The expected value of an action is the mean numerical outcome of the possible results weighted by their probability. It may actually be impossible to get the expected value, for example, if a coin toss decides between you getting $0 and $10, then we say you get “$5 in expectation” even though there is no way for you to get $5.
The expectation of V (often shortened to “the expected V”) is how much V you expect to get on average. For example, the expectation of a payoff, or an expected payoff, is how much money you will get on average; the expectation of the duration of a speech, or an expected duration, is how long the speech will last “on average.”
Suppose V has discrete possible values, say or or . Let refer to the probability that . Then the expectation of V is given by:
Suppose V has continuous possible values, x. For instance, let . Let be the continuous probability distribution, or of the probability that divided by . Then the expectation of V is given by:
Importance
A common principle of reasoning under uncertainty is that if you are trying to achieve a good G, you should choose the act that maximizes the expectation of G.
Anyone objects to deleting this page? There seems to be no significance to it, it’s even not linked from anywhere. --Vladimir Nesov 23:03, 8 July 2009 (UTC)
Video to demonstrate how to NOT think about expected value
http://youtu.be/kuXIpxoMYtc?t=20s
George Gervin (NBA Legend) says that the 3-point shot is the worst shot in basketball. His argument is basically that 3-point percentages are almost always lower than 2-point percentages. He seems to not give any weight to the fact that 3-point shots provide you with one extra point...
Perhaps the example should include probabilities
The example with the 6-sided die doesn’t explicitly show how probabilities are part of the calculation. Perhaps the example should do this.