Should you play a dice payout game?

Q: Should you play a dice payout game?

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.

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Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

Question

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

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

Should you play a dice payout game?

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