On coin flips, how do I calculate a run of "at least" 7 heads, versus a run of "exactly" 7 heads?

Question

I am trying to figure out what the frequency of "at least" 7 runs in a row for coin flips. I know that "exactly" 7 heads in a row is 0.5^7 = about 0.75%. But what at about runs of "at least" 7 heads in a row (i.e., it could be 8 or 9 or 10 or more)?

Answer 1

Well for the second part you have to consider sets of 7,8, 9, 10 .... throws and evaluate the probability of a run of at least 7 heads for sets of 7, 8, 9, 10 ..... throws and sum these probabilities which isn't a trivial problem. You could simulate it using a computer program simulating say a million times for each set.