Mean value versus the spread of outcomes
A loot box might contain prizes worth 5, 10, 50, or 200 gold, with probabilities 0.4, 0.3, 0.2, 0.1 respectively. The expected value is 0.4(5) + 0.3(10) + 0.2(50) + 0.1(200) = 34 gold per box. If a box costs 30 gold, the expected value calculation says buy it. But expected value masks the variance: you're 40% likely to get 5 gold (a loss), and only 10% likely to break even.
High-variance boxes feel worse even at positive EV because consecutive losses are psychologically painful. A player in a unlucky streak may quit before reaching the long-run average, making the perceived fairness matter as much as the math.
Why volatility shapes spending behavior
Games publish 'odds disclosures' stating the EV, but players buy loot boxes for the hope of rare pulls, not for expected value. A box with expected value 10 but a 1-in-500 chance of a 1,000 gold prize is more seductive than a box with EV 50 but 50 guaranteed gold. Designers use variance as a core engagement mechanic because variance creates memorable highs.