Game1 : a dice roll with a 100-faces dice, labeled from 1 to 100. 1. You get to roll once and receive the amount of dollars labeled on the face, how much would you like to pay for this roll. 2. How much would you pay if you can roll the dice twice if you are unsatisfied with the first outcome? 3. You can roll the dice infinite times, and costs 1 dollar for each roll except the first one. What is your strategy? Game2: you are competing in a game with 2 other players. with a 21-faces dice (labeled 1-21). All three of you gets to choose a number and then roll the dice. Whoever chose the number closest to the outcome wins. What is your strategy? another twist: what if all three of you can communicated?