100-side dice with number 1,2,...,100 on each side. You get paid $50 if you roll a 50, $75 if you roll a 75 etc. If you are unsatisfied with the result, you can pay $1 to roll again, you can roll as many times as you want. Question: what's the maximal amount you are willing to pay to enter this game (roll for the first time). Note that each subsequent play you only need to pay $1 to play again. What's your strategy?