blakew hit the nail on the head.

The distribution doesn't move from the realms of Binomial to Poisson until the ratio of events to probablities gets much lower than the 10:1 in the OPs example.

Increasing the size of the circle, and/or reducing the size of the ranges--eg. 10,000 & 10 respectively--and the expect behaviour starts to manifest.

This is true for the MT and even Windows default 15-bit rand() respectively:

C:\test>874353 -M=10e3 -R=10
 10000:  0.100  0.098
0.1002 0.098369796979698

C:\test>874353 -M=10e3 -R=10
 10000:  0.102  0.101
0.1024 0.100724312431243

[download]
Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.
RIP an inspiration; A true Folk's Guy

In reply to Re^4: Unexpected under-dispersion in random simulations by BrowserUk
in thread Unexpected under-dispersion in random simulations by daverave

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.