New deck at cut

[toolyp]

All the calculators give you a choice of saying the streak has to be exactly x (no more or less) or at least x. I always am interested in at "least." If you achieve a streak of 10, are you going to say you didn't achieve a streak of nine? That would be somewhat dumb.

Don

Of course, of course. You achieved a streak of 9 alright. Plus a streak of 8, a streak of 7, a streak of 6…a streak of 1. Which one you prefer? I prefer the one of 1 for losing streaks.

“at least” is a favourite of mine too. There is a formula for that too. The probability of heads/tails is 0.5 or 1 in 2. Based on your reasoning, we toss 2 times and get heads. Nope. The chance to get heads in 2 tosses is 0.75. The chance to get heads in 4 tosses is 95%. The chance to get heads in 7 tosses is 99%. The chance to get heads in 10 tosses is 99.9%.

It keeps going... But you don’t know how many streaks of 4, or 7, or 10 losses you get in a number n of trials. That was the point here. Number of streaks not probabilities for n losses/successes in a row. Streaks are real-life, events consisting of trials. Probabilities are numbers on a calculator.

No offence, just my honest opinion.

[Cacarulo]

Of course, of course. You achieved a streak of 9 alright. Plus a streak of 8, a streak of 7, a streak of 6…a streak of 1. Which one you prefer? I prefer the one of 1 for losing streaks.

“at least” is a favourite of mine too. There is a formula for that too. The probability of heads/tails is 0.5 or 1 in 2. Based on your reasoning, we toss 2 times and get heads. Nope. The chance to get heads in 2 tosses is 0.75. The chance to get heads in 4 tosses is 95%. The chance to get heads in 7 tosses is 99%. The chance to get heads in 10 tosses is 99.9%.

It keeps going... But you don’t know how many streaks of 4, or 7, or 10 losses you get in a number n of trials. That was the point here. Number of streaks not probabilities for n losses/successes in a row. Streaks are real-life, events consisting of trials. Probabilities are numbers on a calculator.

No offence, just my honest opinion.

I will chime in. I want to see if I understand correctly what is being discussed. If I have the following streak from consecutive coin flips: HTTTTTTTTTTH, how many streaks of length 10 do you see? And of length 9?
Another question: above you said that in 1000 tosses of a fair coin it is not possible to obtain a streak of length 9 or longer, is that correct?
Thank you.

Sincerely,
Cac

[toolyp]

I will chime in. I want to see if I understand correctly what is being discussed. If I have the following streak from consecutive coin flips: HTTTTTTTTTTH, how many streaks of length 10 do you see? And of length 9?
Another question: above you said that in 1000 tosses of a fair coin it is not possible to obtain a streak of length 9 or longer, is that correct?
Thank you.

Sincerely,
Cac

“HTTTTTTTTTTH” is a 10-T(ails) streak. “THHHHHHHHHHT” is a 10-H(eads) streaks.
“HTTTTTTTTTH” is a 9-T(ails) streak. “THHHHHHHHHT” is a 9-H(eads) streaks.

Don’t take me word. Take Warren Weaver’s word. He was a well-respected scholar. His acclaimed book “Lady Luck” is studied at universities worldwide. Pages 346-347 present a conclusive analysis of streaks. If you don’t understand it- there is nothing I can do about it.

No offence, just my honest opinion.

[toolyp]

I will chime in. I want to see if I understand correctly what is being discussed. If I have the following streak from consecutive coin flips: HTTTTTTTTTTH, how many streaks of length 10 do you see? And of length 9?
Another question: above you said that in 1000 tosses of a fair coin it is not possible to obtain a streak of length 9 or longer, is that correct?
Thank you.

Sincerely,
Cac

“Another question: above you said that in 1000 tosses of a fair coin it is not possible to obtain a streak of length 9 or longer, is that correct?”
Sorry I missed the another part. I don’t say it is not possible.

The probability to get 9 consecutive heads/tails has a probability, like anything else: 1/.5^9= 0.001953125 or 1 in 512. The probability for the streak is another beast: 1/.5^9*.5^2= 0.00048828125 or 1 in 2,048.

Simulations show results closer to these calculations Warren Weaver did before you and I. Of course there will be a string of 9-length outcomes, but a lower probability than an 8-length streak and much lower than a 4-length streak.

Switching gears – How are doing in casino with your CAC counting system? I said in your thread: Honestly I dont like its name and your penname. Sorry, it sounds cacophonic and self-deprecating. I don’t really trust self-deprecation.

Your system appears to me a tweaking of HiOptII, or OmegaII, or ZenII. My favourite is the easiest. 3,4,5,6=+1; T=-1. The true advantage is in taking insurance. BC is more like BS (not basic strategy). The fluctuations are very dangerous. The casino beasts also make it harder and harder. 1-10 spread min-max?

No offence, just my honest opinion.

[aceside]

Based on your reasoning, we toss 2 times and get heads. Nope. The chance to get heads in 2 tosses is 0.75. The chance to make get heads in 4 tosses is 95%. The chance to get heads in 7 tosses is 99%. The chance to get heads in 10 tosses is 99.9%.

Let me try to understand you here first. This coin toss example is confusing. You seemingly are saying this: the chance to get an at-least-one-head in two tosses is 0.75. The chance to get an at-least-one-head in 4 tosses is 95%. The chance to get an at-least-one-head in 7 tosses is 99%. The chance to get an at-least-one-head in 10 tosses is 99.9%. Is my understanding correct?

I like my streak of 777 in a 100-time-dice-rolling game. If I roll 100 times, each of the following examples is counted as ONE 777 streak:
777 …,
X777 …,
XY777 …,
XYZ7777 …,
XYZ777PQW77777Y ….

Do you agree?

[toolyp]

Let me try to understand you here first. This coin toss example is confusing. You seemingly are saying this: the chance to get an at-least-one-head in two tosses is 0.75. The chance to get an at-least-one-head in 4 tosses is 95%. The chance to get an at-least-one-head in 7 tosses is 99%. The chance to get an at-least-one-head in 10 tosses is 99.9%. Is my understanding correct?

I like my streak of 777 in a 100-time-dice-rolling game. If I roll 100 times, each of the following examples is counted as ONE 777 streak:
777 …,
X777 …,
XY777 …,
XYZ7777 …,
XYZ777PQW77777Y ….

Do you agree?

NOPE.
See me post above in reply to Cacarulo(!)

No offence, just my honest opinion.