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This is a classic, but for some reason I am completely blanking on it. Something I would have read more than 30 years ago, so late 1980s at the latest.

In the story a man wishes to buy life insurance, but he keeps getting refused. He finally gets some manager interested in why this is, since theoretically, in the worst case, they should be willing to sell insurance for the full amount plus a small markup. (That is, if someone wishes to buy $1000 in life insurance, but they might die at any time, you could still sell them that insurance if they paid $1050 for it.)

As I recall, the approval of policies is done by a computer, so they debug the program. In the end it turns out that the computer has deduced that when this man dies the world will end. Thus he is, literally, uninsurable.

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    Which of course is backward logic, because if the insurance company gets paid now there's no risk of a payout. – Spencer Feb 6 at 17:26
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    @Spencer You're thinking like a manager, not a computer. ;) – DavidW Feb 6 at 17:27
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    Whoever approved the code should be fired for breach of fiduciary duty. XD – Spencer Feb 6 at 17:29
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    @Spencer ah, that's the problem. They are legally required to payout but it will be impossible to do so. They are impossible to actually insure. – PyRulez Feb 7 at 15:03
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    @Spencer and of course, there is an XKCD for it – SJuan76 Feb 7 at 22:35
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Prototaph by Keith Laumer.

The machine didn’t say much. They took me down to the sub-vault where the big voice panel is located and where the primary data goes in, and let me hear for myself. It didn’t give any explanations; it just told me. Funny; in a way it was like something I’ve always known, but when you hear Fate come right out and say it, it’s different.

When I die, the world ends

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    Aha! 100 Great Science Fiction Short Short Stories, a source of many classics. I must track that anthology down. – DavidW Feb 6 at 17:49
  • @DavidW: It's also in Thinking Machines, which you can read (with a free Internet Archive library card) here. – Quuxplusone Feb 7 at 17:05
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    This reminds a lot of the Machine of Death anthologies (one of which was simply called Machine of Death, and one of which is available free online legally). Doesn't work exactly like that, of course, but they're a series of short stories about machines that can predict your cause of death before it happens. All kinds of viewpoints, from societal changes to individuals trying to escape their fate to alternate histories and sci fi and more. – gatherer818 Feb 7 at 21:51
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    Machine of Death: machineofdeath.net/about/books – studog Feb 8 at 16:33

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