Chapter 11.2, Problem 29E

A reader wrote to the "Ask Marilyn" column in Parade magazine, "Say you're in a public library, and a beautiful stranger strikes up a conversation with you. She says: 'Let's show pennies to each other, either heads or tails. If we both show heads, I pay you $3. If we both show tails, I pay you $1. If they don't match, you pay me $2.'… As the game is quiet, you can play in the library. But should you?" Source: Parade magazine.

(a) Find the optimum strategy for you and for the stranger, as well as the value of the game. Should you play?

(b) Marilyn replied, "She can win easily. One way: If she shows you twice as many tails as heads, she wins an average of $1 for every six plays." What strategy is Marilyn assuming that you use?

(c) If the stranger did use the strategy in part (b), what strategy should you use to maximize the value of tire game for you? What is the value in that case?