Vocabulary - Expected Value

Expected value is the average outcome if you repeated an experiment infinitely many times. For a dice roll, the expected value is $(1+2+3+4+5+6)/6 = 3.5$. You'll never roll 3.5, but it's the long-run average. Formula: $E[X] = \sum_{i} p_i \cdot x_i$ where $p_i$ is the probability of outcome $x_i$.

If you flip a coin where heads gives $10 and tails gives $0, the expected value is $0.5 \cdot 10 + 0.5 \cdot 0 = 5$. Expected value lets you compare random outcomes. "On average, which choice is better?" That's what probability DP answers.