Toss a fair coin for one unit, winning one unit on heads: half the time you gain one, half the time you lose one, and the expected value is zero. The bet is fair. Casino bets are never fair: a one-unit bet on red at European roulette wins one unit with probability 18/37 and loses one with probability 19/37, an expected value of minus 1/37, about minus 2.7% of the stake. That negative number is the house edge, seen from your side of the table.
Expected value says nothing about a single evening, where anything can happen. It says what the average converges to as play accumulates, which is why it is the right tool for pricing a bet, a bonus or a whole game, and the wrong tool for predicting tonight.
Why it matters
It is the one number that lets you compare unlike things: two bets, two bonuses, two games. Anything gambling-related that someone offers you can be reduced to its expected value, and almost everything a casino offers has a negative one.
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