Dominus,
I think you read more into what I was saying then I intended. Emphasis should have been on the fact that the process I outlined would be trivial to recognize as not being randomly distributed. The point of my reply was to say I recognize that not only was the process I outlined flawed but it wasn't even a good fake. Changing the process could make it harder to detect but that wasn't the point of my reply.

Your proposal for determining the fake is in alignment with other responses. Unfortunately, it requires multiple lists to be generated where I was asking for only 1. 1 list is obviously not statistically valid so my question was flawed. For the benefit of others I am going to characterize the problem one more time but rest assured I have no argument with what you are saying.

I am assuming a list of numbers (1 - 64) has already been generated in sequential order. The task then is shuffle them randomly. According to the Wikipedia entry I linked to previously, the Fisher-Yates shuffle does this in linear time consuming N Log N bits of entropy. My proposal would have been to perform that same shuffle some number of times where sometimes groups were treated as single elements and sometimes as individual elements. The process was obviously flawed because I wasn't changing the selection criteria for each group.

Setting the flaw aside, my question was how many times you would need to shuffle before you had an acceptable fake and how you would go about telling the difference between a list done with a single Fisher-Yates shuffle having sufficient entropy against the same list down with many Fisher-Yates shuffles (on different scales) without sufficient entropy.

If I have understood the replies from you, blokhead, and others - using a single list wouldn't be statistically sufficient to determine an anomoly. For a single list, leaving the sequential order is just as valid as any other permutation of this list. Again, I don't mind being wrong for the sake of a good discussion.

Cheers - L~R

In reply to Re^2: Random Math Question by Limbic~Region
in thread Random Math Question by Limbic~Region

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.