Katkat
Back

Decide if a dice-betting game is favorable

PayPalData Scientist · Onsite
EasyData ScientistOnsiteStatistics & Math

Last updated

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.

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).