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A Monte Carlo Simulation with loop structure

     I'm learning Mathematica programming in AutoDidactic [mode], and
I'm working on conditionals and loop structures.  The problem that follows
is prototypical, and perhaps I can benefit from seeing some of your
I owe the problem to J. Laurie Snell from his book, "Introduction to
     In the early 1600s, Galileo was asked to explain the fact that,
although the number of triples of integers from 1 to 6 with sum 9 is
the same as the number of such triples with sum 10, when three dice are
rolled, a 9 seemed to come up less often a 10 supposedly in the experience of
     Can you suggest native Mathematica code not emulating a procedural
language for a Monte Carlo simulation experiment that runs many times
keeping track of the proportions of 9s and 10s?  Thanks in advance,
I'm interested in the looping mechanism.

Daniel Sanders

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