Answer
See below.
Work Step by Step
By definition, the expected value is the sum of each outcome multiplied by its probability.
Hence here the expected value: $\frac{1}{6}\cdot(5-1)+\frac{5}{6}\cdot(-1)=-\frac{1}{6}$.
This means that in the long run a player is expected to lose $\frac{1}{6}$ each turn he plays on average.
