Expected value or EV is the average return one can expect to get from a repeated decision, such as from a gamble, if it is repeated over and over again an infinite number of times. It can be either positive (expected gain) or negative (expected loss). Expected return is a more-or-less synonymous term with usage more firmly tied to financial investments or other monetary gambles.
EV is one of the simplest measures to evaluate whether a decision is good or bad, with the choice that results in the highest EV being the best choice one can make, assuming maximizing average returns is the goal.
EV can be calculated by multiplying the probability of each possible outcome by the value of that outcome and summing that product across all possible outcomes. For example, in a 50/50 coin flip, if a gambler wins $1 every time the coin lands on heads and loses $1.50 every time the coin lands on tails, the expected value of that gamble is -$0.25 (0.5*$1.00+0.5*-$1.50), which can be described as an expected loss of 25 cents per coin flip.
Expected value can be usefully converted into a percentage advantage or disadvantage, standardizing the expected return and making it easier to compare the relative merits of different risky decisions. See the link in the previous sentence for details.
In the context of casino gambling, expected value is a particularly useful initial way to assess the rationality or normativity of a gamble. Among professional gamblers, as with investors, estimates of expected value tend to be the most critical piece of information when deciding whether or not to make a gamble. Casino gambling involves well defined choices, outcomes, and monetary values associated with those outcomes, along with known—or at least (often) knowable—probabilities, making it possible to calculate expected value for many casino games.
One of the themes of the associated Substack, however, is that expected value is a far less appropriate standard for rationality in casino gambling than one might first assume. In part this is because the probabilities are less transparent and more dependent on subjective assessments than most non-gamblers realize and in part because there is much more behind why most people gamble in casinos than the desire to maximize expected value.
See the Wikipedia entry on Expected Value for a more detailed discussion. See the Glossary entry on expected utility for a more psychological version of expected value.