easy Games

8-Sided Dice

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

Question

Lewis is playing a game with a fair 8-sided die. If Lewis rolls any value from $1 - 7$, he adds that value to his total and can choose to roll again. If he rolls an $8$, he loses all of his money and the game ends. If Lewis plays optimally then there is a value $v$ such that once he has a total of at least $v$ he should stop rolling. What is $v$?

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.