Game 1: You roll a 100-faced die labeled from 1 to 100. 1. You roll once and receive the amount in dollars that appears. How much would you pay for this roll? 2. How much would you pay if you can roll twice and keep the higher result? 3. If you can roll the die an infinite number of times, but each additional roll after the first costs $1, what is your optimal strategy? Game 2: You are competing with two others and a 21-faced die labeled 1 to 21. Each player picks a number, then the die is rolled. The player whose number is closest to the result wins. What is your optimal strategy? How does your strategy change if all players can communicate?