Maximum Fair Penalty in a Dice Payout Game

$ through $n$). Let $A$ and $B$ be disjoint subsets of the $n^2$ possible outcomes. - If the roll lands in $A$, you receive $\$p$. - If the roll lands in $B$, you pay $\$q$. - If the roll lands in neither $A$ nor $B$, you re-roll at no cost, and keep re-rolling until the outcome falls in $A$ or $B$. Given that $p$ is fixed, find the maximum value of $q$ such that your expected payout is non-negative. Evaluate for the specific case $p = 100$, $n = 10$, $|A| = 25$, and $|B| = 50$.