100-sided dice roll problem When should I stop rolling if it costs $1 for each roll and I earn only the value of the final roll shown on a 100-sided dice roll? My intent is to maximise profit and I have unlimited rolls

Maybe I don't understand your question, in which case I apologise. The expected payoff after $n$ rolls is the value of the last roll. This is,
$$
\mathbb{E}[R_n]=\sum_{i=1}^{100} p_i i = 50.5
$$
where $R_n$ is the revenue from the last roll; $R_n$ takes values $i=1,\ldots,100$ with each
value having probability $p_i=1/100$. Therefore the expected payoff is not a function of $n$. The cost of $n$ rolls is $n$ dollars. So my expected payoff is $50.5-n$. The maximum expected payoff is for $n=1$.
