"Well, of course, it should be obvious that if you want to simulate a probability of 0.00463, all you require to be successful is that the shooter roll a 3. You could ask him to roll an 18, which is the symmetrical result; however, we are looking for distinct probabilities, so we pick one or the other. We pick 3." Roscoe waited a second, and then sprang his first surprise.
"But what happens if you define 'success' as rolling either a 3 or a 4? Now the probability of rolling a 3 is 0.00463, and the probability of rolling a 4 is 0.01389, so the probability of rolling either a 3 or a 4 is simply 0.00463 + 0.01389, or 0.01852. So you can see that we can create some new distinct probabilities by considering multiple totals as 'successful.'"
"Let me see if I get this," I replied. "To simulate 0.00463, I demand that the shooter roll a 3. To simulate 0.01389, I require that he roll a 4. And to simulate 0.01852, I ask that he roll either a 3 or a 4. Is it that simple?"
"Yeah, you've got the hang of it. But how do you start to figure out all the other possibilities?" Roscoe smiled that smile that bordered on a smirk. I started to crank up my "thinking on my feet" engine.