Problem

1. A person randomly types an eight-digit number into a pocket calculator. What is the probability that the number looks the same even if the calculator is turned upside down?

2. You play a dice rolling game where you have two choices:

(a) Roll the dice once and get rewarded with a prize equal to the outcome number (e.g, $3 for number "3") and then stop the game.

(b) You can reject the first reward according to its outcome and roll the dice a second time, and get rewarded in the same way.

Which strategy should you choose to maximize your reward? That is, for what outcomes of the first roll should you chose to play the second game? What is the statistical expectation of reward if you choose the second strategy?