New deck at cut

[aceside]

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?

[Cacarulo]

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?

Perhaps, before reaching definitive conclusions such as "This is incorrect", it's good to consider what is known as the benefit of the doubt.
For example, you could write: "I'm not sure about that result", It sounds a bit more polite.
On the other hand, when you question something, you should do it based on some personal calculation or a reliable source.
That's different from saying, "It's wrong just because". Do you understand?
Having clarified this, I'll answer your questions, but I want to make it clear that I don't intend to go any further.

If I roll 100 times, each of the following examples is counted as ONE 777 streak:
777A …, ==> One streak of length 3
X777EFG …, ==> One streak of length 3
XYZ7777W…, ==> One streak of length 4
XYZ777PQW777Y …, ==> One streak of length 3
XYZ777PQW77777Y … ==> One streak of length 5

That's the way streaks are counted.

Sincerely,
Cac