When insurance is worth it — and when you're just paying for peace of mind

Personal Money 4 min 80 sources

Insurance is a maths problem, not a comfort purchase. The trick is knowing which risks to pay someone else to carry — and most of us get it backwards.

Key takeaways

Insurance is priced above its expected payout — on average it's a losing bet, so it's only worth it for losses you genuinely couldn't survive.
Most people over-insure small survivable risks (phones, warranties) and under-insure rare ruinous ones (a house, a family's income) — exactly backwards.
The only question that matters at the till: if the worst happens uninsured, could you absorb it? If yes, self-insure; if no, insure and ignore whether it's a "good deal."

Walk into a shop to buy a £400 phone and the assistant will offer you a £90 protection plan before you’ve reached the till. Buy a laptop, a fridge, a used car, and the same pitch arrives: for a little extra, you’ll never have to worry. Most people say yes to at least some of these. And most of the time, the maths says they shouldn’t have.

Insurance feels like it’s about safety. Underneath, it’s about a single calculation called expected value — the average outcome if a gamble were run many times over [1]. Get that calculation right and you can see, clearly, which risks are worth insuring and which ones you’re better off carrying yourself.

What you’re actually buying

When you buy insurance, you hand a company a fixed, certain payment — the premium — and in return they take on a rare, large, uncertain cost on your behalf [2]. The deal only works for them because they pool thousands of customers: most pay in and never claim, a few claim big, and the company keeps the difference [1].

That difference is the catch. The premium is always priced above the expected payout — it has to be, or the insurer goes broke [1]. So on average, across everyone, buying insurance is a money-losing bet. You’re paying a markup to convert an uncertain loss into a certain, smaller one.

That markup is worth paying for some risks and a waste of money for others. The line between them is whether the loss would be survivable.

The risks worth insuring

A risk is worth insuring when the worst case would be financially ruinous — a loss so large you couldn’t absorb it without wrecking your life [3]. A house burning down. A car that kills someone and triggers a million-pound liability claim. A breadwinner dying with a mortgage and young children [4]. These are rare, but if they happen and you’re uninsured, there is no recovering.

Here the expected-value markup is beside the point. You’re not buying insurance because it’s a good average bet — it isn’t. You’re buying it because you can’t afford to be on the wrong side of the rare outcome even once [3]. This is why home insurance, third-party car liability, and term life insurance for anyone with dependents are close to universal advice: the downside isn’t a setback, it’s a catastrophe.

The risks not worth insuring

Now run the same test on the phone plan. The worst case is that the phone breaks and you’re out, say, £400 — annoying, but not ruinous [5]. You can absorb it. So the only thing the insurance buys you is the removal of a survivable loss, and you pay the markup for the privilege.

Extended warranties are the clearest case. Consumer analysts have long found them to be poor value: the products covered rarely fail inside the warranty window, and when they do, the repair often costs less than the plan did [5]. Consumer Reports has reported for years that most buyers never use the coverage, and that retailers push these plans hard precisely because they’re so profitable — much of the price is commission, not expected payout [5][6].

The pattern repeats with home warranties, appliance plans, and smartphone insurance: small, survivable, frequent-feeling risks, sold with a markup, against losses you could simply pay for yourself [7]. Insurers call carrying a risk yourself self-insurance — you keep the money you’d have spent on premiums and cover the occasional loss from your own pocket [8].

The mistake everyone makes

Here’s the strange part: people systematically over-insure the small stuff and under-insure the big stuff — exactly backwards.

The reason is a quirk of how we feel about losses. A small, vivid, likely-feeling loss (a cracked screen) frightens us more, per pound, than a huge, abstract, unlikely one (dying young, uninsured) [9]. So we eagerly spend £90 to cover a £400 phone while leaving a £300,000 mortgage uncovered by life insurance. We’re managing our anxiety, not our risk.

The same wiring explains the lottery, which is insurance run in reverse: a tiny, certain payment for a tiny chance at a huge gain. Its expected value is deeply negative — UK and US lotteries typically return well under half of ticket sales as prizes [10]. The maths is terrible. We buy it anyway, because the vivid dream of the jackpot overpowers the dull arithmetic of the odds [10].

The one question to ask

You don’t need to compute exact probabilities at the till. You need one question: if the worst happens and I’m not insured, can I absorb it?

If yes — the phone, the laptop, the boiler — carry the risk yourself and pocket the premiums. If no — the house, the liability, the family that depends on your income — insure it, and stop worrying about whether it’s a “good deal.” It isn’t, and it isn’t supposed to be. You’re not buying a bargain. You’re buying the certainty that one bad day can’t end you.

02 · Lesson · why it matters

Why we pay to remove the wrong fears

Insurance is worth buying only for what you couldn't survive — yet we spend most on the small losses we could shrug off, and skip the rare ones that would end us.

The till asks you a feeling, not a question

The phone is £400. The clerk asks if you want the £90 protection plan. In the half-second before you answer, you are not running a calculation. You are picturing the cracked screen, the dead battery, the sinking feeling of a broken thing — and reaching for the plan to make that picture go away.

That is the whole trick, and it works on nearly everyone. Insurance is sold to a feeling. But underneath the feeling sits a piece of cold arithmetic, and once you can see it, the feeling stops running the show.

What the arithmetic actually says

Every insurance policy is the same machine. You pay a fixed, certain amount. In return, someone else takes on a rare, large cost if the bad thing happens.

The insurer can only stay in business if it charges you more than the average payout. It pools thousands of people: most pay and never claim, a few claim big, and the company keeps the gap. That gap is built into your premium. So across everyone who buys, insurance is — on average — a losing bet. You pay a markup to turn an uncertain loss into a certain, smaller one.

This sounds like a reason to never buy insurance. It isn’t. It’s the reason to buy it for exactly one kind of risk.

The line is “could I survive it”

Run two losses through the machine.

A broken £400 phone: bad, but you’d survive it. You’d grumble, dip into savings, move on. A house fire, or a car crash that leaves you owing someone a million pounds, or dying young with a mortgage and children who depend on your income: you would not survive those uninsured. There is no grumbling-and-moving-on from a loss that wrecks the rest of your life.

For the phone, the markup is the whole story — you’re paying extra to erase a loss you could absorb anyway. For the house, the markup is beside the point. You’re not buying a good average bet. You’re buying the certainty that one rare, ruinous day can’t end you. The bad average price is worth paying because you cannot afford to be on the wrong side of the rare outcome even once.

So the rule is small: insure what would ruin you, carry what you could survive. One line, two piles.

We sort the piles backwards

Here is where it gets human. People reliably over-insure the small stuff and under-insure the big stuff — the exact opposite of the rule.

We buy the £90 phone plan and skip the life insurance. We warranty the toaster and leave the family’s income uncovered. We do this because a small, vivid, likely-feeling loss frightens us more, pound for pound, than a huge, abstract, unlikely one. The cracked screen is easy to picture. Dying young is not. So we spend our money managing the fear we can feel, and leave the fear we can’t imagine completely unfunded.

The lottery is the same wiring, flipped. A tiny certain payment for a tiny chance at a jackpot — an average return of well under half of every pound spent. The maths is dreadful. We buy it anyway, because the vivid dream beats the dull odds. Whether we’re buying a warranty or a lottery ticket, the feeling is in charge and the arithmetic is nowhere in the room.

You are the one being sorted

It is tempting to read this and feel clever — to nod at the people clutching their warranty quizzes and walk past the protection plan with a smirk.

But the machine isn’t sorting them. It’s sorting you. The clerk’s pitch, the warranty at the checkout, the lottery display by the door — these exist because they work on the way human attention is built, and your attention is built the same way. You feel the small vivid loss and skip the large invisible one because that is what a human nervous system does. Knowing the rule does not switch the wiring off; it only gives you one question to hold up against it.

And the question is quiet: if the worst happens and I’m uninsured, can I absorb it? Most of the time, at most tills, the answer is yes — so you carry the risk and keep the premium. A few times in a life, the answer is no — and those are the only times the cold arithmetic and the warm fear finally agree. The rest of the time, the thing the insurance removes isn’t the risk. It’s the worry. You are allowed to pay for that — but it helps to know that’s what you’re buying.

03 · Lab · your turn

The Insurance Sort

Rehearse sorting five insurance offers by the only rule that matters — could you survive the loss — and watch each choice play out across a thousand lives.

04 · Hope · carry this

The same instinct that makes us overpay to quiet a small fear is the one that makes us protect the people we love before ourselves — once you can see which is which, that care finally lands where it counts.