You are invited to a dice game where you can make some dollars. The rule of the game is as follows:

You keep rolling a six-sided fair die until you get a $6.$ For each non-$6$ die roll, you receive $\$1.$ There is no payout for the $6$ you rolled last, and your game ends there.

How much is your expected return on this game? Keep reading to learn a useful technique of computing expected values, or skip ahead to today's challenge.