You are given a die with 100 sides, numbered from 1 to 100. When you roll the die, you can choose to either (a) take the number of dollars equal to the number of dots that show up, or (b) pay $1 to reroll. You can continue to reroll as many times as you like, but you can only keep the result of your final roll. What is the optimal strategy, and what is the expected value of playing optimally?