Medium

Probability

You are given a fair $6-$sided die and you roll it. You can either choose to keep your roll and receive the observed value in dollars. Alternatively, you are allowed to roll again, but if the sum of your two rolls is at least $7$, you pay the value equal to your first roll. If the sum of the two rolls is less than $7$, you receive the second observed value in dollars. Assuming optimal play, what is your expected payout?

Notes

Hint