Expected value is the average outcome if you repeated an experiment infinitely many times. For a dice roll, the expected value is . You'll never roll 3.5, but it's the long-run average. Formula: where is the probability of outcome .
If you flip a coin where heads gives $10 and tails gives $0, the expected value is . Expected value lets you compare random outcomes. "On average, which choice is better?" That's what probability DP answers.