# Expected Monetary Value

If you could somehow determine precisely what would happen as a result of choosing each option in a decision, making business decisions would be easy. You could simply calculate the value of each competing option and select the one with the highest value. In the real world, decisions are not quite this simple. However, the process of decision-making still requires choosing the most valuable option--most valuable being, in this case, the option that has the highest Expected Monetary Value (EMV), a measure of probabilistic value.

Suppose you are given the opportunity to play a simple game. A friend flips a coin. If it comes up heads, you win \$100. If it comes up tails, you win nothing. What is the value of this game to you?  Stated another way, how much would you pay to play this game?

Each time you play the game you have a 50% chance of winning \$100 and a 50% chance of winning nothing. If you were to play the game many times, on average you would win \$50 for every time you played. Therefore, \$50 is the EMV for this game.

Graphically, this game can be illustrated as follows:

This diagram shows that there is an uncertain event with two possible outcomes. Win, which has a value of \$100, and Lose, which has a value of \$0. Furthermore, there is a 50% chance of each outcome. Finally, the EMV of this event is \$50. This simple diagram does an excellent job of communicating all essential details of the situation you face.

The EMV is calculated by multiplying each outcome value by its probability and adding all of the results together.

In the diagram above, the EMV was calculated using the equation

EMV = \$100 * 0.50 + \$0 * 0.50 = \$50

The value shown under each node name is the expected value of reaching that point in the tree. Before playing the game, you are at the Play Game node and the combined value of all events following this node is \$50. Similarly, if you win, you move to the Win node with a value of \$100.

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