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How Health Insurance Is Like a Lottery Ticket

Because of "expected value" considerations, someone who has deep pockets would do well to "self insure" rather than buy health (or other forms) of insurance. That is, however, not a viable alternative for most people, who need protection against "tail risk" (a small chance of a large loss).

Even so, the buyers of insurance suffer from much the same economics as the purchaser of a lottery ticket. That is, they will spend more than the insurance is objectively worth, thereby providing a profit to the insurance company. For instance, someone may pay $2,000 for $1 million of coverage. But the likelhoold of the event is only 1 in 1,000, not 1 in 500. The "expected value" of the event is only $1,000, with the insurance company pocketing the diference. The insured has paid $2,000 for $1,000 of "insurance," or $1,000 more than necessary. Lotteries work the same way, with buyers of lottery tickets losing "on average" to produce the occasional, dramatic,winner.

There are three things that can happen to the purchaser of health insurance.

1) The insured could "win" the lottery by contracting an illness and getting paid insurance. That's a painful way to "win."

2) The insured could "lose" the lottery by not getting sick while losing the premium.

3) The worst thing that can happen is that the insured pays the premium, gets the illness, and has a legitimate claim denied. That doesn't happen but it does happen. What we do know is that some insurers will delay approving a claim for some hours or days, and the patient may die in the meantime. That is one health claim that need't be paid.

Far fetched? it needn't happen very often for the insurance company to "get lucky.:" After all, they're playing the odds too.