Expected utility matters more than raw probability

In probability theory, most people focus on expected value: the average outcome if you repeated a choice many times. However, for a single decision, expected utility is far more practical. While expected value measures objective units like dollars or time, expected utility measures personal worth. This distinction explains why a rational person buys insurance or avoids a bet with a high payout but a ruinous downside.

The primary difference lies in the law of diminishing marginal utility. For most people, the first 10,000 dollars they earn provides significantly more life impact than the 10,000 dollars between 1,000,000 and 1,010,000. Because the subjective value of gain decreases as you acquire more, the pain of a loss often outweighs the joy of an equivalent gain.

To make smarter decisions, stop asking what the average outcome is. Instead, ask how much the specific outcome would actually change your life. A positive expected value bet is a poor choice if the potential loss results in bankruptcy, as the utility of those remaining dollars is infinitely high. High-leverage decision-making requires weighing the probability of an event against its personal utility, not just its numerical payoff.