How to Calculate Expected Value Probability

Rolling dice.
dice image by redrex from

Expected value uses probabilities to determine what an expected outcome, such as a payoff, will be. Expected value multiplies the probability of each outcome by the possible outcome. For example, in a dice game, rolling a one, three or five pays $0, rolling a two or four pays $5, and rolling a six pays $10. In dice, the probability of rolling a one through six is 1/6 each.

Write out the probabilities and outcomes into a chart. Use the left column for probabilities, the center column for outcome and the right column for probability times outcome. This provides a visual representation of the math.

Multiply each outcome by the probability. In the example, for one, three and five, multiply $0 by 1/6, which equals zero each; for two and four, multiply $5 by 1/6, which equals 0.833 each; and for six, multiply $10 by 1/6, which equals 1.666.


Add all the numbers calculated in Step 2 to determine an expected value. In the example, 0 + 0 + 0 + 0.833 + 0.833 + 1.666 equals an expected value, or expected payoff, of $3.33.