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Should you play a dice payout game?

PayPalData Scientist · Onsite
EasyData ScientistOnsiteStatistics & Math

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This question evaluates understanding of probability, expected value, and payoff-driven decision-making by requiring computation of expected return from discrete game outcomes. It is commonly asked to assess quantitative reasoning in the Statistics & Math category and primarily tests conceptual understanding of expected value and probabilistic reasoning rather than practical implementation.

Two players each roll a fair six-sided die once.

  • If you win (your roll > opponent’s roll), the opponent pays you $n.
  • If the opponent wins or it’s a tie (your roll ≤ opponent’s roll), you pay the opponent $m.

Assume both dice are fair and independent.

Questions

  1. What is the expected value of playing one round as a function of n and m?
  2. For what values of n and m should you choose to play?
  3. (Optional) Show a short Python snippet that computes the expected value analytically.