[TML] Bigass Planet X

[Jerry W Barrington]

On 11/15/07 12:48 PM, Peter L.S. Trevor wrote:

> How about Size code = INT(3d6/1d6)?  This gives mostly small worlds, some
> asteroid belts and some medium worlds, a few large worlds, and very rarely a
> huge  world (of the size suggested).  I personally prefer INT(2d6/1d6) but
> that only goes upto size 12 ... I leave it as an exercise for the reader to
> calculate the actual probabilty curves of both.

Exactly the sort of thing I love to do!  Here's the table (note, assumes
proper rounding, .5 rounds up, to avoid getting 0's):

 1 105
 2 371
 3 265
 4 147
 5  90
 6  66
 7  51
 8  37
 9  29
10  27
11  27
12  25
13  21
14  15
15  10
16   6
17   3
18   1

All frequencies are out of 1296.  Ignoring the low amount of 1's, it has an
R^2 fit of .9267 to an exponential decay.  Rounding down gets an even
smaller amount of 0's than the 1's on the table above, so that doesn't fix
it.  I suspect that to get the 1st value higher than the 2nd (or at least
equal) would require the divisor to be about as large as the dividend, but
that would make the large ones incredibly unlikely.  Also note the odd
flatness at values 9 thru 12.  Overall, summing compressed bell curves tends
towards a 1/X distribution rather than e^-X.

Ah, I see Tim did the analysis too, using round-down...