Decide if a dice-betting game is favorable

You are evaluating a game against a “house” played with fair six-sided dice. Rules:

• You roll one die, and the house rolls one die.
• If your roll is strictly higher than the house’s roll, 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. Find the expected value (EV) of 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 through a simple Python Monte Carlo simulation (no need to write production code). Overview: This question assesses probability theory, expected-value computation, risk-neutral decision criteria, and basic Monte Carlo simulation concepts in the Statistics & Math domain. It probes both conceptual understanding of discrete probabilistic outcomes and the practical use of simulation-based verification. Read the full data scientist interview experience this question came from.