Expected value is the arithmetic that connects a probability to a price: a decimal price of 2.40 implies 41.7% before the bookmaker's margin is taken out, and the distance between that and a 53% estimate is what people call expected value.
This guide works through the coin-flip version, shows how the same outcome changes sign at a different price, and explains why a single match can neither confirm nor refute a probability — which is why every number we publish is graded against the closing line rather than against the result.