Travel insurance is about three things:

1. Making the insurance company rich.
2. Not dying, and not needlessly losing an arm or a leg in case of an accident.
3. Not getting poor in case of an accident where you don’t lose an arm or leg.

If you are OK with (2) and (3) then you can indeed go without travel insurance, and save the money. Otherwise, seeing how travel insurance is really cheap, it’s foolish not to have it.

You have to know that not the entire world is a place of goodwill and commonwealth, nor a socialist paradise.

In huge parts of this world, it’s you pay or you die. You pay or you lose your leg. You pay or you walk (or stay where you fell). Not having an insurance to back you when you could really, really need this backing is a very uncomfortable situation.
That’s even more true in the poorer parts of this world, since you mentioned Himalaya. No money, no be luckee.

Understanding what insurance IS makes decisions much easier.

• Insurance is a means of spreading low probability high cost risk among many people so that for the average insuree it turns into a low cost certain-probability payment.

Insurance is a risk sharing arrangement between a large number of people.
For a large group, if you share the cost of a risk among you then if the probability of an event occurring is say 0.1% per year (on average), and the cost of the event (on average) is $X then you each need to contribute $X x 0.1% = $X/1000 per year.
If a company administers the system on behalf of the large group of people they will (entirely reasonably) expect to be paid for their efforts. The cost to some extent relates to the amount of money involved but not linearly. The cost tends to relate somewhat linearly to the number of people involved – but the cost per person is about the same (very roughly) regardless of size.

Assume:

• A Himalayan emergency averages $100,000 – but could be $5000 and could be $1,000,000.

• That 0.1% of people claim (Everest ascents at long term fatality rate of approaching 10% not covered 🙂 🙁 ).

• Assume the company takes 10% of the actual all up cost. I’m not saying that this is or isn’t a fair rate – just using it as an example.

SO – cost of insurance = $100,000 average x 0.1% probability x (1.10 profit margin)
= $110

If the claim rate was 1% the cost of insurance would rise to $100k x 1% x 1.1 = $1100

Most people would find it vastly preferable to pay $110 to avoid even a small chance of having to pay $100,000. BUT that $100,000 is the average over many accidents. I said above that cost may be in the range $5000 – $1,000,000

Most people will die on the mountain if the cost was $1,000,000 and they had not paid their $110.
Most people will die on the mountain if the cost was $1,000,000 and they had not paid their $1100.

Insurance is a means of spreading low probability high cost risk among many people so that for the average insuree it turns into a low cost certain-probability payment.

In a competitive market the cost of travel insurance ALL THINGS BEING EQUAL is usually good value.

When buying travel insurance – be sure of what you are buying!!!!

It is very well worth noting that in travel insurance (and many similar markets) ALL THINGS ARE NOT EQUAL. Because the costs MAY be high and because people are people a significant proportion of travel insurance terms and conditions will contain clauses which exempt or limit coverage in quite unexpected ways. These provisos may be, and often are, hidden in the finer print, written in lawyerese and are a real trap for the unwary.

As one only example – if hiring a rental car in Australia and you buy related insurance (which may be part of your more general travel insurance policy or may not) then PROBABLY, no matter what you may think the document says, and no matter what the people at the counter tell you, and even no matter what the non binding written promotional blurbs may say, you will almost certainly not be well or at all covered for

• Single vehicle roll over damage

• Vehicle immersion

• Hitting a kangaroo, emu, bull, … in non-daylight hours

• Rear or under vehicle damage or damage caused by driving under a ledge, truck, barrier etc.

Really?
Really!

Your liability may be limited to only $10,000, or $20k or $30k, or not at all.

[Taking out rental car insurance in NZ for an Australian trip avoids almost all these traps, but, that’s another story]. Really? As above :-(.

Read the fine print.

All of it.
I do.
Really (again).

When taking out travel insurance and similar I take time to read all of the relevant portions of the document.
This is a great pain, can take hours and may save you vast sums of money.

Apart from the Australian rental car rorts, the “best” I’ve found was an airline trip insurance offer that paid (notionally) $100,000 in the event of death on the single flight. Cost was under $5. The flight was from Yogyakarta (half way down Java in Indonesia) to Kuala Lumpur in Malaysia. Reading the fine print revealed that it did not cover travel in the country of departure – as we flew in Indonesian airspace for all except the very final part of the journey (maybe 5%) that “seemed a bit rough”. I may have missed a section eliminating Malaysian airspace. BUT the best part was that you assigned access to all your medical records to the “insurer” in perpetuity irrevocably, and after death, and this condition was also binding on your executors. I wonder how much they can sell those rights for for people who buy their insurance?
Really ???? (again).
Really !!!
We passed on that offer.

There are many “reasonably reputable” insurance companies. And some bery terrible ones. In some markets even the top name brand insurers seem to have gone mad – the Australian rental car examples tend to support this thesis. Caveat Emptor. Always.

Basically, timing and luck.

If you average everything, then saving your own money will perfectly reach the target exactly when you need it.

But there’s a small chance that something terrible will happen, at a terrible time.

So, (extreme example) paying insurance means that when you need a team of doctors to fly with you back to your home country, monitoring you with proper equipment on the plane, then you’ll actually have the ~$500k required to do that—even when it happens before you theoretically would have stored up that much in a personal emergency savings account.

If you are reasonably well-off, you may not need all the fripperies of travel insurance. Miss a flight because the scheduled connection failed? Just buy another ticket. Somebody steals your bags? Go shopping. This is self-insurance. If the amounts of money involved are small in the context of your overall wealth, it’s a decent plan. (Do bear in mind that a seat on the next flight may cost ten or more times what you paid for your prebooked non-refundable one).

However, very few of us can afford the costs of a major medical emergency. Insurance for the USA should probably run to ten million dollars. For more civilized parts of the world where they will cure you first and only then ask for payment, you might consider less. If your net worth is small, you might consider letting them bankrupt you (and they probably won’t, because it would involve paying lawyers more than they can get back by bankrupting you). But you should be very sure, that you won’t just be left to die at the roadside for lack of medical insurance, or dumped with impoverished locals in some third-world hospital where you have to hope that the needles they are inserting into you haven’t been recycled from several previous patients. Imagine “They saved my life, but now I have hepatitis-C for life”

Seriously — pay for some decent medical cover. (And make sure you disclose absolutely every pre-existing condition that affects you, however trivial it seems, because they’ll be looking for reasons not to pay up if you are about to cost them half a million).

As a few have already pointed out, your assumptions are wrong. You’d need to go on a lot of trips to make the expected outcome. Insurance pools risk, so medical emergencies don’t bankrupt you or lack of funds prevent you from getting the care you need. Add a few zeros’to both of your assumptions, 0.0001 chance of getting injured (1 out of a 10 000 tourists need this expensive care) and then costs easily in the 100,000s. So the expected costs are the same, but the effect on the individuals are vastly different.

And in case you are thinking, I am loaded, I can self insure, keeping $100,000s in liquid assets incurs a cost as well. So, in short, insurance makes lot of sense for medical emergencies, especially where care can be expensive. But make sure you get one that actually pays out!

Lost luggage insurance, cancellation cover, extra rental car insurance … often have much smaller sums involved (that are also easier to estimate for you), so you may be better off using your cash buffer.

Saving enough money to cover all eventualities is exceedingly prohibitive

In your own simplified example you compare an insurance cost of “0.1*5000 + 0.5*1500 + x” = $1250 + x to a savings requirement of $6500. Even that alone is a huge difference, $5000 is not a trivial amount to save up for many people.

But you are forgetting that the potential costs are far far higher than $6500. If you sustain a head injury or have to be medevac’ed then the cost could be tens or hundreds of thousands. If you cause injury or death to someone your liability could be in the millions. A normal person cannot be expected to save up $10 million to go away for the weekend.

It does not make sense to save up thousands, tens of thousands, hundreds of thousands, millions, or however much just in case of any eventuality. Saving this much would be prohibitive to practically any travel.

That is the benefit of insurance. Instead of requiring millions in savings, you only have to pay a tiny fraction, for somewhere like Everest this may be thousands, but in general it is less than a few hundred even for a very long vacation.

You need travel insurance because otherwise you’d have to save a lot.

I don’t know which country you’re from where a broken leg requiring a helicopter trip sets you back only $5’000. In US, a broken leg in need of a surgery will cost $15’000 to $35’000, and air ambulance services may cost about as much, or even more. Frostbite treatment is not cheap either, and in addition if you need an amputation, you’ll want a prostatic limb which will cost anywhere between $5’000 and $50’000, depending on how much of a limb you’ve lost.

Realistically, if travel insurance is abolished, you’ll need to save about $100’000 (to be sure you won’t run out of money and have to cut your own feet) every time you go on a ski or mountain bike trip. In this case, most people simply won’t be able to afford going to Himalayas.

Self-insurance is worth consideration, though in some places you are required to purchase and provide proof of some kind of insurance by the authorities, especially for longer stays, with minimum insured amounts.

They do that so they won’t get stuck with the bill for an indigent visitor or be forced to deny care. Typically that’s still for relatively long-term visits or for relatively high-risk activities in-country. Thailand, for example, now requires 400,000 Baht (less than $15K USD) for some non-immigrant visa long stay visitors, however even getting that amount of insurance could be a problem for elderly visitors. When I climbed Kinabalu I had to purchase insurance from the park, which had pretty limited payouts (but it was only a few ringitts).

If there is no conflicting requirement, an intermediate option, which may be open to you, is to purchase insurance with a relatively high deductible such as 10,000 USD. If losing $10K won’t make a noticeable difference to your life, you can gamble with it, and on the average may win since the insurance company not only has to make a profit, but they have relatively high costs in servicing smaller claims. A catastrophic incident (probably up to some limit) would still be covered. Of course a few $10K incidents in a row might not be pleasant, even if you can afford it.

Another factor is that in some countries (the US comes to mind) the insurance companies may pay a much different, perhaps lower, but not always, price to the providers than you would as an individual. Sometimes the bill is significantly less if you pay cash. Complicated.

What you’ve described is the case for all insurance. If the expected value of the insurance policy for the average buyer costs more than the premium, the insurance company will eventualy go out of business because they’re paying out more in claims than they collect. All insurance, on average (as phoog notes, if you know your own risk is higher than average in a way the insurance company doesn’t factor into their pricing, it might personally have positive value for you), is statistically a bad bet in the way you describe.

But that doesn’t make insurance useless. You don’t buy car insurance to pay for a $200 window replacement; you buy car insurance because you could be responsible for a ruinous sum of money if you’re liable for someone’s serious injuries or death. You don’t buy homeowners insurance because your mailbox could get knocked over; you buy homeowners insurance because your house could burn down and building a new house is really expensive (and a mortgage lender will make you have insurance anyway). Similarly, travel insurance can cover expenditures that are rare but extremely costly. A helicopter rescue, emergency treatment, and air ambulance repatriation can easily cost in the tens or even hundreds of thousands of dollars. Such services may not be available at all unless you pay up front or an insurance company guarantees payment; even if you have substantial savings, trying to coordinate payment while you’re seriously ill could be difficult.

So you’re right that many of the risks of travel are things you can self-insure out of your savings. If my flight is delayed due to weather and I need a last-minute hotel room, or my baggage is delayed and I need to purchase some clothes, I don’t personally need an insurance policy for that. If my passport was stolen and I had to change my flights, ruin my plans, and travel to another city for a replacement, that would be phenomenally inconvenient, but fortunately wouldn’t leave me destitute, so I wouldn’t need insurance for that. But if I fell down a mountain and broke my legs in the Himalayas, that’s more of a risk than I can personally afford to bear, so I’d want insurance.

Everyone has different risk tolerance, so it’s important to look at both your financial situation, the risks involved in your trip, and the specific details of what a travel insurance policy covers. Even if insurance is financially a bad bet, it’s valid to pay for peace of mind if it makes you feel better. There are other reasons why travel insurance can make sense for some people for some trips:

• Visa/entry requirements A key reason to buy travel insurance is that it may be required. Applicants for Schengen visas are required to have medical insurance coverage (see Article 15). The medical insurance or government-run health system in many countries doesn’t provide coverage, or provides only limited coverage, when you’re traveling. To address this, you can buy travel insurance, either a basic policy that just fulfills the minimum requirement for medical coverage, an annual policy for those who travel regularly, or a fancier one that covers trip cancellation and other situations.

• Trip cancellation coverage Travel can sometimes involve making costly non-refundable bookings for airfares, hotels, cruise ships, etc… Some people want to “protect their investment” with insurance that will cover these costs if something goes wrong, such as getting sick and being unable to travel, bad weather or a natural disaster, and other covered perils. For example, someone who has booked an expensive cruise may be worried about being out the cost of their cabin if their flight is cancelled and they miss the ship. Travel insurance policies can pay for these costs if a covered calamity occurs, giving you the funds to try your trip again another time. Travel insurance can also cover the costs relating to the bankruptcy of a travel provider.

• High medical costs/travel away from high-quality health care Some countries (the United States) have extremely high medical costs for those without insurance. Get appendicitis and need an emergency appendectomy? You will be getting a bill that’s at least in the tens of thousands of dollars. Million dollar hospital bills can happen. While that may be negotiable to some extent, insurance makes a great deal of sense if your medical insurance at home won’t cover this. Other countries and remote regions have very limited medical care, so any serious illness or injury requires evacuation to a major city or another country. This is also quite costly and something you will want insurance for.

• Specialized needs Do you need a service that can coordinate a rescue and repatriation or get you a qualified doctor in a remote area? Are you sending employees to dangerous areas and need kidnap & ransom insurance, including crisis management for advise on dealing with such situations? These are particular reasons to get suitable insurance policies.

So you’re absolute right that it generally doesn’t make sense to buy insurance for risks you can afford to assume yourself. But if the risk is too great for your personal risk tolerance, or insurance is required, it makes sense.

Your math is correct, but only makes sense on a large scale.

Let’s take an even simpler example. Assume the chances of you falling sick on a given trip is 1%, and the medical and transportation costs incurred in case of sickness are $10,000. Furthermore, assume the insurance premium is $150 per trip.

If you took 1,000 trips and fell sick on 10 of them, it would indeed be better to pay for the medical costs out of pocket than getting insurance ($100k vs. $150k).

However, people don’t typically travel like that. Most people take only a handful of trips in their lifetime, which means the chances of falling sick are very low, but as others have pointed out, if you do fall sick, you will have to bear a high bill, which might even be catastrophic for you. As this is not an acceptable option, it’s worth shelling out the money for travel insurance.

What is the insurance’s point of view? If you were their only customer, they would be similarly devastated if you fell sick, but the insurance company has thousands, maybe millions, of other customers as well. So if you fall sick, they lose $9,850 on you, but that is compensated by the $150 profit they make on 99% of their other customers who stay healthy. As demonstrated, this large-scale calculation usually does not make sense for the consumer.

Remark: All this has nothing to do with whether you could afford paying out of pocket. Even if you’re very rich, as long as you take reasonably few trips, the logic stays the same.

Remark 2: Maybe an analogy could be helpful here. Imagine somebody offers you the choice between a sure $100 or a 1% chance of winning $15,000. If you only get one try, you’d probably choose the $100, but given thousands of consecutive tries, you would keep choosing the second option and get an average $150 per try in the end. It’s the same thing here, except you are paying and not getting money.

Travel insurance usually comes with health insurance for the duration of your trip. If you live in a country which has good state-provided healthcare, and travel to a country which does not have a reciprocal arrangement, you will normally have to pay all medical costs you incur.

If you accidentally slip and break a leg, or suffer a heart attack, you can end up with very expensive medical bill. IIRC, for the US, coverage of $1 million is recommended. If you have a full-leg cast as a result of injury, you may need to fly back home in first-class. This is so that you can keep your legs straight. The travel insurance should cover buying a first-class ticket for you (and possibly one of your travel companions). Doing this on your own dime may be costly.

Should you end up an a coma, and need to be medically repatriated across continents, this is very expensive.

NB. This answer is not inviting a discussion on private vs state health coverage.

Doesn’t it make sense to, instead of buying travel insurance, just save the money you would otherwise pay for it and when something happens to you, pay it from this saved money?

Frequently, yes, but as other answers note, some of the things you might have to pay for can cost more than you probably can save. Medical evacuation can cost more than most people make in a year.

The other thing to think of is that most people have other goals for their savings, such as paying for basic living expenses after retiring. You may have enough money to spend recovering from a catastrophic event, but will you have enough left over afterwards?

For myself, I’ve found that the older I get, the more attractive it is to buy travel insurance: my health is more precarious, so risks are higher, and the time I have to recover from unexpected expenses is less.

Another benefit: good insurers will have logistical support that can assist you in cases of disruption.

“Why should you have travel insurance?” – because the insurance company makes money from it. That is their reason to offer it.

What is your reason to have insurances? If you have the need to cover your potential loss because it’s catastrophic for your personal situation. You definitely should cover your house with insurance, because if it burns down, you are out of a significant amount of money, and that would be catastrophic for you (unless you are rich).

Applying this to your specific question about travel insurance: if the potential loss is financially threatening to you, insure your travel. Otherwise, yes, you are better off saving that money, and – in the case of the insured risk happening – sucking it up.
For some people, the (partly imagined) peace of mind is worth the lost insurance premium. ‘partly imagined’ because in many cases, the insurance doesn’t pay, and you end up taking the loss anyway – they typically have many exclusions and rules that allow them to decline payment.

I do not worry about insurance that will pay if I can not make the travel, unless I have to pay most of the travel in advance. By now I have saved enough money that I can forget a ticket bought in advance as long as I can cancel the hotel free of charge (which I often can.)

But that same reasoning will not go for travel insurance which does cover repatriation, medical cost beyond what my health insurance covers and several other huge cost risks.
One time being paid out for one of the huge costs is so much more than what you can safe by not having an insurance, that it is worth paying that money. Especially as most insurance covers cost very little compared to the highest amounts they pay out.

Have you ever seen the cost of repatriation where you need three seats in a regular flight, last minute? You can buy a lot of insurance for that.
And I read the report of a guy who needed to be flown of the mountains in a helicopter, and years of full time coverage with a travel insurance would not have covered that.

It is even likely that many travel insurance companies have insured their risk so that if their customers have a run of bad luck, they do get money to keep paying.