# How to Calculate Expected Value Probability dice image by redrex from Fotolia.com
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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.