This is a pretty well known problem. (First problem the professor in my undergrad algorithms class ever gave to us)

SPOILER

p = probability of heads

1 - p = probability of tails.

flip the coin twice:

head head = p^2

head tail/tail head = 2p(1-p)

tail tail = (1 - p)^2

Notice the two in the middle there. We can just say head tail = Heads and Tail Heads = Tails. If we get HH or PP, just do it again.

Ok, now call the above procedure, our "randomization algorithm"

we can calculate the expected running time -- our algorithm succeeds with probability 2p(1-p). The number of trials we need to run our algorithm for is a geometric random variable. Thus, the expected running time is 1/(2p(1-p)).