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Insurance only works if the majority pay but only the minority get paid. Anything else and you risk not getting paid if the event occurs.

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Nope. Assume you have insurance with a one-time fee of $X. It insures against a single kind of event that happens with 60% probability, and pays out $1.6X. So the majority of people are likely to have the event happen to them. The EV of the cost to the insurer is then $1.6X * 0.6 = $0.96X, so the books are expected to balance.

Obviously I'm ignoring variance in this calculation, but you can easily adjust the numbers to give a margin of safety.

You have an insurer which insures you against an even that happens 1% of the time, but you are its one and only customer. The event happens to you, so the insurer has to pay you out. Since it doesn't have any more money than what you paid into it, it goes bankrupt and you do not get paid.

For insurance to work more people have to pay into the system than people who receive payment, otherwise the insurer will go bankrupt.

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