charms you already have when you start at room $r$.