The question doesn't look right. Without being given the winning criteria, you will have infinite tosses.

Suppose and takes turn in tossing, and the first person who gets a head or three tails will win, then it will be like this:

Suppose goes first, then .

If A got a tail on his first toss, then the probability of B winning will be depend on A getting a tail, then p_B(TH) = (0.5)(0.5) = 0.25

Suppose that got a tail, then probability of winning will be

, in this case, has the advantage for getting the first toss. In this game of toss,

whereas only.