aceside said
Bill Clinton said (Monica Lewinsky deposition) It depends upon what the meaning if the word IS, isI guess what matters here IS how you define a streak.
https://youtu.be/j4XT-l-_3y0?si=bckUb7LimNJW0U9s
aceside said
Bill Clinton said (Monica Lewinsky deposition) It depends upon what the meaning if the word IS, isI guess what matters here IS how you define a streak.
https://youtu.be/j4XT-l-_3y0?si=bckUb7LimNJW0U9s
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.
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
Luck is what happens when preparation meets opportunity.
@Don
Per request from Toolyp, I have attached attached streak examples
https://youtu.be/qSrRLEThRMo?si=8bZMDAscTIWjyi_v
https://youtu.be/LvkwfR-0jbI?si=wVvhqKUNyBdjRRTw
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?
Last edited by aceside; 05-03-2024 at 06:25 PM.
“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.
“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.
Simply to clarify
toolyp said
The probability of winning x in a row is y - the probability of winning any of the then present tosses is .5 or 2-1 or 50%. Now as for streaks, I can provide additional examples as those already displayed.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%.
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