Dice payoff via Wald

You roll a die and are paid its face value; on a 4, 5, or 6 you must reroll (forfeiting the current value), and the game stops on a 1, 2, or 3. What is your expected total payoff (in dollars)?

Show hints (2)+
  1. How many rolls do you expect to make?
  2. Wald: E[sum]=E[N]E[X]E[\text{sum}] = E[N]\,E[X].

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Asked at: Optiver, SIG

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