One day your rival invites you out to an old fashion duel. The rules are as follows:

-You each take turns shooting each other.

-The duel stops when one person hits the other.

-Both of you are honourable enough to not take shots out of your turn.

-The probability of one person hitting the other is 1/2 and is independent of the probability of the other person hitting you.

Clearly, whoever shoots first has a distinct advantage. So your friends suggests flipping a coin for it. Little did you know that your rival uses a coin rigged in such a way that the probability of getting heads is only 1/3.

If you chose heads, what is the probability of you winning the duel?