What's the probability of tossing $r$ heads in a row before $s$ tails in a row? I know that the probability of tossing $r$ heads in a row is eventually $1$, but how about tossing $r$ heads in a row before $s$ tails in a row? What's the easiest way to compute this probability? And what if the coin is biased, say, with probability $p$ showing a head?

Here is a good and unambiguous answer. Read the first and fifth post.
