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It is known that humans are worse than computers at random number generation, and that even computer's random numbers are often imperfect and predictable.

What strategies could a human employ to generate truly random numbers from a given range, and how uniformly distributed will they really be?

P.S. One trick I use, when generating a number from 1-9, is to select a random large number, say 2349, then find its digital root (2+3+4+7 = 16, 1+6=7, so digital root is 7). I don't know how random it truly is, but it's definitely better than just instinctively selecting a number from 1 to 10.

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ghosts_in_the_code
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One strategy for ranges that are powers of 2 is to split the range in half and flip a coin. If it's heads, the upper half is your new range. If it's tails, the lower half is your new range. Repeat until you have a single number. This gives you a truly random number.

Another strategy comes from George Marsaglia, on this Google Groups page: https://groups.google.com/forum/m/?hl=en#!msg/sci.math/6BIYd0cafQo/Ucipn_5T_TMJ

Choose a 2-digit number, say 23, your "seed".

Form a new 2-digit number: the 10's digit plus 6 times the units digit.

The example sequence is 23 --> 20 --> 02 --> 12 --> 13 --> 19 --> 55 --> 35 --> ...

and its period is the order of the multiplier, 6, in the group of residues relatively prime to the modulus, 10. (59 in this case).

The "random digits" are the units digits of the 2-digit numbers, ie, 3,0,2,2,3,9,5,... the sequence mod 10. The arithmetic is simple enough to carry out in your head.

I don't know what the distribution is, but the numbers look random, at least to me. You could also concatenate digits to create larger numbers. You could then get a pseudo-random number for any specified length of number (i.e. 2 digits, 3 digits, etc).

A similar question with many potential answers in the comments can be found at https://philosophy.stackexchange.com/questions/1961/are-people-capable-of-generating-a-random-number.

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Jacob
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  • That doesn't give uniform distribution if your range is not an exponent of 2. – ghosts_in_the_code Mar 05 '17 at 13:33
  • This does not provide an answer to the question. Once you have sufficient reputation you will be able to comment on any post; instead, provide answers that don't require clarification from the asker. - From Review – Robin Kramer-ten Have Mar 06 '17 at 07:24
  • @RobinKramer It does answer the question. I imagine there are better answers, but it does answer the question. The first part (the pseudo-comment) is completely separate from the answer. – Jacob Mar 06 '17 at 07:26
  • I hope that one of the moderators can move your answer to the comments because the philosophical perspective is very interesting. The solution you gave is, in my opinion, not what is expected at CogSci. At CogSci, we seek to have answers that are grounded in psychological sciences with scientific references. Your answer seems to be more or less a life-hack. – Robin Kramer-ten Have Mar 06 '17 at 07:31
  • The question was what strategies can a human use to find random numbers, correct? I'll edit my answer to make it more clear that the link to the philosophy question (which has many practical examples of how a human can generate random numbers) is not the point of my answer. – Jacob Mar 06 '17 at 07:35
  • @RobinKramer And if you feel that my answer can be improved, feel free to edit it! Or post the link in the comments yourself, and I'll delete it from my answer. That's the beauty of the Stack Exchange system. – Jacob Mar 06 '17 at 07:39
  • @RobinKramer His answer was exactly the kind of answer I was looking for. Maybe that makes it off-topic here, where should I post it then? – ghosts_in_the_code Mar 06 '17 at 17:29
  • So, with the coin-flip strategy, your approach to generating a random number is... use a binary random number generator? – Nuclear Hoagie Mar 06 '17 at 17:57
  • @Matt Haha, yeah, I'm cheating a bit on that one… – Jacob Mar 06 '17 at 18:11