+- Southperry.net (https://www.southperry.net)
+-- Forum: Social (https://www.southperry.net/forumdisplay.php?fid=14)
+--- Forum: Rubik's Cube (https://www.southperry.net/forumdisplay.php?fid=58)
+--- Thread: Statistical Anomaly (/showthread.php?tid=28195)
Statistical Anomaly - CautionSin - 2010-07-25
If flipping a coin is completely random 50/50 chance, and you flip it 10 times and all 10 times it lands on heads. I realize the next time you flip it, it still has a 50/50 chance, but can it also be said that statistically it wants to even its results out, or land on tails. I mean if you were to flip it 10,000 times wouldn't it come out nearly even, so it cant just keep landing heads, so would that make landing on tails more likely? Or is that reasoning flawed b/c i used something that shouldn't happen to attempt to show something that should happen?
I seem to think something that happens a lot of times, giving it a statistically low probability of happening, should be more likely to not happen once more. Like if i ran the scenario 100 times, 10 heads in a row, what comes next, would tails or heads come next more often(at that 11 mark).
I guess in one hand if you get 11 in a row you have even more of a statistical anomaly, but if you get a tail next then you won't have the even more unlikely anomaly. So, i guess what im doing is comparing the chance of the anomaly continuing vs. the chance that it ends.
L> this actually ran out, and in order for it to be legitimate, it has to be a program to give a random 0 or 1, each one has a 50% chance. Now run the program until it naturally gets 10 in a row, what comes 11th. Would it be 11 0's or would a 1 come next more often and break the anomaly? And record this until you have 100 of the same scenarios, would there be a noticeable break in the anomaly?
Statistical Anomaly - Stereo - 2010-07-25
http://changingminds.org/disciplines/argument/fallacies/gamblers_fallacy.htm
It is still 50/50 no matter what happened earlier.
In fact if you have a coin come up heads that often I'd say it's slightly more likely that it's a biased coin, and will keep coming up heads. But if it's a fair coin then it's always 50-50.
HHHHHHHHHHT is no more a statistical anomaly than HHHHHHHHHHH, it just looks tidier as 11 heads in a row. Any specific sequence of 11 results is very unlikely to occur (1 in 2048, or 0.05%
, but in general if you flip a coin 11 times, you are going to hit one of the sequences.
Statistical Anomaly - sicnarf - 2010-07-25
Also regarding the "evening out," that reasoning behind that is that your total results will approach the theoretical amount. For example, you may have flipped 10 heads and 0 tails, meaning 100% heads and 0% tails. If you continue to flip, that proportion will (theoretically, at least) approach 50%/50%. (e.g. You flip another 40 times and magically end up with 20 heads and 20 tails that time. Your total is now 30 heads and 20 tails, or 60%/40%. You flip another 450 times and end up with 225 heads and 225 tails, making for 255 heads and 245 tails total, or 51% heads and 49% tails, etc)
Statistical Anomaly - CautionSin - 2010-07-25
Stereo Wrote:http://changingminds.org/disciplines/argument/fallacies/gamblers_fallacy.htm
It is still 50/50 no matter what happened earlier.
In fact if you have a coin come up heads that often I'd say it's slightly more likely that it's a biased coin, and will keep coming up heads. But if it's a fair coin then it's always 50-50.
HHHHHHHHHHT is no more a statistical anomaly than HHHHHHHHHHH, it just looks tidier as 11 heads in a row. Any specific sequence of 11 results is very unlikely to occur (1 in 2048, or 0.05%
Well, its not a biased coin b/c its a theoretical coin that has a 50/50 chance. I like the 2nd part, maybe I wasn't looking at the "anomaly" characteristic of every sequence.
Omg, actually thats all I needed, you could have said "all sequences are 'anomalies'" and that would have been enough. I was having the same question discussion on facebook and just wasn't convinced. I'm kind of disappointed there wasn't more discussion of all the dispute theories here, so...
Say i flip a coin infinite times, wouldn't it work itself into a 50/50 split. If its a 50% chance each flip, then after infinite flips it should reflect that probability otherwise i'd say the probability isn't really a correct probability after all. So if i got 10 heads wouldnt it eventually work to a 50/50 split and wouldnt that make tails more likely than heads. It seems unlikely that something unlikely would become even more unlikely more often than becoming slightly less unlikely. (i used unlikely a lot there, but the point is there, the verb'age isnt b/c its getting late for me =P)
Statistical Anomaly - Stereo - 2010-07-25
Moving towards the exact probability does only happen with infinite trials - in the short term, it only moves towards 50-50 as fast as the 10 heads becomes insignificant.
The 50-50 thing is a property of the coin that shouldn't (doesn't) depend on previous flips. Each time you flip it, it's equally likely to come up heads or tails, no matter what you've already seen. If this weren't true, then there's some sort of mechanism that communicates previous flips to future flips. And how would you explain that?
Statistical Anomaly - CautionSin - 2010-07-26
Fair enough explanation. Now, this is why we don't "scroll burn" before we scroll, b/c it has no bearing on the future results, no matter how many u get in a row (streaks) or how many u fail (if i get bad a lot i hv to get good). I'm disappointed though, when I gave my dispute to other people, and when i gave it aloud, I had them questioning their commonly held rules on statistics.
Statistical Anomaly - larmie - 2010-08-12
CautionSin Wrote:Fair enough explanation. Now, this is why we don't "scroll burn" before we scroll, b/c it has no bearing on the future results, no matter how many u get in a row (streaks) or how many u fail (if i get bad a lot i hv to get good). I'm disappointed though, when I gave my dispute to other people, and when i gave it aloud, I had them questioning their commonly held rules on statistics.
Ever heard of "random number adjustments"? In old computer games you could adjust the random variables by timing it or pressing random buttons. Imagine the slot machine fraud in Ocean's 13. That's the technique people use in TAS (tool-assisted speedplay). People may believe something like that is possible which would explain the nonsense that is scroll burning (otori syo in japanese).
The success rate is determined by the server; unless you hack the server, you can't influence the outcome in anyway.
Statistical Anomaly - Random_Overlord - 2010-08-12
CautionSin Wrote:If flipping a coin is completely random 50/50 chance, and you flip it 10 times and all 10 times it lands on heads. I realize the next time you flip it, it still has a 50/50 chance, but can it also be said that statistically it wants to even its results out, or land on tails. I mean if you were to flip it 10,000 times wouldn't it come out nearly even, so it cant just keep landing heads, so would that make landing on tails more likely? Or is that reasoning flawed b/c i used something that shouldn't happen to attempt to show something that should happen?
I seem to think something that happens a lot of times, giving it a statistically low probability of happening, should be more likely to not happen once more. Like if i ran the scenario 100 times, 10 heads in a row, what comes next, would tails or heads come next more often(at that 11 mark).
I guess in one hand if you get 11 in a row you have even more of a statistical anomaly, but if you get a tail next then you won't have the even more unlikely anomaly. So, i guess what im doing is comparing the chance of the anomaly continuing vs. the chance that it ends.
L> this actually ran out, and in order for it to be legitimate, it has to be a program to give a random 0 or 1, each one has a 50% chance. Now run the program until it naturally gets 10 in a row, what comes 11th. Would it be 11 0's or would a 1 come next more often and break the anomaly? And record this until you have 100 of the same scenarios, would there be a noticeable break in the anomaly?
The point about coin flipping to, is the psyics of the area you flip in.
The Dynamics of the coin
The shape, the density
The Force at which you flip, and the fatigue from previous attempts.
The direction in which you flip, the height, the wind current.
You also have to consider where your hand is or if you even catch the coin.
You have to take consideration of all the factors that could intervien in the results.
When you calculate the EXACT chance to get a coin on a cirtain side, it's 50%, but each factor places the coin at millions of instances if you were to flip elsewhere.
Statistical Anomaly - Lord Xela - 2010-08-12
larmie Wrote:In old computer games you could adjust the random variables by timing it or pressing random buttons.My personal favorite example of this? Pokemon TCG for Gameboy Color. That game had a fixed RNG (as in it didn't reset the seed every time the game was turned off/on), so EVERY COIN FLIP was manipulatable. If you do something that needs a coin flip, you can save before hand. If it doesn't come up the way you want, reset and do something else and let the enemy burn off the bad flip, because no matter what the next coin flip will be that bad flip. Poor programming at its finest.
Stereo Wrote:HHHHHHHHHHT is no more a statistical anomaly than HHHHHHHHHHH, it just looks tidier as 11 heads in a row. Any specific sequence of 11 results is very unlikely to occur (1 in 2048, or 0.05%), but in general if you flip a coin 11 times, you are going to hit one of the sequences.I've been wanting to comment on this for a while, because (unless I overlooked it) no one has made this point yet. The reason that a 50/50 H/T ratio is the most normal is because, while each specific sequence in a 10 coin flip has 1/2^10 (1/1024) chance of occurring, that's each specific permutation. If we look at combinations instead, we see that HHHHHTTTTT is exactly the same as HTHTHTHTHT. So while the permutation HHHHHTTTTT has the same 0.1% chance of occurring as HHHHHHHHHH, the combination HHHHHTTTTT has significantly more permutations and thus chances of occurring. I'm terrible with probability, so I'm not sure of the exact numbers, but I know enough to say with certainty that the most likely combination will be one with equal numbers of heads and tails.
Statistical Anomaly - Russt - 2010-08-12
^ in fact you can envision it as Pascal's triangle.
Every row represents a coin flip. For each heads you go down and to the left, for each tails you go down and to the right. Reading across the rows tells you the number of permutations possible for each split of heads and tails.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
1 10 45 120 210 252 210 120 45 10 1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
1 10 45 120 210 252 210 120 45 10 1
In particular, there are 252 permutations of 5 heads and 5 tails, so it has a 252/1024 chance (just under 1/4) of occurring.
Statistical Anomaly - Stereo - 2010-08-12
Lord Xela Wrote:So while the permutation HHHHHTTTTT has the same 0.1% chance of occurring as HHHHHHHHHH, the combination HHHHHTTTTT has significantly more permutations and thus chances of occurring.
But if you've already flipped the coin 10 times and got HHHHHHHHHH then the prior chance can be ignored - the only possible sequences are HHHHHHHHHHT and HHHHHHHHHHH. You'll never flip that 11th coin and end up with 6 tails.
Statistical Anomaly - ImagineAll - 2010-08-13
Each coin toss will remain 50/50 as each individual toss happens independently.
Statistical Anomaly - Lord Xela - 2010-08-13
Stereo Wrote:But if you've already flipped the coin 10 times and got HHHHHHHHHH then the prior chance can be ignored - the only possible sequences are HHHHHHHHHHT and HHHHHHHHHHH. You'll never flip that 11th coin and end up with 6 tails.
Yes, this is true. The point I'm making is that yes, as you said before HHHHHHHHHHT is just as rare as HHHHHHHHHHH as permutations, but as combinations, the former is 11 times as likely. It's quite true that past flips have no impact on future flips. I just wasn't making my point with the assumption that we had flipped 10 coins already - I was commenting on those first 10 flips themselves.
Statistical Anomaly - Hanabira.Kage - 2010-08-13
ImagineAll Wrote:Each coin toss will remain 50/50 as each individual toss happens independently.
True. Every probability of every single coin toss is calculated with replacement; in other words, the probability of getting either a Heads or Tails is always 50%.
This is, of course, assuming that every coin toss is performed in the exact same conditions with exactly the same amount of force applied every time. The coin also has to be perfectly "unbiased".
Just because the first 10 coins turned out Heads, it doesn't make the next flip more likely to give you a Tails; you'll still have an equal chance of getting a Heads or Tails.
This doesn't mean that each and every set of coin tosses you do will always give you an equal number of Heads and Tails; all "probability" means is that as n, the number of coin tosses, approaches infinity, the ratio of the results you obtain will approach a certain value (in this case, it's 1:1). Technically speaking, it's impossible to flip a coin an infinite number of times (infinity doesn't technically exist). However you'll notice that the higher n is, the closer the ratio of Heads to Tails gets to 1:1.
This is, of course, assuming that every coin toss is performed in the exact same conditions with exactly the same amount of force applied every time. The coin also has to be perfectly "unbiased".
Just because the first 10 coins turned out Heads, it doesn't make the next flip more likely to give you a Tails; you'll still have an equal chance of getting a Heads or Tails.
This doesn't mean that each and every set of coin tosses you do will always give you an equal number of Heads and Tails; all "probability" means is that as n, the number of coin tosses, approaches infinity, the ratio of the results you obtain will approach a certain value (in this case, it's 1:1). Technically speaking, it's impossible to flip a coin an infinite number of times (infinity doesn't technically exist). However you'll notice that the higher n is, the closer the ratio of Heads to Tails gets to 1:1.