You have a fair dice. If you roll it and get number X, you are paid $X. You can also choose to roll the dice again and you will be paid with the new number instead. You have 2 more chances to roll again after your first roll. What is the expected amount you will get from playing this game?
If the above dice is fairly unfair, i.e. the weight on certain faces are higher than the other faces, however you don't know which faces are heavier. Now the expected payoff of this game will be higher, same or lower than that in Q1?
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