As a contribution to the ongoing discussion of this subject, I would
like to add what I found in the famous book of Dr. Alexander Buchner
(Alexander Buchner, Mechanische Musikinstrumente, Aventinum, Praha 1992,
Verlag Werner Dausien, Hanau/Main, ISBN 3-7684-4268-3), page 192:

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  Wolfgang Amadeus Mozart, who wrote more than 600 compositions, is
mentioned as author of the "Instruction for composing any number of
waltzes or other dances with the aid of two dice, without musical
education and knowledge of how to compose", which was published at the
end of the 18th century in Amsterdam.  The publisher hoped that this
print could find considerable public interest and a huge number of
reprints proved that he was right.

  The publishing house of Nikolaus Simrock published another instruction
by Mozart at the beginning of the 19th century, describing how to
compose counter dances.  Both instructions are based on the principle
of two numerical tables and consist of a system of 8 by 11 rectangles,
filled with numbers.  The first table supports the composition of the
first eight measures, the second table for the second half.  Each one
of the eleven horizontal rows is named by a letter A to H.

  After each throw with the two dice the figures are added (e.g. 6 +
3 = 9) and the result guides to the corresponding figure (9) at the
left side of the system.  There one has to go to the figure in the
corresponding rectangle, i.e., to the letter A after the first throw,
to B after the second throw, etc.  After one has found by this way
eight figures, one has to copy the notes of the measures with the same
eight figures, one after the other. ... If the composition has to be
longer than eight measures, one continues the same way with the second
table until the composition is completed with 16 measures. ...

  Even if it is not absolutely sure that Mozart really is the author
of both these instructions, there is a high probability for that,
because of the fact that he wrote compositions for music clocks and the
fact that in his opinion composing music for dance and entertainment
was wasting his creative genius.

 - - -

I hope I translated in a reasonable way what A. Buchner wrote and I
will see whether I can find a reprint of the instructions somewhere.
Or does anybody know where to search for them?

Regards from Germany
Christian Greinacher