easy Games

Evenly Double

A release-checked easy problem for training Expected Value/LOTUS, Dice.

Question

A standard fair $(2n)-$sided die is rolled. If the upface is odd, you are paid out the upface. If the upface is even, you are paid out twice the upface. You are also given the opportunity to roll your die again if you're unhappy with the first roll. Under an optimal strategy, what is your expected payout when $n = 4$?

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.