A release-checked easy problem for training Expected Value/LOTUS, Dice.
Question
Suppose that you are playing a game with two fair dice $-$ one which is 6-sided and one which is 8-sided. You first roll the 6-sided die and have the option to keep the value on that die, or to roll the 8-sided die instead and keep that value. If you are paid whatever the value of your last die roll was, what is your expected payout if you play to maximize your expected payout?
Practice focus
This Games problem is tagged Expected Value/LOTUS, Dice. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.