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Why buy insurance?
You don't mention what kind of insurance you're talking about, but I'll just address one angle on the question. For some kinds of insurance, such as health insurance (in the US), auto insurance, and homeowner's insurance, you may be insuring against an event that you would not be able to pay for without the insurance.  For instance, if you are at fault in a car accident and injure someone, they could sue you for $100,000.  A lot of people don't have $100,000.  So it's not even a matter of "I'll take the risk of having to pay it when the time comes"; if the time comes, you could lose virtually everything you own and still have to pay more from future earnings.  You're not just paying $X to offset a potential loss of $Y; you're paying $X to offset a potential derailment of your entire life.  It is plausible that you could assign a reasonable monetary value to that potential "cost" that would mean you actually come out ahead in the insurance equation. It is with smaller expenses (such as insuring a new cellphone against breakage) that insurance becomes harder to justify.  When the potential nonfinancial "collateral damage" of a bad event are less, you must justify the insurance expenses on the financial consequences only, which, as you say, is often difficult.