You can get insurance for cars, phones, vacations, health, houses, ... —pretty much anything that can accidentally fail you. When is it a rip-off and when is it worth it?

The big thing to keep in mind about insurance is that the insurance company makes money by charging people more than they pay out. If the chance of your house burning down is 0.1%/year then to get insurance to pay out the value of your house if this happens you should expect to pay a bit more than 0.1% of the value of your house every year. Insurance, considered strictly on expected value terms, is a losing bet. So when should you go ahead and buy it anyway? Where does this simple theory fail to apply?

• When you're required to: If you drive a car you might hit someone, and then you owe them, possibly quite a lot, so the government typically requires you to carry liability insurance. Or if you want to get a loan to buy a house the bank will make the loan conditional on you maintaining various kinds of insurance on the house, so that their collateral maintains its value.

• When you know something: The insurer is trying to estimate how likely you are to need money from them and how much that's likely to be, but often we know our situation better than others. If I've dropped my last five phones in the toilet, and someone's offering insurance that covers this, I may be pretty sure that I'm more accident prone than their typical purchaser and figure I come out ahead. This is adverse selection, however, so you need to be careful. First, sometimes it's illegal: if you buy insurance on your car and then go run it into a wall to collect the insurance money, that's insurance fraud. Don't intentionally do something you've bought insurance against. But if it's just that you think you're more likely to need it than the average buyer, that's fine. (But keep in mind that the people who think they're less likely to need it often won't buy, so the pool of buyers may be more accident prone than you think.)

• When it's collective bargaining: Health insurance is weird in lots of ways, but one of the main ones is that insurers negotiate with doctors to get them to charge less than they normally would. That means health insurance is often worth it on expected value terms alone.

• When someone else will pay for it: Unlike health insurance, vision and dental insurance usually don't involve collective bargaining by your insurer, but like health insurance your employer may be willing to pay part of the cost.

• When replacement would be really hard: Someone who's paid off their mortgage and so is no longer required to hold homeowners insurance should probably still keep it up, because if their house burned down that would be a huge hardship. Just as most people shouldn't take a 55% chance of $2M over a 100% chance of $1M, when we're talking about large financial swings the diminishing marginal utility of money means taking some deals that are somewhat negative in expected value can still make you better off on average.

That's a lot of exceptions! Does the simple "don't buy insurance for things you could afford to replace" rule ever apply? Yes! Consider vacation insurance: if you have to cancel your vacation because of a hurricane you'll get your money back but not your vacation, plus you'll have the hassle of documenting things and convincing the insurance company to pay. Or portable electronics: insurance prices are high because mostly the most accident prone people buy, and the price only looks attractively low because it covers less than you think. When the exceptions above don't apply, saving the money is generally a much better investment than buying insurance.