There is a game I play that utilizes a particular mechanic that I am trying to assess mathematically. Me being a layman, I am having some problems figuring out one of the aspects for myself.
The basic mechanic works like this: you roll a number of 6 sided dice. Any die that rolls a 5 or a 6 nets you a success. You count your total number of successes, and the more of them there are the better.
Now, I know how to calculate the chance that I will succeed when I am trying to roll a fixed number of successes. But, sometimes the game has you roll against someone else's roll. For example:
Player A rolls X number of dice with 6 sides. Player B rolls Y number of dice with 6 sides. The person who rolls more results of 5 or 6 succeeds.
How do I calculate the probability that player A will succeed?
Thank you very much in advance!