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Insurance companies are always going to give you unfavorable odds, unless you think for some reason youre more likely than average to have an accident.

I don't understand why car/home insurance isnt nationalized

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Reducing variance in a random outcome still has value. For instance, you might have the money to cover an adverse outcome, but if you could guarantee you wouldn't need the money, then you could park it in an illiquid asset (e.g. some type of investment).

Car insurance is nationalized in a few Canadian provinces.

https://en.wikipedia.org/wiki/Public_auto_insurance

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