We're going to play a game. You go first. You flip a coin; if you get heads, I give you $30. If you get tails, you give me the coin and I flip. If I get heads, you give me $30; if I get tails, I give it back to you. We keep going until one of us gets heads. What is the maximum amount you would be willing to pay to go first? Give a 50% confidence range and a 90% one for your answer. Why?