Medium · Expected Value & Decision Theory · Numerical · ~6 min · #47
Die Game with Two Rerolls
You roll a fair six-sided die and are paid its face value in dollars. After each roll you may stop and take that value, or roll again — but you get at most three rolls in total, and if you reroll you forfeit the earlier value.
What is the fair value of this game under optimal play?
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Worked solution
Give the problem an honest attempt first, then reveal the full explanation.
Reported in interviews
- Jane StreetGlassdoor interview question
Asked as a three-part sequence: one roll, one reroll, two rerolls.
Followed by a question on comparing poker tournaments by entry fee, prize and win probability.
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.