Re^4: Unexpected under-dispersion in random simulations

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
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