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Understanding Expected Value, Risk, and Uncertainty The expected value of a risk is equal to the sum of each probability times the potential payoff. You can model uncertainty on the basis of willingness to risk loss or gain. Individuals or institutions can be classified as risk-neutral, risk-inclined, or risk-averse. In studying uncertainty, you always have to begin with the expected value of an outcome: the expected value of any outcome is the sum of the odds of each outcome times the value of that outcome. Assume that in a coin toss, you could win a $2 bet on heads. The expected value of the gamble is found by the formula on the left. That value is $1. The expected value is the average outcome if you played this exact game repeatedly. You want to now ask how much someone (or some institution) would be willing to pay to play this game. A risk-neutral person would pay only $1, the expected value; a riskinclined person would pay more than $1; a risk-averse individual would pay less than $1. The analysis of risk behavior has applications in financial markets, insurance, and sales.