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Jordan

...and yes, that's a reference to a Dominican beer.

zbicyclist

Well, it depends on how many coins you started off with. If we started off with some very, very, very large number of coins (to Gelman's point, an impossible number), it would not be unusual that we'd get one fair coin that landed heads 1,000,000 times in a row.

But we can easily move this problem into the space of the possible. If we look at how advisory (not index) mutual funds are marketed, a strategy is to start a large number of funds with small seed money. Some strategies will perform well, possibly by accident. These get heavily promoted and the rest get quietly folded.

We're told that the fund has a glowing track record (for instance, it has always gone up -- the equivalent in this space of always coming up heads) but not given full information about the sampling space.

So, the best conclusion in these situations isn't that those who run the fund are geniuses for having a run of X excellent years, but people who've flipped a whole bunch of coins and will return to coin-flip accuracy as soon as you invest in the fund.

(I note the sum of coin flips is a random walk, and there's a whole literature on stock prices as random walks)

Max

The example seems related to Gambler's fallacy http://en.wikipedia.org/wiki/Gambler%27s_fallacy

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