I have a system of two dice. Each die is rolled, and if it comes up with its maximum number that die is rolled again and the next die is added, and so on indefinitely. I've worked out the probability of getting each particular answer (1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, etc for a 6 sided die... 6 is an impossible value). I can work out the chance of getting X or more by adding probabilities of that number and higher. Okay, good, great. Here's what I'm trying to figure out how to calculate:
If I roll two dice in this fashion, and select the higher roll every time, how do work out what the chances are of a particular number showing up?
Example: I roll a d6 and a d8. What are the odds of getting a 3 on that by selecting the higher number?