Expected value

The expected value is the basic tool for assessing a bet: it summarises in a single number “how much one expects to win on average”.

Definition — Expected value (average winnings)

Let a partition $\{e_1,\ldots,e_n\}$ of the universe be given (for example the outcomes of an experiment) with probabilities $p_i = P(e_i)$ and associated net winnings $v_i$ (positive if one gains, negative if one loses). The expected value (or average winnings) of the bet is: $\bar V = \sum_{i=1}^n p_i\, v_i.$ It is the weighted mean of the winnings, with weight equal to the probability of each outcome.

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Topics: Probability
Concepts: Expected value · Random variable
Methods: Expected value
Skills: Probability calculation · Using formulae