My coworker and good friend Tim has provided a bunch of good information in response to my last post. I'm posting it here (mostly) unedited, because it sheds light on the underlying principles.
"sir, you have posted something false to the internet and it is my duty to berate you for it!
combining multiple random numbers is not the same thing as choosing a random number between bigger values.
it flys in the face of one of the most beautiful underlying principles of statistics (possibly the only beautiful thing about statistics):
If you add together many random numbers, you get a NORMAL DISTRIBUTION!
Isn't that interesting... I wonder why the normal distribution pops up so often? Oh that's right because this sort of thing happens all the time. Think about it for a bit; if you flip a coin 6 times, what is the probability of getting all heads? Is it the same as rolling a 6? Nope... you have a might higher probability of getting 3 heads than getting 6 heads. You might not notice it much for six goes, but if you flip a coint 18 times, you are very unlikely to get 18 in a row. It's because the distribution of outcomes is very different, not because one is more or less random than the other.
d&d is built on this principle; creating pseudo normalized random distributions by combining dice rolls.
If you want a better explination of this (and the 3 principles of statistics) I highly recommend reading the short chapter on statistic from "The Art of Game Design: A Book of Lenses" -- Jesse Schell. You can get it from the local library for free and the chapter is really concise and illuminating. The whole book is excellent actually."
Many thanks to Tim for the info!