For some homework in one of my classes, we are given this problem:
In a certain dice game, player $A$ rolls six six-sided dice vs. player $B$ who rolls nine four-sided dice. Each player rolls exactly once, and $A$ wins provided that the sum of his dice is strictly greater than $B$'s, otherwise $B$ wins. What is $A$'s probability of winning? Solve this analytically.
So, seeing how the highest number either one can get is $36$, I calculated each player's probabilities of making a number from within $1\dots 36$. However, I am stuck in terms of how to figure out $A$ probability of winning the dice roll. Can anyone explain to me the steps to figure this out?
Thank you kindly.