To calculate the expected return for one roll of this die, we need to determine the probability of each outcome and multiply it by its respective return.
Given:
Red result wins: This occurs on one of the faces, so the probability is 1/3. The return is 1 (winning).
Blue result: This occurs on one of the faces, so the probability is also 1/3. The return is 0 (no win or loss).
White result: This occurs on the remaining face, so the probability is 1/3. The return is -1 (losing).