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Originally Posted by Ken G
... your formula tells you that when you encounter the $10 subset, you should pay $10. But as soon as it does so, you no longer have any expectation of breaking even in that particular subset of trials! This last remark is crucial.
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But only if you believe that this subset of trials has any relevance to the real world. I say it hasn't.
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Originally Posted by Ken G
Someone says, "let's have all the people who were among the first 5% born to one corner of the room." Of course there's going to 1/20 of the attendees in the corner. Now they say "OK, can I have every being that was the 10 billionth born to raise their hand". Why would you expect 1/20 of those people to be in the corner? Generally, that would not be the case!
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I'm very happy with that. I can't see why there should be any correlation between these two groups. If most populations are very long-lived, then a lot of those with the 10-billionth birth number are going to be in the corner. Carter doesn't care, so long as 5% of
each population was wrong in its assertion that it was in the last 95% of all births.
I think you're chasing some sort of symmetry that doesn't have to be there for Carter to work.
Grant Hutchison