Dark Weaver's coin analogy was definitely what you described before. QuantumT's explanation described a different method (one that used average values from multiple selections, instead of randomly choosing one of multiple selections). If QuantumT's description was what you meant, then I think that clears things up, but it's substantially different from when you described:
"We take 20 pieces at random from that bowl, and place them into a smaller container.
We take 10 of those 20 pieces, at random, from the container."
The initial selection of 20 pieces is trivial. Every piece would have the same chance of being in the final 10 whether or not a 20 piece selection was taken first.
When QuantumT said "Now to do it Timer's way, we'll roll twice and take the average," he may have been correct in describing what you were thinking, but that wasn't clear before. You didn't describe an average.
That said, the programming for QuantumT's method would be simple, since actually doing multiple rolls would be unnecessary, one could just pull a random number 1-36 for instance and assign more numbers to the results they want to be more common. The actually methodology is trivial, though, so basically my understanding is that you just want certain results to be more common and some to be less common. I disagree, but I hope the misunderstanding is straightened out.
