Medium · Expected Value & Decision Theory · Numerical · ~6 min · #10

Roll Once, Maybe Reroll

Real interview · Citadel, Jane Street +1

You roll a fair six-sided die and are paid its face value in dollars. After seeing the first roll you may either take that payout or roll again once and take the second roll's value (you cannot go back to the first).

Under the optimal strategy, what is the expected payout?

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Worked solution

Give the problem an honest attempt first, then reveal the full explanation.

Reported in interviews

CitadelGlassdoor interview question
Jane StreetGlassdoor interview question
Part (b) of a three-part question.
Squarepoint CapitalGlassdoor interview question

Candidate-reported and unverified; the firm may phrase it differently or no longer ask it. The wording here is our own paraphrase, and the solution was written and checked independently of any answers posted at the source.

Concepts

Backward inductionOptimal stopping

Relevant for

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