Expected Value, and When to Ignore It

One more pricing tool, because every insurance offer, extended warranty, and lottery-shaped investment in this book is built on it. The expected value (EV) of an uncertain payoff is its probability-weighted average:

— multiply each outcome by its probability, add the results. Worked once: an extended warranty costs $300 on an appliance with roughly a 15% chance of an $800 repair. The expected benefit is $0.15\times \$800=\$120$, so you are paying $300 for $120 of coverage — a $2.5\times$ markup. The markup is not an anomaly; it is the business model, which is why the default answer to point-of-sale coverage is no. Price every offered bet this way and you will decline most of them.

Then know when to ignore the tool, because the exception carries the rest of the book’s insurance philosophy. EV governs decisions you make repeatedly with stakes you can absorb — there, the law of large numbers grinds you toward the average, and taking every positive-EV bet while refusing every negative one is simply correct. It stops governing when a single bad outcome is unaffordable. A fire that destroys an uninsured house is not one draw in a long series; it is the end of the series. For unrepeatable, ruinous stakes, survival dominates expectation — you buy the homeowner’s policy at a markup for the same reason you refuse a coin flip that pays $+\$5$ million or $-$everything: a bet you cannot afford to lose is not priced by its average (section “Beyond the Questionnaire: Kelly Sizing and the Barbell”). The whole of chapter “Insurance: Shielding Your Assets and Family” compresses to this rule: self-insure the small and repeatable, where EV says the markup is a waste, and insure the large and unrepeatable, where ruin says the markup is cheap.