[Giroflex]

> You can think of it probabilistically.

But probabilistically doesn't it make sense to skip insurance altogether?

If insurance manages to turn a profit despite having overhead expenses (salespeople, infrastructure, lawyers, etc) and assuming they don't have a special discount in whatever they're ensuring then there are more people paying without using than there are people who need it.

If I'm an average or above average driver, for example, then it doesn't make sense to have insurance, does it? Wouldn't it make more sense to save the money I'd otherwise be using for insurance and pay myself in case something happens? That way my money would go only towards my problem and not towards worse drivers and insurance company expenses.

Is the product that insurance offer really just peace of mind?

[chronial]

Have a look at the expected utility Wikipedia article. In short:

The difference between owning a total of 0 and a total of 10000 USD is way more important than the difference between owning 10000 and 20000 USD.

So assume you have 20000 USD. There's a 10% change that you will lose it all and become homeless. It makes sense for you to pay 2000 USD at the start to get 10000 USD back in case that happens. Because being homeless in 10% of the cases is way worse than having 18000 USD instead of 20000 USD in 90% of the cases.

[perl4ever]

If I were trying to explain insurance to a person from Mars, I guess I would say humans will pay a premium to reduce variance in cash flows. This is a win-win situation, not a case of one party taking advantage of the other. It's one of the basic services that underpins civilization.

[tkxxx7]

> If I'm an average or above average driver, for example, then it doesn't make sense to have insurance, does it?

You’re waiting at a red light when a drunk driver smashes into you. Your skills as a driver can’t affect the probability of this. It may not be your fault, but someone needs insurance.