Dice payoff via Wald

You roll a die repeatedly and are paid the face value of every roll, including the last. A 4, 5, or 6 forces another roll; the game stops as soon as you roll 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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