Decide if a dice-betting game is favorable

You are considering a game against a “house” using fair six-sided dice. Rules: - You roll one die; the house rolls one die. - If your roll is strictly higher than the house’s, you **win** and the house pays you **n dollars**. - If the house’s roll is higher **or the rolls tie**, you **lose** and you pay the house **m dollars**. Tasks: 1) Compute the expected value (EV) of playing one round as a function of `n` and `m`. 2) Derive the condition on `n` and `m` under which you should play if you are risk-neutral. 3) Briefly describe how you would verify the EV via a simple Python Monte Carlo simulation (no need to write production code).