d30 against a d20 with one optional reroll

Alice rolls a fair $30$-sided die and Bob rolls a fair $20$-sided die. Without seeing Alice's result, Bob may choose to reroll his die once, in which case the new value replaces the old one. The higher number wins, and Bob wins ties. If Bob plays optimally, what is the probability that Alice wins?

$17/30$. Keeping a value $b$ wins for Bob with probability $\tfrac{b}{30}$, while a reroll is worth $\tfrac{10.5}{30}$, so he rerolls exactly when $b\le10$. His win probability is $\tfrac1{20}\sum_{b=11}^{20}\tfrac{b}{30}+\tfrac12\cdot\tfrac{10.5}{30}=\tfrac{13}{30}$, so Alice wins with $\tfrac{17}{30}$.