MediumMarket Making & Games
Roll, Keep or Re-roll
Jane StreetSIG / Susquehanna
You roll a fair die and are paid its face value in dollars, but you may re-roll up to two times, keeping only the final roll. Playing optimally, what is this game worth?
Approach
Value the game with zero re-rolls first, then step back.
At each stage keep the roll only if it beats the value of continuing.
Answer
Show the final answer
The answer is 4.67. Sign in free for the full worked solution and to check your own answer.
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