> The part about driving skill is definitely just wrong, there are many reasons why cars get damaged.

There is a long list for sure - but they are all very unlikely. The risk of having your car stolen can be mitigated with a 50$ GPS transmitter. Fire? What year is this, cars still spontaneously combust, or maybe do you live on an active volcano? A moose going though your window sounds like a life and death situation, having your car totaled and walking away safe and sound would be glorious.

If you were to purchase insurance for such risks, it would be negligible compared to the major source of insurance claims, trafic accidents. So you are are either paying for other's people accidents, and it makes no sense to continue to do so, or you are actually getting a positive value out of it because you are a bad driver, case in which it makes sense to try to improve your driving, while keeping the insurance.

All of my non-mechanical car damage has been either from someone else's driving or while the car was parked. The last one involved a guy who had a seizure at the wheel and barrelled through a red light in a truck. There wasn't any way to avoid it, fortunately it was a light swipe though.

My most expensive repair was in a parking lot where someone scraped and dented the entire side of my car trying to get into a space they really should not have. I'm under the impression most damage to cars happens in parking lots or street parking.

Still, as I wrote above, I still agree that insurance for the car isn't worth it, even though at some points it would have had positive value for me. In the long run it statistically won't.

For experienced and attentive drivers that tend to be hit by others, it's important to have proof of liability. The dashcam (preferably one that operates when the car is stopped) has saved me multiple times. Insurance companies control the claims process and setup rules that disadvantage the uninsured. Whenever I am in a trafic incident, I stop the car on the spot and take at least a bunch of photos with both vehicles involved from multiple angles, the damaged area and any debris , the general vicinity, lanes etc. The capacity of self delusion and/or outright lying of people is fantastic, I have had one claim the incident happened in a completely different intersection.

If you have such proofs and credibly convey the message that you know the law and are willing to sue, then all damage becomes fixable on someone else's insurance and you pay only normal wear and tear on your vehicle. In 200.000 Km, I only had a single fender bender that was my fault, around 200€ in damage - while insurance would have costed me in the 5000-10000€ range for the same period. Since I am an aggressive (within the limits of the law) driver, I was involved in a dozen or so minor accidents.

It's not really a capped risk, because there's nothing stopping your car from being stolen more than once.

That's a good point. So more precisely, at any instant your current risk is capped. I think that's more important, since it defines your worst case outcome. You could keep buying new cars, and after the 20th one is stolen go bankrupt, but you probably wouldn't do that if you can't afford it, so bankruptcy isn't a possible outcome.

The capped instantaneous risk lets you go for the option with highest expected value without having some chance you'll get instantly bankrupted.

I don't think it works like that. If you're just talking about avoiding bankruptcy, well you could just buy a car and not replace it the first time if it's stolen/destroyed.

Presumably in this scenario you actually require a car. That said, insuring it will cover you for any number of losses in the year, whereas setting aside an amount of savings equal to the value of the car will cover you for only one loss.

You can't just be chasing the positive EV when the variance is potentially large. For example, if Warren Buffet offered to flip a coin with you for your net worth, plus $100 bonus if you win, the expected value is very slightly positive but I believe you'd be unwise to take bet that unless your current net worth was very low already.

The risk depends on your net worth and earning power, as you allude to. Your net worth might have low variance if the ratio between it and your car's cost is high.

This is the most precise way to phrase the original recommendation. Don't get insurance for things that are easy for you tolerate the variance on. That can be true if you buy a cheap car and are pretty well off. What's the actual chance your car gets stolen 3 times in a year? After the first 2 times maybe you could change the place you store your car, get a GPS tracker or something?

There were 6858 vehicles stolen in NYC in 2020 (nearly doubled 2019) [0]. There are roughly 2M cars registered in NYC [1]. That's a 1 in 300 yearly chance to have your car stolen at least once. If we assume events are uncorrelated, there's a 1 in 100000 chance of two or more thefts, and a 1 in 25000000 chance of three or more. The odds of dying in a motor vehicle accident in the next year is something like 1 in 8000 [2].

That aside, there's all sorts of optional coverage that most people definitely can tolerate the variance on without calculation.

> You can't just be chasing the positive EV when the variance is potentially large.

There are many investment strategies that are exactly this. Writing options is one example. Forgoing insurance, like option writing, isn't possible without sufficient collateral of your own. I recognize that this is not possible for everyone. There are some cheap cars that work fine though. The biggest takeaway is to second guess the sales pitch on premium insurance plans.

Your example is another instant bankruptcy case, with reward that doesn't come close to compensating the risk.

[0]: https://www.nytimes.com/2021/01/06/nyregion/car-thefts-nyc.h... [1]: https://dmv.ny.gov/statistic/2018reginforce-web.pdf [2]: https://www.iii.org/fact-statistic/facts-statistics-mortalit...