Calculate Expected Payoff from Two Dice
Company: Sig
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Online Assessment
# Calculate Expected Payoff from Two Dice
Roll two fair six-sided dice. If the rolls differ, the payoff is the larger roll in dollars. If the rolls are equal, the payoff is negative and its magnitude is the sum of the two rolls.
Compute the expected payoff and express it as a decimal rounded to the nearest cent. Use ordinary half-up rounding.
### What a Strong Answer Covers
- All 36 ordered outcomes with the correct sign for doubles.
- A nonredundant way to sum unequal outcomes by their maximum.
- Division by 36 and correct rounding to two decimal places.
- A check that gains and losses are not accidentally combined as absolute values.
### Follow-up Questions
- What is the probability that one play has a negative payoff?
- How would the expectation change for fair `n`-sided dice?
Overview: Calculate the expected payoff of a two-dice game that rewards unequal rolls by their maximum and penalizes doubles by their sum. The derivation groups ordered outcomes by maximum, handles signed double losses, and obtains a nearest-cent expectation of 2.72 dollars.
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