Too Much Match I

Question

You roll two fair n-sided die with the values $1-n$ on the sides. If you roll two ones on the dice, you receive $\$p$ as a payout. If you roll a $1$ and something else that isn't a $1$, you must pay $\$q$. If you receive anything else, you re-roll with no penalty until one of the two above outcomes occurs. If $p$ is fixed, find the maximum value of $q$ such that the game has non-negative expected payout when $p = 120$ and $n = 7$.