This question is similiar to a thread I created before... see the second post, change homer and marge to A and B, and the probability from of winning to
So assuming that A goes first;
Yup, exactly.. he can win on his first roll, his second roll, his third roll etc..
So, if we let W be the event that a 6 is rolled, and N be the event any other number, and A rolls first, then A will win if the following happens;
W
NNW
NNNNW
NNNNNNW
NNNNNNNNW
etc.
So the probability of these happening;
1/6
etc.
So the Probability of A winning is the sum of the combinations of those events happening
Which is a geometric series