You are given a fair sided die and 100 actions in a game. The die starts with upface . The two options you can perform are to roll and to take. Performing a roll re-rolls the current upface of the die. Performing a take allows you to cash out the current upface of the die. Note that the game does not end when you perform a take and that you do not have to roll between takes. Therefore, for example, you can just perform takes on the initial upface and walk away with guaranteed. Your strategy is to cash out the upface when you roll at least some threshold for the first time. You fix this at the beginning of the game. Assuming rational strategy in selecting , what is your expected payout on this game?