This is simply not true. People are risk averse, and buy insurance to protect them from unlikely negative outcomes, not because they believe that the insurance

This is simply not true. People are risk averse, and buy insurance to protect them from unlikely negative outcomes, not because they believe that the insurance company will, on average, pay out more than they pay in premiums. I can invest $200 a month for the next 10 years, or I can buy health insurance. On average, I will have more money after 10 years of investing. But the additional $24,000 of savings will increase my happiness very little relative to getting the healthcare I need in the case of a catastrophic injury or illness. So I'll gladly lose a little bit of money every month (statistically) to avoid the possibility of that outcome. Edited to add: one way to think of this is to pose the following thought experiment. Imagine that tomorrow you have a 50% chance of doubling your wealth and income, and a 50% chance of losing everything. What would you be willing to pay to guarantee that you keep your current wealth and income? If you're like most people, the answer is nonzero and positive. That's how insurance companies make money.