01 / The decision
Would you keep a 3?
Compare the payout in front of you with the expected value of one fresh roll. Decide before looking at the solution.
JANE STREET–STYLE INTERVIEW QUESTION
You rolled a 3. Keep it or roll again?
Roll a fair six-sided die and win its face value in dollars. You can keep your first roll or roll once more, but then you must accept the second result. What is your strategy, and how much is the game worth?
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Your turn · Jane Street–style probability question
How much is the game worth?
A fair die pays its face value in dollars. After your first roll, you may keep the result or reroll once for free. If you reroll, you must accept the new result. What is the expected payout with the best strategy?
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Three decisions. One interview question.
02 / The price
What would you pay to play?
Work out the expected payout when you follow your best strategy. Explain your calculation as you would in an interview.
03 / The follow-up
What if the rules change?
Add a $1 reroll fee, then try two free rerolls. Work backward from the final decision to find the new strategy.
THE PRACTICAL DETAILS
Before you take the next step.
What does this question test?
Expected value, decision-making under uncertainty and working backward from a final choice. A strong answer explains both your strategy and what the game is worth.
How do I see the solution?
Choose your answer and enter your email to unlock the worked explanation and two follow-up questions on this page. You’ll also receive Quant Blueprint practice questions, preparation tips and program emails. Unsubscribe anytime.
What should I try after solving it?
Try the $1 reroll fee and the two-reroll version in the worked solution. Then explore more probability questions or book your free quant consultation to discuss your preparation goals.