Consider a game where Ann and Bob play against each other in a dice game, Ann wins if her score is higher than Bob's, Bob wins if his score is higher or if the scores are the same. What is the probability of Ann winning? I calculated and got 1 - summation from 1 to 6 of n over 36 which gave me 15/36.

Question

Consider a game where Ann and Bob play against each other in a dice game, Ann wins if her score is higher than Bob's, Bob wins if his score is higher or if the scores are the same. What is the probability of Ann winning? I calculated and got 1 - summation from 1 to 6 of n over 36 which gave me 15/36. 
Now if Ann can roll a second time what is the probability that she will win?I calculated and got 1 - summation from 1 to 6 of n^2/216 which got me 125/216
Finally if Ann can roll twice and Bob rolls twice what is the probability that Ann will win? Again I calculated and got 1 - summation from 1 to 6 of (n^2)(2n-1) over 1296 which got me the answer 505/1296. Now my question how do I calculate the probability in further cases where Ann and Bob roll n times, by finding a general formula?