But probabilistically doesn't it make sense to skip insurance altogether?
If insurance manages to turn a profit despite having overhead expenses (salespeople, infrastructure, lawyers, etc) and assuming they don't have a special discount in whatever they're ensuring then there are more people paying without using than there are people who need it.
If I'm an average or above average driver, for example, then it doesn't make sense to have insurance, does it? Wouldn't it make more sense to save the money I'd otherwise be using for insurance and pay myself in case something happens? That way my money would go only towards my problem and not towards worse drivers and insurance company expenses.
Is the product that insurance offer really just peace of mind?