No, I'm right and I'm damn sure of it (there are actually some other conditions I may agree with but none of been mentioned).
I also don't like to get into the whole "if you do enough trials". I am not trying to talk about the LLN or the like.
If something has a probability of happening 1 in 4, that's its probability - it WILL happen 1 in 4 times.
Since the event of the scorchstone NOT healing actually theoretically HAPPENED (21 times), the probability changes due to the unique results. You know the probability and you know the initial outcome - and you know that this probability hasn't been previously tested. Since the probability is exactly what it is, and will never change (here is one of my agreements - that the probability was never actually what the probability was), it will be so in the theoretical (read: forever as defined by all necessary (not humanly possible in practice) (1/4)) trials that proceed. To get the precise average from that point on (up to the probability from less than one per cent), a significant (albeit infinitesimally small) tendency towards the other event will be present.
The number one divided by anything is not zero.
Remember : 1/8 = .125 and .125*8=1. Nothing * zero = 1.
[Note: I also fully understand what you are trying to tell me and I feel it is flawed when talking about (something's) probability, please do not repeat the same thing over and over.)
joe10 Wrote:No, I'm right and I'm damn sure of it (there are actually some other conditions I may agree with but none of been mentioned).
I also don't like to get into the whole "if you do enough trials". I am not trying to talk about the LLN or the like.
If something has a probability of happening 1 in 4, that's its probability - it WILL happen 1 in 4 times.
Since the event of the scorchstone NOT healing actually theoretically HAPPENED (21 times), the probability changes due to the unique results. You know the probability and you know the initial outcome - and you know that this probability hasn't been previously tested. Since the probability is exactly what it is, and will never change (here is one of my agreements - that the probability was never actually what the probability was), it will be so in the theoretical (read: forever as defined by all necessary (not humanly possible in practice) (1/4)) trials that proceed. To get the precise average from that point on (up to the probability from less than one per cent), a significant (albeit infinitesimally small) tendency towards the other event will be present.
The number one divided by anything is not zero.
Remember : 1/8 = .125 and .125*8=1. Nothing * zero = 1.
[Note: I also fully understand what you are trying to tell me and I feel it is flawed when talking about (something's) probability, please do not repeat the same thing over and over.)
I haven't take collage probability or anything, however, I do know is that the results of each use is totally unneffected by the results of any other uses. just because the chance is 1/4 doesn't mean that that it WILL happen 1/4 times. It simply means that each use independently has a 1/4 chance of it happening. Think about it this way: I have a perfectly normal quarter. I flip it 9 times, it comes up heads every time. Would you be willing to make a bet where if it comes up heads again, I get 2 dollars, but if it comes up tails, you only get 1 dollar, simply because it coming up tails would move the data closer to the theoretical odds? If you look at expirimental statistics, they rarely are identical to the exact theoretical odds.
Let's put it this way:
A lot of people have the exact same misconception as joe10.
A lot of people have also lost huge amounts of money at the casino.
drspyder, I would appreciate it if you actually read what I have said before you make a comment. I have no misconceptions and I would never gamble on that kind of favor. I am simply pointing out that you were not correct yourself when you went bashing on other people.
If you think I did something wrong, point it out to me, please.
drspyder Wrote:Here, I'm going to quote Wikipedia then.
http://en.wikipedia.org/wiki/Gambler%27s_fallacy
C'mon man, you still haven't shown me where in my explanation or theory I am wrong. I have heard that article many times before and I am not saying anything that would go against the provided examples.
"If the next coin flipped were to come up heads, it would generate a run of five successive heads. The probability of a run of five successive heads is (1 / 2)5 = 1 / 32; therefore, the next coin flipped only has a 1 in 32 chance of coming up heads."
Am I saying that? NO.
In fact, the article somewhat supports my theory:
"If the coin is fair, then by definition the probability of tails must always be 0.5, never more or less, and the probability of heads must always be 0.5, never less (or more)."
Now, this just goes against what your supporters have said. If something has a probability of .5, that IS its probability (because we just said so - its not close to that or almost that). Now, if you have a coin and you flip it 20 times and get heads each time, you are now at a breakdown of 20/0 (heads/tails). A probability of .5 means 50/50, does it not? If the coin is going to be 50/50, you tell ME what you would need to get to that (50/50 overall).
No, I am not saying that you will have 20 tails in a row now, I am not saying you even need 20 consecutive tails at all. I am saying that because you KNOW it got 20 times in a row and those 20 are part of your COLLECTIVE (not independent) data, there will be an everso theoretical slight bias towards tails to get the actual probability. As you approach the actual probability (not humanly possible), you will get just that - 50/50 and to get 50/50 you would need more tails then heads.
Now that I've made it simple for you, you would understand I am not supporting a gambler or young person's mis-belief, just showing you my theory on the subject (higher chance for tails) and if you think you know what you, dyspyder, are talking about,
show me where I am wrong - don't tell me more silly little stories and treat me like I haven't taken multiple calculus courses.
In cases where you're flipping a coin multiple time, disjoint events, probability is independent. If you flip a fair coin and get heads 20 times in a row, congratulations, that happens one in a million times (1,048,576, but that's close enough).
What you are saying is that probability will stabilize itself towards the expected probability. In a sense, this is true. After all, if you flip a coin 20 times in a row...
less than 0.001% of the time, 0 heads will turn up.
~0.002%, 1 head
~0.018%, 2 heads
~0.109%, 3 heads
~0.462%, 4 heads
~1.479%, 5 heads
~3.696%, 6 heads
~7.393%, 7 heads
~12.013%, 8 heads
~16.018%, 9 heads
~17.620%, 10 heads
~16.018%, 11 heads
~12.013%, 12 heads
~7.393%, 13 heads
~3.696%, 14 heads
~1.479%, 15 heads
~0.462%, 16 heads
~0.109%, 17 heads
~0.018%, 18 heads
~0.002%, 19 heads
...and less than 0.001% of the time, you'll get 20 heads.
As you can see, there's a natural tendency to shift over time towards 50% heads, 50% tails. This is the reason why when you do something a large amount of times, the trial probability will eventually shift towards the actual probability. Even though the probability of getting exactly 50% heads is rather low, the probability of getting anywhere between 8 to 12 heads is pretty high - 73.682%. If you graphed it out, it'd look a lot like a bell curve with a standard deviation of slightly under 2 coin flips.
Finally, think about it this way - if you get bored one day and flip 468031 heads and 467914 tails, does a streak of 20 heads in a row really matter?
drspyder Wrote:In cases where you're flipping a coin multiple time, disjoint events, probability is independent. If you flip a fair coin and get heads 20 times in a row, congratulations, that happens one in a million times (1,048,576, but that's close enough).
What you are saying is that probability will stabilize itself towards the expected probability. In a sense, this is true. After all, if you flip a coin 20 times in a row...
less than 0.001% of the time, 0 heads will turn up.
~0.002%, 1 head
~0.018%, 2 heads
~0.109%, 3 heads
~0.462%, 4 heads
~1.479%, 5 heads
~3.696%, 6 heads
~7.393%, 7 heads
~12.013%, 8 heads
~16.018%, 9 heads
~17.620%, 10 heads
~16.018%, 11 heads
~12.013%, 12 heads
~7.393%, 13 heads
~3.696%, 14 heads
~1.479%, 15 heads
~0.462%, 16 heads
~0.109%, 17 heads
~0.018%, 18 heads
~0.002%, 19 heads
...and less than 0.001% of the time, you'll get 20 heads.
As you can see, there's a natural tendency to shift over time towards 50% heads, 50% tails. This is the reason why when you do something a large amount of times, the trial probability will eventually shift towards the actual probability. Even though the probability of getting exactly 50% heads is rather low, the probability of getting anywhere between 8 to 12 heads is pretty high - 73.682%. If you graphed it out, it'd look a lot like a bell curve with a standard deviation of slightly under 2 coin flips.
Finally, think about it this way - if you get bored one day and flip 468031 heads and 467914 tails, does a streak of 20 heads in a row really matter?
Wow.. once again:
I KNOW WHAT YOU ARE TRYING TO TELL ME
I am not in 5th grade math, I FULLY understand that definition of probability, stop reciting to me what your teacher taught you a few months ago, I am honestly not interested.
I still don't think you have read anything that I have said, and I've explained it to you numerous times with numerous examples and various wordings.
All of your replies have been just silly little copies of math notes/ideas.
Quote:If you flip a fair coin and get heads 20 times in a row, congratulations, that happens one in a million times (1,048,576, but that's close enough).
The fact that you just gave me the "exact" number further supports my previous statements.
How is that number, 1,048,576 derived?
(NO DON'T TELL ME 1/(.5^20))
If you flip 20 heads in a row and then do that 700 times in a row (yes, you flip 20 heads, then stop, flip 20 more, for 700 times), it would be really "odd" correct?
Well, as you do more trials (a humanly impossible amount), this outrageous average that you currently have (many heads and zero tails) would begin to even out - AGREED?
For this ratio/average to even out, you NEED something to
balance it out (as this IS the definition of something's actual probability) - AGREED?
So, to balance out, you would need more tails than heads - AGREED? (answer this question independently from any others!)
Conclusion: The frequency of tails will be increased (very very small).
Quote:less than 0.001% of the time, 0 heads will turn up.
...
If you graphed it out, it'd look a lot like a bell curve with a standard deviation of slightly under 2 coin flips.
How does that answer anything or prove anything I've said wrong?
Quote:468031 heads and 467914 tails
That's not nearly enough trials and yes, the difference does matter as that is what I have been saying the whole time.
Quote:Conclusion: The frequency of tails will be increased (very very small).
Fail/10. You're the one being unreasonable here.
I still don't understand where you're coming from, Joe.
If you have a fair coin and flip a head 20 times by some godsend, there's absolutely no reason why it would be any more likely to turn up as a tail. Each flip is an independent event, one flip does not affect another. It can't read your mind, it can't find out what the result was and give the opposite. The reason why it balances out more towards a 50/50 distribution is because as you approach an infinite number of trials, it becomes closer and closer to it.
IE: Suppose for some forsaken reason, you end up with 99 heads and 1 tail. That makes 99% heads, 1% tails. More flipping. 2000 flips later, you end up with the expected 1000 heads and 1000 tails. That makes your running total 1099 heads and 1001 tails, or 52.3% heads and 47.7% tails. You continue flipping. A couple decades later, you've ended up flipping it 2 million times. It would be expected to be 1 million heads and 1 million tails. Suppose you end up with the expected value, so the total samples is 1,001,099 heads and 1,001,001 tails, or 50.002% heads and 49.998% tails, which is near the true proportion. However, besides from the set of flips, it has been even the entire time. Although it started at 99% and 1%, over time it approached the true proportion of 50% and 50%. Tails was never ever flipped more times than heads.
Let me ask you a question: What is x/(x+50) equal to when x equals 1? 500? As x goes to infinity?
That's basically what the coin-flipping example is.
that would mean as x tended to infinty f(x) tended to 1 from the plus or minus side and it had a horizontal asymptote at -50 *which doesnt exist in the context of the question)- could you explain the relationship to the coin flipping example?