New deck at cut

[aceside]

I believe James989 and Gronbog know this stuff very well, but they have been silent.

[Cacarulo]

I believe James989 and Gronbog know this stuff very well, but they have been silent.

Perhaps they prefer not to get involved in an endless questioning. Didn't you think about it?

Sincerely,
Cac

[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

[aceside]

I agree I’m rude. Apologies! I have been seeking some clarification on these things, but nobody really cared, so I guess you are my answer. On these online calculators, the following is how they define a 777 streak though:

777A …, ==> One streak of length 3
X777EFG …, ==> One streak of length 3
XYZ7777W…, ==> One streak of length 3
XYZ777PQW777Y …, ==> One streak of length 3
XYZ777PQW77777Y … ==> One streak of length 3

[DSchles]

I was just rereading the thread and came across your question, which I had failed to respond to previously. So, the 0.52 would correspond to the 0.48, and then 0.43 would become 0.48, if we exclude ties. For the streak question, I suppose we can define the streaks either way, but normally, if we push a hand, we say by convention that it doesn't interrupt a streak.

Don

[DSchles]

I believe James989 and Gronbog know this stuff very well, but they have been silent.

Yeah, seems like you're stuck with Cac and me. What do we know? Sorry you can't get any real authorities on the subject to respond.

Don

[iCountNTrack]

I am no real authority either, but luckily I can write basic code for a basic mathematical concept

For a game of blackjack:

A winning streak including pushes (p = 0.4222 + 0.0848 = 0.507) , the probability of a winning streak of 20 in 7000 rounds is 0.00428600

A winning streak excluding pushes (p = 0.4222) , the probability of a winning streak of 20 in 7000 rounds is 0.00428600 is 0.0001288758

A losing streak including pushes (p = 0.491 + 0.0848 = 0.5758), the probability of a losing streak of 20 in 7000 rounds is 0.0470625

A losing streak excluding pushes (p = 0.491), the probability of a losing streak of 20 in 7000 rounds is 0.002329314

[Freightman]

To put in simple terms the proportion issue of losing streaks proportion exceeding winning streak - the sum total of wins exceeds the sum total of losses - translates to higher bets on winning streaks and lower bets in losing streaks.

[Cacarulo]

I am no real authority either, but luckily I can write basic code for a basic mathematical concept

For a game of blackjack:

A winning streak including pushes (p = 0.4222 + 0.0848 = 0.507) , the probability of a winning streak of 20 in 7000 rounds is 0.00428600 (0.00433)

A winning streak excluding pushes (p = 0.4222) , the probability of a winning streak of 20 in 7000 rounds is 0.00428600 is 0.0001288758 (0.00013)

A losing streak including pushes (p = 0.491 + 0.0848 = 0.5758), the probability of a losing streak of 20 in 7000 rounds is 0.0470625 (0.04643)

A losing streak excluding pushes (p = 0.491), the probability of a losing streak of 20 in 7000 rounds is 0.002329314 (0.00235)

Pretty close! They are all probabilities of "at least".

Sincerely,
Cac

[Cacarulo]

I was just rereading the thread and came across your question, which I had failed to respond to previously. So, the 0.52 would correspond to the 0.48, and then 0.43 would become 0.48, if we exclude ties. For the streak question, I suppose we can define the streaks either way, but normally, if we push a hand, we say by convention that it doesn't interrupt a streak.

Don

Correct!

Sincerely,
Cac

[iCountNTrack]

Pretty close! They are all probabilities of "at least".

Sincerely,
Cac

Are you using double or single floats?

[Cacarulo]

Are you using double or single floats?

Double.

Cac

[iCountNTrack]

Double.

Cac

I will post my code when I get home. It's interesting that our numbers are not matching.