Consider \(f(x) = x/10\) over \(R\) = {1,2,3,4} where the payout is 10 euros if x=1, 5 euros if x=2, 2 euros if x=3 and -7 euros if x = 4. Then your value function would be
\begin{equation*}
v(1)=10, v(2) = 5, v(3)=2, v(4) = -7.
\end{equation*}
Computing the expect payout gives
\begin{equation*}
E = 10 \times 1/10 + 5 \times 2/10 + 2 \times 3/10 - 7 \times 4/10 = -2/10
\end{equation*}
Therefore, the expected payout is actually negative due to a relatively large negative payout associated with the largest likelihood outcome and the larger positive payout only associated with the least likely outcome.