That's what I mean.

Suppose you want to insure your home against fire, which could create damage of say $1m with probability 0.1%.

Without insurance, you'd have to put aside savings of $1m (the maximum loss), that would remain untouched with 99.9% probability, and be used to cover the fire damage otherwise.

With insurance, you'd pay the insurer $1m * 0.1% = $1000, plus a bit on top to cover their cost and profit. In case of fire, they cover your loss. Everyone wins.

So, with insurance you replace provisioning for the maximum loss by provisioning for the expected loss plus a fee.

(That's why one should not get insurance for small items (where one can cover the max), such as baggage or mobile phones or so, but for large items, such as house, life, health).

Oh, that's what you mean. Yes, insurance is there to smooth out risks. And I agree that items you can self-insure, you probably should.

Similarly, I can't really understand insuring against expenditures that are certain. Eg insuring for the cost of routine pregnancy (as opposed to insuring for complications only). Or even worse: yearly allowances like 100 dollars flat for new glasses: just decrease my insurance premiums by that 100 dollars, please. (Unless it's a tax dodge, then it makes sense.)