Expected Value

The expected value is the long-run average of a random variable: the value you would get per try if you repeated the random situation forever and averaged the results. It is each possible outcome weighted by its probability, then summed.

It is how you compare gambles, price insurance, and judge decisions under uncertainty. A key caution is that the expected value need not be a value you can actually observe — a die's expected roll is 3.5, which no single face shows — and it can be dragged far by rare extreme outcomes.