RE: VMs: magical voynich dice game

[Jorge Stolfi <stolfi@xxxxxxxxxxxxx>]

  > [Marzio:] While playing with unique occurrencies of sentences I
  > decided to do myself a word-length statistic. I read (don't
  > remember the author - excuse me) about the similarity of the word
  > length frequences distribution in VM and a gaussian curve produced
  > by two dice shifted by 1.

It was actually nine coin tosses, shifted by 1, namely f(x) =
choose(9,x-1) for x from 1 to 10. That's because one can get  

    0   1   2   3   4   5   6   7   8   9  heads in  
    1   9  36  84 126 126  84  36   9   1  possible ways.
    
This graph is very similar to a Gausian with average value 5.5, but of
course not the same.

The (shifted) distribution of values generated by two dice is not at
all similar to a Gaussian. It is a triangular graph, 6 - abs(x - 6),
for x from 1 to 11. That's because one can get the sum

    02 03 04 05 06 07 08 09 10 11 12  in
     1  2  3  4  5  6  5  4  3  2  1  possible ways.
  
--stolfi



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