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Suppose someone is asked to provide a long string of random digits, for example:

4866710938572235108576927175549668592830123185576923856998372006958477486523 (just typed on keyboard, not generated in any way) 

How good is it expected to be if used as random source?

For example, can I ask someone to think up a list of {1,2,3,4,5,6} numbers and use it instead of a dice (and expect each number to come with p=1/6 knowing the previous numbers).

Is it safe enough to just think up UUIDs without looking for UUID generator tools?

Is there some simple (not requiring any devices or pencil&paper) algorithm to improve "thought up" random sequences?

Update: Trying little experiment as suggested in one comment:

$ xxd -r -p > test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paq8l -4 test      Creating archive test.paq8l with 1 file(s)...     test 250 -> 270         250 -> 292     $ tail -n +3 test.paq8l  | wc -c 272 $ dd if=/dev/random of=test2 bs=10 count=25 iflag=fullblock 2> /dev/null     $ paq8l -4 test2  Creating archive test2.paq8l with 1 file(s)... test2 250 -> 274          250 -> 297 

Both files (manualy typed and /dev/random-generated) seem to be uncompressible.

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    This isn't really a mathematical question. It's more of a psychological one.2012-12-03
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    I thought measuring the randomness/entropy is a mathematical thing.2012-12-03
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    This seems a bit like asking “how good are people at estimating the areas of triangles?” There’s certainly a mathematical aspect to it, but the main question itself is about how good humans are at something, so it’s essentially a psychological question.2012-12-03
  • 0
    There are statistical test suites to test quality of PRNGs - for example TestU01 or DieHard tests.2012-12-03
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    The thing here is that randomness depends on perception. For example, there are mathematical theories on electoral fraud based on the assumption that humans percieve numbers like 333, 123, etc to be less random than, say, 738. As consecuence, if one individual is altering large ammounts of data, the distribution of digits, adjacent numbers, etc, won't be natural. Of course, as any other _soft_ theory, it can be rebated very well.2012-12-03
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    I don’t remember the source, but I’ve seen it reported that human-generated strings typically have fewer repetitions than would be expected of a randomly generated string.2012-12-03
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    There are programs that typically beat a human at rock-paper-scissors, so in that sense I think it's psychologically difficult for a human to make up good impromptu pseudorandom sequences: http://ro-sham-bot.appspot.com/ If you memorize digits from a table of random numbers, you can do as well as any computer pseudorandom number generator. You could also learn some mentally computable algorithm for generating pseudorandom numbers.2012-12-04
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    @Ben Crowell, Tried that "rock-scissors-paper" bot. When I click the buttons at random the result is usually approximately equal score (as opposed of slightly losing if I try to think about moves and predict strategy).2012-12-07

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