Compute Optimal Die Re-roll Strategy
Company: Capital One
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Onsite
A fair six-sided die pays its face value in dollars. You may roll up to three times total.
- After the first or second roll, you may either keep the observed value and stop, or pay $1 to reroll.
- After the third roll, you must accept the result.
What strategy maximizes expected net payout, and what is the resulting expected value? State the optimal stopping rule after each roll.
Quick Answer: This question evaluates a candidate's understanding of optimal stopping, expected-value computation, and decision-making under uncertainty in probabilistic settings. It is commonly asked in Statistics & Math interviews to assess quantitative reasoning and trade-off analysis, representing a practical application of probability and expected-value calculations rather than purely conceptual knowledge.
