You play a game with the following rules: You will roll a standard fair sided die. If you roll a , the game ends and you receive no payout. Otherwise, you have two options: You may quit and receive , where is the upface of the previous roll, or you can roll again under the same rules. There is no limit on how many times you can re-roll if you don't obtain a . Assuming you play optimally, what is your expected payout?