Fair price of a die that rerolls on a six
You roll a fair die. If it shows a 6 you roll once more and are paid the value of that second roll; on any other first result you are paid the first roll. What is the fair price to play (its expected payout, in dollars, to four decimals)?
Show hints (2)+
- Condition on the first roll: a 1–5 pays its face (average 3), a 6 triggers a reroll.
- The reroll branch is worth a full die's mean 3.5, not 6 - weight the two branches by 5/6 and 1/6.
Answer
Reveal answer →Final answer
3.0833 (± 0.001)
Want the full step-by-step worked solution? It's part of Premium - along with a worked solution for every question in the bank.
Asked at: Game-Based Aptitude, ETF Market-Making