Unless you know something the insurance seller does not that makes you more likely to be paid out than others, then it is a waste of money to buy insurance for a loss that you can afford.
Assuming you have no extra information that gives you an edge over the insurance company, insurance is only beneficial for a loss which you cannot afford. Otherwise you’re basically paying someone else to invest your money when you can do it for 3 basis points at Vanguard/Fidelity/Schwab.
This is also why whole life insurance is a waste of money, ignoring any tax advantages which don’t apply to most people.
Edit: This is also why states allow people with sufficient funds to self insure their vehicle. If you have a couple million liquid assets, you don’t need to pay someone else to pay for your lawyers and and healthcare costs, you can just do it yourself.
I don't think many people want to buy insurance whose maximum possible payout comes down to a couple of hundred bucks. People generally only insure against risks which they can't afford.
When the likelihood of the risk is small, but the potential damage bill could be financially catastrophic, I think it's perfectly rational to buy insurance if the premium is so low.
It isn't even that big a number. People with lots of assets carry that much or more liability insurance and they aren't paying enormous amounts for it.
As an aside, this is why buying insurance, despite being a financially bad bet (or the insurers would go out of business), actually is a sensible thing to do from a quality of life perspective.
You're forced to spend money to mitigate losses. If you can do something to decrease the losses, or the likelyhood of suffering one, then the insurance will cost less.
But people routinely buy insurance, and it's considered a right and moral thing to do. Though the math is exactly the same as with the lottery. Statistically, odds are unfavorable. But it buys peace of mind, so people pay.
I love that you think there is one and only one reason to buy insurance. I suspect that people buy insurance for both reasons. Which is to say that you're both right, and both a little bit wrong.
You're missing the point that, on average, insurance benefits the insurance company, not the policy holders. How do we know this? Because insurance companies are eager to sell you a policy.
As a general argument, this is not valid. Consider a parallel argument: on average, selling food benefits the grocery store, not its customers. How do we know this? Because the store is eager to sell you food.
The argument ignores the fact that the things being exchanged have different value to the two parties to the exchange. In the grocery store case, the store values the food less than the money you pay them, while you value the food more than the money you pay them. The exchange is a net gain for both parties.
Similarly, if you value the transfer of risk highly enough, buying insurance can be a net gain for you as well as the insurance company. That's really the underlying logic of your statement that you should only buy insurance if you cannot afford to lose the item.
Because you're not buying it to win money. You're buying it to limit downside loss, because aside from the massively wealthy, we are loss averse. It's worth our while to pay $200 to insure against a 1% chance of losing $10000, even though in purely probabilistic terms that's a bad deal, because most people can't afford an unexpected expense that large. Even people who can afford that, it's still more painful to lose it than to have a 99% chance of having wasted $100. The larger the potential downside, the bigger the incentive to insure against it, even when it's a bad deal.
Insurance still works even if insurer knows exactly how probable is given outcome and how much exactly will it cost and adjusts the fee to that. People don't insure themselves because it's a good deal. They do it because they know they won't be able to survive financial burden of some rare event that most likely won't happen but they need to be sure that in the case it happens they'll be covered. And they are willling to pay for that.
Risk is still pooled because payouts come from fees of the people that didn't (and won't) experience costly events themselves.
More information just makes the business more just and less random for insurer.
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