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In pure game theory terms, taking out insurance is always a losing proposition - by which I mean on average people who take insurance lose money on it. Simplistically the amount you get back times the percentage chance of you needing it is always less than the premium, and you know this is true because insurance companies (who are very, very good at statistics) design it to be that way. After all, they do want to make a profit.

So why do people take insurance? It's about risk. You insure your house because, even though the chance of it being destroyed is very small, if it does happen (and you are not insured) it will impact your life in a major way. You might never recover financially from a loss like that. On the other hand the downside of taking insurance is just a few hundred bucks a month, which you can almost certainly afford (at least if you are rich enough to own a house). The same is true of most people's cars, and certainly of the liability insurance for a car, which can bankrupt you faster than losing a house. For medical insurance (if you are not in a country with universal healthcare) this is even more true - in the US most bankruptcies are because of medical bills.

If you decide to insure a small item, then you are on average going to lose money on it. And if you can easily afford to replace it, then you are not reducing your risk in any significant way, so there would appear to be no point. Most people who do this either do it because the statistics are not obvious to them, or because they psychologically feel better about not 'losing money' if something bad happens, even if it is a bad thing they can easily afford, and they are psychologically OK with spending small amounts of money on something that will probably do them no good.

It's probably also worth mentioning that companies love insurance for small items because not only to they make a profit each time it is taken out, but lots of people either forget they insured something when it breaks, or they can't be bothered to make the claim, or they can't find the paperwork. The company profits in every case.

Also be aware that all 'extended warranties' that cost you money are essentially insurance, just marketed in a different way.

TLDR: Insurance will lose you money on average, and the only benefit to insuring things you can afford to replace is to make you feel better.

An insurance is a gamble with the insurance company where you bet that something bad will happen to you and they bet that everything will be fine. The insurance company decides the odds for that bet, and they do that based on detailed analysis of a huge amount of statistical data. So you are betting against the house. If an insurance would be worth it from a cost/risk assessment in the long run, then no insurance company would offer it.

There are only three cases where an insurance makes sense economically:

• There are some circumstances the insurance company doesn't know which make your risk a lot higher than for most people (and not disclosing that fact isn't insurance fraud in this case).


• The potential damage is so high that it wouldn't just be inconvenient to pay for it, it would completely ruin you. Any emergency you can pay out of your emergency fund isn't worth insuring against.


• It's an insurance which is directly or indirectly subsidized by a 3rd party (government, employer...) making it a winning bet for both you and the insurance company.

So unless having to replace your phone out of your own pocket would be something you wouldn't be able to do or your personal lifestyle makes phone mishaps magnitudes more likely than for other people, it is likely not worth it.

Health insurance, on the other hand, is an insurance almost everyone should have if possible.

• There are many medical problems which can happen to everyone and which generate costs which greatly exceed the emergency funds of most people.


• When you need medical help, you are already in a situation where you feel extremely bad. You don't want to have an additional stress factor in form of worrying about how to pay for all the stuff the doctors do to you in order to help you.


• Being able to go to the doctor whenever you feel you should without having to consider whether or not it's worth it can fix many medical problems before they become expensive (and painful).

All insurance is a waste of money until you need it.

I don't spend money to insure the small stuff. Most of the time there's no problem and when there is, the replacement cost is reasonably inconsequential when you compare the insurance cost saved versus the cost of replacing the item.

Where the dividing line is between inconsequential and a painful expenditure to replace the item is a personal decison ($$$).

According to utility theory, one should adopt the strategy that maximizes one's expected utility. So when it comes to insurance, one needs to look at the probability of each scenario, and the utility of that scenario. For small amounts, utility and money can be treated as being close to proportional: losing $2 is about twice as bad as losing $1. But for larger amounts, it gets more complicated, and generally losing a large amount is larger loss of utility per dollar than a small loss. This is where insurance comes in: if you have a 1% chance of losing $100,000, then paying $1,100 to avoid that possibility may increase your expected utility, even though it decreases your expected money, if the loss of utility from losing $100,000 is more than 100 times the loss in utility in losing $1,100.

One method of modeling utility is to assume that it's proportional to the log of one's money. If we use the natural base, then going from $200,000 to $100,000 is a loss of 0.69 utils. If that has a 1% chance of happening, then the expected utility loss is 0.0069 Going from $200,000 to $198,900 is a loss of 0.0055 utils. So in this case, insurance increases your expected utility, since 0.0069 > 0.0055.

Now let's go through the above numbers, except with a loss of $100 instead of $100,000. Going from $200,000 to $199,900 is a loss of 0.0005 utils, so the expected loss is 0.0000050. If you have to pay $1.10 for insurance, that's a loss of 0.0000055 utils. So in this case, the insurance decreases your expected utility.

So whether insurance makes sense depends on how large a loss it is, how likely it is, how expensive the insurance is, and also personal factors such as how much money you currently have (if you have a billion dollars, the possibility of losing $100,000 isn't that big of a deal) and what your utility function/tolerance of risk is.

TLDR; If the item isn't expensive enough to be willing to put in so many hours of your time and effort, then just always skip it. If the item wouldn't cause a major financial hardship for you to replace, skip it.

The big problem with small insurances is they are in most places poorly regulated, and even when operating legally are doing so in a way that is "technically legal" but actively deceptive using small print and ridiculously time-consuming claim processes. This is a polite way of saying they are, 95%+ of the time, a total rip-off.

One example is a major retailer here in the US sold (and maybe still sells) insurance on air beds. A friend of mine bought it, thinking it was only a few dollars and air beds go bad all the time, so maybe this would be a good bet?

Naturally the air bed started leaking, and my friend asked for my help because the process didn't seem to make any sense, so I called up the company. The operator read out the exact requirements on the insurance and had trouble not laughing while doing so, because it was one of the most rediculous things I ever heard. To be covered the bed would need to be losing air through no visible rip or tear, not through a seam, and not through the inlet valve assembly.

...so how, pray tell, could any item actually be covered? One that loses air through some form of internal teleportation? They gave a small nervous laugh and said that basically, yes, that does seem like how it would need to happen.

Similarly I worked for a company that sold electronic insurance, and I got to talk to customers that did and did not get the insurance on the items to work for them. I always asked how the process went, and not a single one said that they needed to make less than 4 phone calls, usually waiting for half an hour or more each time, they kept their original receipt and sometimes even cut out the UPC code from the box, usually sent a few emails back and forth as well, and it took around 2-3 weeks to get a gift card back. And that was when the company agreed to cover the item in full.

The trick is, most people don't have that kind of free time or sheer force of will to collect on what amounts to usually under $100 of 'insurance'. I know of one single major US electronics retailer that offers a 'protection plan' that is actually worth the money and not a hassle, out of the dozens of companies with similar claims.

Another common trick is to sell insurance on an item, but it turns out the fine print says it only kicks in after the manufacturer period expires (usually 1-3 years), even if the insurance you bought was supposed to protect from things the manufacturer wouldn't cover regardless.

There are an infinite variety of clever ways these companies have developed to take advantage of people, engaging in rent-seeking behavior to increase their profits while providing no useful service to most or all of the people who buy their goods.

Add this reality together with the uncertain risk that you would need it at all, and you'll find that the vast majority of the time these things end up as losing propositions.

If the item you are looking at is considerably expensive enough to be a real burden if it has a problem - like a car, house, etc. - then you'll need to try to do some research to see if that particular option you have seems to operate in a legitimate way. Then you'll need to read the fine print, keep up with all required paperwork and documentation kept in a safe place, and if it comes to time that you need it be prepared and diligent because you will usually spend many hours on the phone and by email/website/letter to get what is owed you.

The simple way to evaluate insurance against an event is to look at 1) the potential loss if an event occurs, and 2) the probability of an event occurring.

With medical insurance, the odds are generally irrelevant because the potential loss is enormous. Very few people can afford to cover catastrophic medical expenses out-of-pocket.

With consumer insurance (phones, tires) it's a little less clear. If you broke your phone, could you afford to replace it (or if you couldn't, would you be willing to go without?). What are the odds that your phone will get broken? Once you have those numbers, you can determine if insurance is statistically worth it.

If your phone costs $500 and insurance costs $10/month, that means that in any given year they think the odds of you needing to replace your phone is about 24% ($120/$500). It's actually a little less since they bake in some profit to their rates. If you think the odds of you needing a new phone are higher, or you would absolutely need to replace your phone and can't afford $500, then buying insurance might make sense.

However, an alternative would be to just save the amount that you would put toward insurance in case one of these events occurs. That's called self-insurance. You can actually get away with saving less that the combined insurances you're offered, since the odds of multiple events happening are much lower. So if you save $50/month, and in one year have $600, then you can afford to either replace your phone or tires, but maybe not both. But the odds of both happening are much smaller. Plus if neither event happens, you don't need to save any more.

The very short answer is: No, small insurances are not worth it. The reason is called the calibration theorem.

If you accept a sure loss to remove a small risk (which is exactly what a cell phone insurance is), then under standard assumptions on rational behavior over gambles (von Neumann Morgenstern expected utility maximization), you will be committed to also reject huge potential profits for a medium risk. Think about drawing a curve that represents how much you value every dollar, every cent in terms of utility. This is what expected utility maximization tells you to do. If you make the function concave, you will be risk averse and in some cases want to buy insurance. The issue is that locally, this function will still be almost flat. But if the curve is approximately flat, you are approximately risk neutral and will therefore reject insurances over small risks.

Insurance is a complete waste of money. You would be better off making a bet at a roulette wheel. For example, a straight up bet on a roulette table is has 35:37 odds, which means the net present value of $100 of that bet is about $94. In other words you lose about $6 out of every $100 bet straight up. By comparison, most insurance policies have payoff odds of about 1:16, which means for every $100 you spend on insurance your net present value is about $6 dollars and you lose $94. If that sounds crazy bad, it's because it is. It is pure stupidity to buy insurance. You would be better off burning your money, because at least you would have the fun of watching the fire.