Vladimir_M comments on Verifying Rationality via RationalPoker.com - Less Wrong
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Yes, in fact it happens that some of the same people I know claim to be able to beat the stock market too. I think your theory is probably true: both in gambling and on the stock market, people get deluded by occasional lucky windfalls and fail to keep track of the big picture. Yet few of them actually get deluded to the point where they'll go ahead and bankrupt themselves; the others remain rational at some level and refuse to actually put really significant sums where their mouth is, although they will brag around about their wins, possibly talking under honest delusions (but not actually acting on them, as with most beliefs that are held for signaling value).
Of course, as the EMH predicts, being smart and hard working people, if they really applied themselves to gambling systematically and full-time, they would probably be able to squeeze out something of roughly the same magnitude as what they earn in their existing day jobs. (But certainly nothing like these spectacular wins they're talking about.)