Challenge: Infinite Expected Value

Some probability processes have infinite expected value. Example: flip coin until heads. Expected flips = 2. But: pay $2^n$ if first heads is on flip $n$. Expected payout = $\sum_{n=1}^{\infty} 2^n \cdot 2^{-n} = \infty$.

This is the St. Petersburg paradox. In DP, watch for recurrences like $E = 1 + E$ with probability 1 (infinite loop). The expected value is undefined. make sure your probability DP has absorbing states (termination) with positive probability from every state.