> Révész in [Strong theorems on coin tossing] tells the following amusing story attributed to T. Varga: “A class of high school children is divided into two sections. In one of the sections, each child is given a coin which he throws two hundred times, recording the resulting head-and-tail sequence on a piece of paper. In the other section, the children do not receive coins, but are told instead that they should try to write down a ‘random’ head-and-tail sequence of length two hundred. Collecting these slips of paper, [a statistician] then tries to subdivide them into their original groups. Most of the time, he succeeds quite well.”
> The statistician’s secret is [...] in a randomly produced sequence of length 200, there are usually runs of length 6 or more: the probability of the event turns out to be close to 97%. On the other hand most children (and adults) are usually afraid of writing down runs longer than 4 or 5 as this is felt as strongly “non-random”. The statistician simply selects the slips that contain runs of length 6 or more as the true random ones. Voilà!
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Obviously, the way to beat this site (or the above classroom trick) would be to use "true" random numbers. But if one doesn't have access to coins or computers, it raises the question: what is a good way to generate a long sequence of reasonably random coin flips in one's head? For example, if you've memorized many digits of pi or e or some such "believed to be normal" constant, you could use whether each digit is odd or even (or maybe even something like throw away 8 and 9, and read each remaining digit in octal to get 3 random bits). But that only gets you so far...
It feels easier to ditch some of my biases generating a sequence this way.
I don't expect the brain to work like any computer we've ever built (which seems to be the point of view this writer is attacking), but I do expect that it has the capacity to store, retrieve, and process information and so the computer analogy seems useful.