Decide if a dice-betting game is favorable
Company: PayPal
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Onsite
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).
Overview: This question evaluates understanding of probability theory, expected value computation, risk-neutral decision criteria, and basic Monte Carlo simulation concepts within the Statistics & Math domain, testing both conceptual understanding of discrete probabilistic outcomes and practical application of simulation-based verification.
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