A release-checked medium problem for training Cards, Expected Value/LOTUS.
Question
Suppose that you have two standard fair 8-sided dice, one of which is colored black and one of which is colored white. Find the fair value of the following game: Each dice is rolled at the same time. If the two dice show the same value, the game ends. If the white dice shows a value at least $2$ greater than the black dice, you earn $\$1$ and get to roll again. In any other case you earn nothing, but are allowed to roll again.
Practice focus
This Probability problem is tagged Cards, Expected Value/LOTUS. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.