This may have been mentioned ..
There are many tests for "goodness of randomness" but an easy starting point
is to plot pairs of numbers on an XY scatter graph. A genuinely random
generator will of course produce an evenly distributed scatter diagram
whereas if there is a consistent correlation between adjacent numbers it
will show up on this diagram. This test will not show every form of
non-randomness BUT any variation from random that it does show will be
genuine.

        RM


----- Original Message -----
From: "Rob Hamerling" <r.hamerling@PLANET.NL>
To: <PICLIST@MITVMA.MIT.EDU>
Sent: Wednesday, August 14, 2002 7:28 PM
Subject: Re: [PIC] Random sequence


> Robert A. LaBudde wrote:
>
> >
> > Here is a table of the first few values to make the algorithm easier
> > to follow:
> >
> >         HAMMERSLEY SEQUENCE FOR RADIX 2
> >
> > Index   Binary  Reflection              Decimal Die Roll
> > Count                                   100
> > Average                         3.4
> > Std Dev                         1.71
> >
> > 1       00000001        10000000        0.50000 4
> > 2       00000010        01000000        0.25000 2
> > 3       00000011        11000000        0.75000 5
> > 4       00000100        00100000        0.12500 1
> > 5       00000101        10100000        0.62500 4
> > 6       00000110        01100000        0.37500 3
> > 7       00000111        11100000        0.87500 6
> > 8       00001000        00010000        0.06250 1
> > 9       00001001        10010000        0.56250 4
> > 10      00001010        01010000        0.31250 2
> > 11      00001011        11010000        0.81250 5
> > 12      00001100        00110000        0.18750 2
> > 13      00001101        10110000        0.68750 5
> > 14      00001110        01110000        0.43750 3
> > 15      00001111        11110000        0.93750 6
> > 16      00010000        00001000        0.03125 1
> > 17      00010001        10001000        0.53125 4
> > 18      00010010        01001000        0.28125 2
> > 19      00010011        11001000        0.78125 5
> > 20      00010100        00101000        0.15625 1
>
> The distribution may look good, but the sequence doesn't look 'very'
> random to me.  As far as I understand the algorithm: the result is
> alternating between a digit in group 1..3 and a digit in group 4..6. For
> example a 6 is always followed by a 1,2 or 3, never by 4,5 or another 6.
>  Is this 'good enough'? Not for a good casino game, I think.
>
> Regards, Rob.
>
> --
> Rob Hamerling, Vianen, NL phone +31-347-322822
> homepage: http://www.robh.nl/
>
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