A release-checked medium problem for training Conditional Expectation, Games.
Question
Suppose you play a game where you continually roll a die until you obtain either a $5$ or a $6$. If you receive a $5$, then you cash out the sum of all of your previous rolls (excluding the $5$). If you receive a $6$, then you receive no payout. You also have the decision to cash out mid-game for the sum of all your previously obtained rolls. Assuming optimal play, what is your expected payout? Round your answer to the nearest hundredth.
Practice focus
This Probability problem is tagged Conditional Expectation, Games. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.