Hard · Expected Value & Decision Theory · Numerical · ~12 min · #54
100-Sided Die, Rerolls Cost a Dollar
Real interview · Jane Street
You roll a fair 100-sided die (faces 1–100). After each roll you may stop and receive the face value in dollars, or pay 1 dollar to roll again. You may reroll as many times as you like; the first roll is free.
What is the fair value of the game under the optimal strategy?
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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
- Jane StreetGlassdoor interview question
Part 3 of a longer question that starts with one and two rolls.
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.
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