I believe what you're looking for is described in these two pages.

http://math.stackexchange.com/questions/383704/probability-of-streaks
http://www.askamathematician.com/2010/07/q-whats-the-chance-of-getting-a-run-of-k-successes-in-n-bernoulli-trials-why-use-approximations-when-the-exact-answer-is-known/

Not to be rude, but I'd say the maths is beyond the capabilities of most and as it is a recursive function it would need a computer for large values. Hope this was what you're after. Either way it's interesting reading.