In broad terms, you don't buy insurance because it has a positive expected return.

You buy it to hedge against risk, to spread risk out.

Let's say

completely pulling numbers out of the air

that there are 10,000 houses in a town. On average, one of them burns down each year.

What the insurer does is take money from all of those people, pool it, and pay out to the one person who gets impacted.

You buy insurance and pay maybe, I don't know, 1/5000th the price of the house per year. In the long run, you'd expect to come out behind on that, since that's more than 1/10,000th the price of the house.

But...people don't necessarily value things linearly.

In the absence of insurance, the person whose house burns down is out a house, which he may consider to be really bad. He may not consider 1/10,000th the price of a house a year or 1 in 10,000 possibility of losing his housing entirely to be equivalent.

If you'd rather have a predictable expense that you can plan around, that's what insurance provides for.

There can be some other benefits

like, an insurer has time to evaluate relevant factors, like to determine things that might reduce fire risk and to say that you have lower rates if you do X, Y, and Z. An individual probably doesn't have the data or time to do that. But it's really the risk mitigation that's the driving force behind insurance.

In general, you want to take the highest deductible you can afford to take on insurance. If you can afford to cover a $5k unexpected expense, then you want a $5k deductible, so that in the event of an incident where insurance pays out, you pay the first $5k. That way, you're not paying for risk mitigation that you don't care about, on that first $5k. Your rates will be lower.

If you can afford to cover an unexpected expense at any level, then you may well not want insurance at all, since you don't need risk mitigation.