I examined Cacarulo’s sim results above but found that Cac probably missed the point here. He lists the exact number of 20-Head streaks as 0.0796950% and that of 20 or more-Head streaks as 0.1534580%. This is incorrect. These probability numbers should be too close to simulate.

As I said earlier, this coin toss example is confusing. I like my streak of 777 in a 100-time-dice-rolling game, because the probability number p(100)=31.89% is large enough to tolerate errors.

If I roll 100 times, each of the following examples is counted as ONE 777 streak:
777A …,
X777EFG …,
XYZ7777W…,
XYZ777PQW777Y …,
XYZ777PQW77777Y ….
What is the 777 streak probability?

However, if I roll 100 times, the following example is counted as TWO 777 streaks:
XYZ777PQW777Y ….
What is the 777 streak probability? Can you help simulate the results out?