Why Insurance is usually a waste of money

Imagine someone says to you. You pay me 30 cents and if you throw a 6 (with dice), I’ll give you $1.20. Does it make sense to give them 30 cents? No of course not (6X30=180 therefore on average you wil pay 50% more than you get back). Insurance is just the same equation. Insurers use scientific techniques called actuarial science to work it out so that on average you lose money by paying them. So over a long period, if you buy insurance, you will always lose money by buying insurance just like you will always lose with enough throws of the die in the above example.
But it gives you peace of mind, I hear you insurance salesmen say. But it doesn’t give me peace of mind to know that I am giving money to someone on the basis that probability says I will lose money in the long run as against not giving them money.
There are 2 exceptions when I do pay for insurance.
1. When I’m forced to by the law. In the case of car insurance, this is fair enough – see reason 2. But in the case of insurance for my rubber motor boat engine, it’s bollox – another story.
2. When if the thing happened I could never pay for the consequences – e.g. house burns down, write off a lamborghini – etc…
Otherwise, even if the amount is large – e.g. a car, it still doesn’t make sense. The dice equation doesn’t become invalid just because the amounts are larger – as you can actually cover it…