jman19
Lifer
- Nov 3, 2000
- 11,225
- 664
- 126
Hehe, I actually came to this thread to post about the Gambler's Fallacy: http://en.wikipedia.org/wiki/Gambler%27s_fallacy
Hehe, I actually came to this thread to post about the Gambler's Fallacy: http://en.wikipedia.org/wiki/Gambler%27s_fallacy
I think the best way to explain this is as follows:
To roll a die 100 times and NOT roll a 6 is statistically unlikely - (5/6)^(100).
But even if you beat the odds and do so, the odds of your next roll not being a 6 is still 5/6.
This is because rolling dice, flipping coins, or picking numbers on a roulette wheel are all (or at least should be) independent events. Past results do not predict future outcomes.
alkemyst
No Lifer
- Feb 13, 2001
- 83,769
- 19
- 81
I really give up on this...great google searches guys and changing the question to suit your purposes.
I WILL REPEAT:
The odds to get a 6 on any ONE roll is 1/6. The odds of getting a 6 when one has not occured in a series of rolls is not 1/6.
You guys would have been the same group of idiots claiming the world was flat because everyone else thinks so.
The bolded part is wrong. Once again I will work it out using rigorous probability notations and equations:
Let A = probability of getting a 6 on roll 101
Let B = probability of not getting a 6 on rolls 1-100
Now P(A|B) = P(AB)/P(B)
P(AB) = (5/6)^100*(1/6)^1
P(B) = (5/6)^100
Therefore, P(A|B) = 1/6
So you can see that the probability of getting a 6 on roll 101 has absolutely no bearing on the fact that no 6's were rolled in any of the previous 100 rolls.
The number 100 was chosen arbitrarily - the math works out exactly the same for any number of rolls, or even the general case of N rolls.
If you still disagree, show me exactly where exactly the error is in my calculation above.
silverpig
Lifer
- Jul 29, 2001
- 27,703
- 12
- 81
*sigh*
For the purposes of this simple analogy it's 50/50. And having the inclusion of hermaphrodites does affect the probability because there is some non-zero probability of having one. This means that the sum of P(B) + P(G) must be less than 1, therefore they can't both be 50%.
There are many many other factors that go into it, but that's well beside the point.
As for 2, you are 100% completely wrong. No matter how many more times you post, the odds of you getting it right won't change
FallenHero
Diamond Member
- Jan 2, 2006
- 5,659
- 0
- 0
TuxDave
Lifer
- Oct 8, 2002
- 10,571
- 3
- 71
So you agree on my first two points because I was referring to "one" roll but what about the 3rd case?
Truth) Person A just flipped a coin 100 times and got 100 heads. Person B just started playing. The chance of getting a tail within the next 100 flips is equal for both people.
P.S. I just made up this example to point out exactly what you are saying. No googling needed for this counterexample. I guess you may be correct that I may be a person who "claim the world was flat" because I'm taking at face value that independent events mean that they are not affected by past results. And I also take at face value that there is no magic zen floating in the air that makes the things that fall under 'gambler's fallacy' true. So yeah, maybe in the future it'll be proven that there's a higher being making things happen just because he wanted it to but for now, I don't believe it.
You can't be serious. Are you really that special?
1 roll and no 6? Next roll = 1/6 chance of getting a 6
2 rolls and no 6? Next roll = 1/6 chance of getting a 6
10 rolls and no 6? Next roll = 1/6 chance of getting a 6
100 rolls and no 6? Next roll = 1/6 chance of getting a 6
IOW, whether it has already occurred or not has no bearing on the future. These are independent events.
jman19
Lifer
- Nov 3, 2000
- 11,225
- 664
- 126
You have just described the gambler's fallacy that was mentioned above. The odds don't change because the EVENTS ARE INDEPENDENT.
I also suspect you have a misunderstanding of the Law of Large Numbers...
You can "REPEAT" saying the same thing again and again, but it doesn't make it true. You haven't supported your position in any way other than saying it is "true".
alkemyst
No Lifer
- Feb 13, 2001
- 83,769
- 19
- 81
DrPizza
Administrator Elite Member Goat Whisperer
You really should give up on this... because like it or not, it's November, and the pwnage of the year thread will be coming out soon. You are absolutely, undeniably, 100% incorrect. You are a victim of the gambler's fallacy.
DrPizza
Administrator Elite Member Goat Whisperer
I'm not sure what you know.
You either have a firm grasp of the English language, else you have a firm grasp of statistics. One thing is certain: you don't have a firm grasp of both. Because what you stated (and I quoted a couple posts ago) is absolutely incorrect. Furthermore, your link to the Math Forum does absolutely nothing to support your claim.
Thus, your statement:
is either wrong because the statistics you're suggesting are laughably incorrect, else it's wrong because it doesn't state what you think it states.
edit: wft??? Actually, your link actually supports what I thought was a silly premise: that you can't understand the English language. What part of:
didn't you understand??? That's the same thing everyone here has been telling you.
DrPizza
Administrator Elite Member Goat Whisperer
Are you asking what the probability is of getting just 1 six in 100 rolls?
100*(5^6)^99*(1/6)
Are you asking what the probability is of getting at least 1 six in 100 rolls is?
It's pretty damn good!
1 - (5^6)^100
As a percent, 99.99999879253265275863333993072% probability of getting at least 1 six.
However, I think I see where your logic if failing you.
This still doesn't mean that if you roll 99 times and not get a 6 that you're more likely to get a 6 on the 100th roll to make up for it. You seem to think that if you roll a non-six 99 times that the probability of getting a 6 on the 100th roll is
99.99999879253265275863333993072% to make up for the non-6 rolls. This is (for the 10th or so time in this thread), called the gamblers FALLACY. As in false. As it "it just ain't true."
If you roll 99 times and don't get a 6, then there's a 1/6 chance that you're going to get a 6 on the next roll, and a 5/6 chance that you're about to succeed in rolling 100 times and not getting a 6. Dice don't have brains. They can't remember what just happened.
Maybe I can help.
First, look at my table of possible rolls for rolling a die twice.
11 12 13 14 15 16
21 22 23 24 25 26
31 32 33 34 35 36
41 42 43 44 45 46
51 52 53 54 55 56
61 62 63 64 65 66
Now, let's say you rolled a 5. According to your argument, a 1,2,3,4,or6 would be more likely on the next roll, because they haven't occurred yet. They're "over-due."
Look at the 5th line: After rolling a 5, there's a 1, a 2, 3, 4, 5, and a 6 possible for the next roll. All with equal probability.
If you were to make a sample space table for every possible outcome with 100 rolls of a die (good luck, it'll be freaking huge, far surpassing the number of grains of sand on a beach, heck, the number of grains of sand on earth, even exceeding the number of grains of sand on all possible planets in all of the universe. i.e. freakin huge number) Anyway, out of the huge freaking number of possibilities, every one of them having the exact same odds of happening, you'll notice that there are a heck of a lot of them where the first 99 rolls don't have a 6. Of these, the 100th roll is a 1 1/6th of the time, a 2 1/6th of the time, a 3 1/6th of the time, ..., and you guessed it (but want to deny it) a 6 1/6th of the time.
For what it's worth, the odds of rolling:
1,2,6,4,5,2,3,1,3,5,2,3,1,1,2,5,3,2 in that exact order are EXACTLY the same as rolling:
6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6
Or another way to put it, in a lottery drawing, the odds of 1,2,3,4,5,6 coming up are exactly the same as any other 5 ball combination.
Oh, and for "anyway you must not teach that high a level of math" - actually, yes, I do. This concept is taught in 9th grade in New York. (But I teach up to the level Calculus II as an adjunct professor - I don't have the students available in my school to teach a higher level course, and I hate teaching statistics.)
100*(5^6)^99*(1/6)
Are you asking what the probability is of getting at least 1 six in 100 rolls is?
It's pretty damn good!
1 - (5^6)^100
As a percent, 99.99999879253265275863333993072% probability of getting at least 1 six.
However, I think I see where your logic if failing you.
This still doesn't mean that if you roll 99 times and not get a 6 that you're more likely to get a 6 on the 100th roll to make up for it. You seem to think that if you roll a non-six 99 times that the probability of getting a 6 on the 100th roll is
99.99999879253265275863333993072% to make up for the non-6 rolls. This is (for the 10th or so time in this thread), called the gamblers FALLACY. As in false. As it "it just ain't true."
If you roll 99 times and don't get a 6, then there's a 1/6 chance that you're going to get a 6 on the next roll, and a 5/6 chance that you're about to succeed in rolling 100 times and not getting a 6. Dice don't have brains. They can't remember what just happened.
Maybe I can help.
First, look at my table of possible rolls for rolling a die twice.
11 12 13 14 15 16
21 22 23 24 25 26
31 32 33 34 35 36
41 42 43 44 45 46
51 52 53 54 55 56
61 62 63 64 65 66
Now, let's say you rolled a 5. According to your argument, a 1,2,3,4,or6 would be more likely on the next roll, because they haven't occurred yet. They're "over-due."
Look at the 5th line: After rolling a 5, there's a 1, a 2, 3, 4, 5, and a 6 possible for the next roll. All with equal probability.
If you were to make a sample space table for every possible outcome with 100 rolls of a die (good luck, it'll be freaking huge, far surpassing the number of grains of sand on a beach, heck, the number of grains of sand on earth, even exceeding the number of grains of sand on all possible planets in all of the universe. i.e. freakin huge number) Anyway, out of the huge freaking number of possibilities, every one of them having the exact same odds of happening, you'll notice that there are a heck of a lot of them where the first 99 rolls don't have a 6. Of these, the 100th roll is a 1 1/6th of the time, a 2 1/6th of the time, a 3 1/6th of the time, ..., and you guessed it (but want to deny it) a 6 1/6th of the time.
For what it's worth, the odds of rolling:
1,2,6,4,5,2,3,1,3,5,2,3,1,1,2,5,3,2 in that exact order are EXACTLY the same as rolling:
6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6
Or another way to put it, in a lottery drawing, the odds of 1,2,3,4,5,6 coming up are exactly the same as any other 5 ball combination.
Oh, and for "anyway you must not teach that high a level of math" - actually, yes, I do. This concept is taught in 9th grade in New York. (But I teach up to the level Calculus II as an adjunct professor - I don't have the students available in my school to teach a higher level course, and I hate teaching statistics.)
Your chance of getting a 6 in 100 rolls is 1 - (5/6)^100 = very close to 1 or 100% rounded up.
However, in the incredibly unlikely event that you just rolled 99 straight times and never hit a 6, your 100th roll still only has a chance to hit a 6 1/6 of the time. Your argument this whole time, is that your current roll is somehow dependant to all of the previous 99 rolls you just did, and should be assured of hitting a 6 on your 100th roll.
You sir, are the reason why casinos exist.
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