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Jeyson Vicious
Red Federation RvB - RED Federation
30
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Posted - 2012.08.06 02:35:00 -
[61] - Quote
1 - According to quantum theory probability exists for sure.
2 - In a coin flip randomness is not the same as the numerous values you can't account for when a person does it.
3 - you must have never been in a casino. I have seen roulette wheels land an amazingly long streak of red or black wins. They post the results for the reason you mention. I have personally lost a chunk of change before because I thought surely it won't be red an 10th time... |
Whang'Lo
Set Sail to Epic Fail
2
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Posted - 2012.08.06 06:19:00 -
[62] - Quote
Quote:The so-called "law of averages" is a misconception, a logical fallacy, closely related to the gambler's fallacy.
This is actually pretty easy to prove, with a simple computer program. This was one of the very first things I ever programmed ages ago.
So you write a program that randomly generates the numbers 1-10. Then you just add a simple counter for every time it hits one of the numbers.
If you let it run for a few minutes, you will see that after awhile the counts for each number hit will average out. So it pretty much hits all the numbers equally over time. There are spikes here and there but they don't last long.
This is my understanding of the law of averages.
Also don't forget LUCK. Pretty well documented.
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Eternum Praetorian
True Creation
832
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Posted - 2012.08.06 11:36:00 -
[63] - Quote
Xenuria wrote: So thats it then? You are just going to ignore the fact that you are wrong and your argument is built on fallacy?
The only way a coin toss could be 50/50 is if it was in a vacuum, 2 dimensional and without any markings on either side to unbalance it. So even if you amended your original post to account for this lapse in reasoning you would still only be talking about hypothetical coins and not actual coins. What you think you are referencing is a "fair coin" but once again a "fair coin" is not something that can exist in reality.
Seriously, Get on my level bro. I know **** squat about math but I still know enough to realize that your a terrible troll at his best.
They are talking about hypothetical coins.
Bro...
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Xenuria
Marcabian 5th Invasion Fleet
588
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Posted - 2012.08.06 15:17:00 -
[64] - Quote
Eternum Praetorian wrote:Xenuria wrote: So thats it then? You are just going to ignore the fact that you are wrong and your argument is built on fallacy?
The only way a coin toss could be 50/50 is if it was in a vacuum, 2 dimensional and without any markings on either side to unbalance it. So even if you amended your original post to account for this lapse in reasoning you would still only be talking about hypothetical coins and not actual coins. What you think you are referencing is a "fair coin" but once again a "fair coin" is not something that can exist in reality.
Seriously, Get on my level bro. I know **** squat about math but I still know enough to realize that your a terrible troll at his best.
They are talking about hypothetical coins. Bro...
So you admit that none of what you have said can actually apply to the real world? Ok then by all means carry on. Xenuria CSM 8 |
dexington
107
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Posted - 2012.08.06 15:24:00 -
[65] - Quote
Eternum Praetorian wrote:I am sitting here with nothing to do but ponder this question. I took a coin and I flipped it 70 times. I got a streak of 7 heads in a row after only 70 flips and I got a streak of 5 tails in a row after only 43 flips. Here is the interesting part (and the question I would like to ask)
The odds of getting 7 heads in a row is 1:128 (so I got it in half the time then the math says that I should) The odds of getting 5 tails in a row is 1:32 ( so it took 2.6 times as long as the math says I should)
So are both statements not false in this experiment?
Only a fool would base a statistical experiment on a set of data this limited. Had you flipped the coin only once, and gotten heads, you could say that the coin has a proven 100% chance of flipping heads. You assume that events happens in a pattern that guarantee you get 4 flips of 5 tails in the time it takes to flip 7 heads, the only thing that is safe to assume is that you are 4 times more likely to flip 5 tails them 7 heads.
This so reminds me of playing wow, where people a dumb enough to believe that if creature has 5% chance of dropping the item you need, you have 100% chance of getting the item after killing it 20 times. GÇ£The best way to keep something bad from happening is to see it ahead of time, and you can't see it if you refuse to face the possibility.GÇ¥-á |
Xenuria
Marcabian 5th Invasion Fleet
588
|
Posted - 2012.08.06 15:25:00 -
[66] - Quote
dexington wrote:Eternum Praetorian wrote:I am sitting here with nothing to do but ponder this question. I took a coin and I flipped it 70 times. I got a streak of 7 heads in a row after only 70 flips and I got a streak of 5 tails in a row after only 43 flips. Here is the interesting part (and the question I would like to ask)
The odds of getting 7 heads in a row is 1:128 (so I got it in half the time then the math says that I should) The odds of getting 5 tails in a row is 1:32 ( so it took 2.6 times as long as the math says I should)
So are both statements not false in this experiment? Only a fool would base a statistical experiment on a set of data this limited. Had you flipped the coin only once, and gotten heads, you could say that the coin has a proven 100% chance of flipping heads. You assume that events happens in a pattern that guarantee you get 4 flips of 5 tails in the time it takes to flip 7 heads, the only thing that is safe to assume is that you are 4 times more likely to flip 5 tails them 7 heads. This so reminds me of playing wow, where people a dumb enough to believe that if creature has 5% chance of dropping the item you need, you have 100% chance of getting the item after killing it 20 times.
I am 90% certain at this point that the OP is trolling. Xenuria CSM 8 |
FloppieTheBanjoClown
The Skunkworks The Marmite Collective
2122
|
Posted - 2012.08.06 16:09:00 -
[67] - Quote
The OP claims that the odds of a coin toss are determined by previous coin tosses.
This is easily refuted. By his logic, flipping four coins in sequences has a one in 16 chance of landing all heads. Therefore when you've flipped three heads in a row, only one time in sixteen will that fourth flip yield heads. The other fifteen will result in tails.
As the odds of getting three heads in a row is one in eight, if I did 128 (8*16) coin tosses, I should get only one sequence of four heads. To the random bit generator!
The follow is 64 bytes. That's 128 sets of 4. I will assume each set of 4 is independent of the others in order to keep this simple. I have bolded all the sequences of "1111".
Quote: 00100010 00001110 00101010 10101010 01111010 01010110 00011001 00010001 00001011 11110111 11011111 11000110 10111011 00110110 10010111 10111010 10001100 10001010 00111010 00010101 10001110 01000011 01100100 01000101 11100010 11110110 11011111 11001101 01111010 01101101 01101110 11010110 00011100 01001110 01110001 00111010 11010010 01100111 00100101 00011011 01111101 00101111 11011111 01011001 00010100 01010101 01010010 01100110 01000001 00100101 10100010 00110110 00100010 00011001 01100010 01111100 01001001 11100100 01100000 01111000 11100011 10111101 10010111 00010000
Now the claims of the OP indicate he expects that for every "1111" there should be fifteen "1110". The reality of the sample above shows that they are actually evenly distributed.
Another interesting point: There were two separate runs of seven. The Skunkworks is recruiting. -áhttps://forums.eveonline.com/default.aspx?g=posts&m=1540711#post1540711 |
FloppieTheBanjoClown
The Skunkworks The Marmite Collective
2122
|
Posted - 2012.08.06 16:18:00 -
[68] - Quote
Picking out a post to best demonstrate the flaw in logic.
Eternum Praetorian wrote:At the end of the experiment, although each coin had a fixed 50:50 chance of falling either heads or tales, relativistic ally the odds were against his desired outcome by a factor of 4095:4096. The more flips the observer does the more unlikely his desired outcome becomes from a relative perspective,
The static probability does not change.
As in my previous post, let's condense this into something more testable.
The odds of me flipping two coins and getting heads on both is 1:4. For the sake of clarity, here are all possible outcomes:
00 01 10 11
What you're saying is that if I'm hoping to land heads twice, once the first coin lands on heads, I have a 75% chance that the second coin will land on tails?
Try it. Try it a hundred times. That's only two hundred coin tosses. Your whole argument falls on its face in the SIMPLEST of tests.
You've done a great job trolling. I fell for it for a while, then played along because I haven't had a good argument in forever. Now you're just stuck in a loop, saying the same thing over and over again. The Skunkworks is recruiting. -áhttps://forums.eveonline.com/default.aspx?g=posts&m=1540711#post1540711 |
Xenuria
Marcabian 5th Invasion Fleet
588
|
Posted - 2012.08.06 17:32:00 -
[69] - Quote
9/10
You got plenty of people to bite. Xenuria CSM 8 |
Eternum Praetorian
True Creation
832
|
Posted - 2012.08.06 21:01:00 -
[70] - Quote
FloppieTheBanjoClown wrote:The OP claims that the odds of a coin toss are determined by previous coin tosses..
No but I see how you could come to that conclusion. I should have just talked about regression to the mean and left it at that.
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Eternum Praetorian
True Creation
832
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Posted - 2012.08.06 21:02:00 -
[71] - Quote
Xenuria wrote:Eternum Praetorian wrote:Xenuria wrote: So thats it then? You are just going to ignore the fact that you are wrong and your argument is built on fallacy?
The only way a coin toss could be 50/50 is if it was in a vacuum, 2 dimensional and without any markings on either side to unbalance it. So even if you amended your original post to account for this lapse in reasoning you would still only be talking about hypothetical coins and not actual coins. What you think you are referencing is a "fair coin" but once again a "fair coin" is not something that can exist in reality.
Seriously, Get on my level bro. I know **** squat about math but I still know enough to realize that your a terrible troll at his best.
They are talking about hypothetical coins. Bro... So you admit that none of what you have said can actually apply to the real world? Ok then by all means carry on.
I didn't make it up. People who hold PHDs come up with this crap not me.
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FloppieTheBanjoClown
The Skunkworks The Marmite Collective
2134
|
Posted - 2012.08.06 21:15:00 -
[72] - Quote
Eternum Praetorian wrote:FloppieTheBanjoClown wrote:The OP claims that the odds of a coin toss are determined by previous coin tosses.. No but I see how you could come to that conclusion. Yeah. Because you said it. The Skunkworks is recruiting. -áhttps://forums.eveonline.com/default.aspx?g=posts&m=1540711#post1540711 |
Surfin's PlunderBunny
Sebiestor Tribe Minmatar Republic
1781
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Posted - 2012.08.06 21:19:00 -
[73] - Quote
Eternum Praetorian wrote:Xenuria wrote:Eternum Praetorian wrote:Xenuria wrote: So thats it then? You are just going to ignore the fact that you are wrong and your argument is built on fallacy?
The only way a coin toss could be 50/50 is if it was in a vacuum, 2 dimensional and without any markings on either side to unbalance it. So even if you amended your original post to account for this lapse in reasoning you would still only be talking about hypothetical coins and not actual coins. What you think you are referencing is a "fair coin" but once again a "fair coin" is not something that can exist in reality.
Seriously, Get on my level bro. I know **** squat about math but I still know enough to realize that your a terrible troll at his best.
They are talking about hypothetical coins. Bro... So you admit that none of what you have said can actually apply to the real world? Ok then by all means carry on. I didn't make it up. People who hold PHDs come up with this crap not me.
Ph.D* |
Eternum Praetorian
True Creation
832
|
Posted - 2012.08.06 21:23:00 -
[74] - Quote
FloppieTheBanjoClown wrote:Eternum Praetorian wrote:FloppieTheBanjoClown wrote:The OP claims that the odds of a coin toss are determined by previous coin tosses.. No but I see how you could come to that conclusion. Yeah. Because you said it.
No you just failed to read it correctly. But that is ok.
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Eternum Praetorian
True Creation
832
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Posted - 2012.08.06 21:34:00 -
[75] - Quote
Surfin's PlunderBunny wrote:Ph.D*
I believe that PhD is also accepted. In forum speak who knows what is socially acceptable.
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Eternum Praetorian
True Creation
832
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Posted - 2012.08.06 21:36:00 -
[76] - Quote
P.S.
Since this thread is still going can someone explain to me the meaning of "regression to the mean"
And why you think that it has nothing to do with how a sequence of heads and tails will play out over the course of large strings? I think this is what I was referring to as consecutive probability but I just didnGÇÖt know it.
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Akita T
Caldari Navy Volunteer Task Force
1204
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Posted - 2012.08.06 22:15:00 -
[77] - Quote
Eternum Praetorian wrote:Believe it or not... you may have convinced me. My word usage has been incorrect. What do you do in RL if you don't mind me asking? Computer science and industrial automation engineer by training, switched a few jobs since I graduated from the university a decade ago, from IT&telecom liason for the Romanian national power company, technical writer and equipment coder for Mitsubishi, then electrical power station design (mostly the automation part) to most recently game designer (the economy part mostly) for a web-based MMO.
Eternum Praetorian wrote: So here is a question I am sitting here with nothing to do but ponder this question. I took a coin and I flipped it 70 times. I got a streak of 7 heads in a row after only 70 flips and I got a streak of 5 tails in a row after only 43 flips. Here is the interesting part (and the question I would like to ask) The odds of getting 7 heads in a row is 1:128 (so I got it in half the time then the math says that I should) The odds of getting 5 tails in a row is 1:32 ( so it took 2.6 times as long as the math says I should) So are both statements not false in this experiment? The odds of getting 7 heads in a row if you throw it 7 times is 1:128 (0.78125%). But the odds of throwing at least 7 heads in a row if you throw it 8 times is actually 3:256 (1.171875%), because you have 256 possible combinations where at lest successive 7 heads pop up (7h+1t, 1t+7h, 8h). The odds of throwing at least 7 heads in a row if you throw a coin 9 times is actually 8:512 (1.5625%) because the combos that include 7h or more in a row are 7h+t+t, 7h+t+h, t+7h+t, h+t+7h, t+t+7h, 8h+t, t+8h, and 9h. The more coins you throw, the number of combinations that include 7 heads in a row divided by the number of total possible combinations of that many throws grows too.
There's nothing there telling you making an insanely impossible throw series is impossible even with a small number of total throws, it only tells you how likely or unlikely it is to get it. The math only tells you how many throws you need to make to have a good chance of actually getting that many throws in a row. That chance is not very easy to calculate EXACTLY, however it is much easier to APPROXIMATE.
For instance, take the example of 7 heads across 70 throws. If we wanted to compute the ACTUAL chance to get 7 heads in a row in 70 throws, we'd have to count all the possible combinations which include at least 7 heads in a 70-throw series and divide that by the total possible combinations (2^70=1,180,591,620,717,411,303,424), but that's pretty damn painful to accurately calculate. I'm pretty sure there are some decent methods for actually calculating that without actually counting everything, but I'm not really in the mood for exact calculations of that magnitude yet.
For the most conservative inaccurate estimate, we APPROXIMATE that with 10 separate sets of 7 throws (it is an approximation AGAINST the actual chances to throw 7 heads because we discard the possibilities of things like 4h at the end of one set followed by 3h at the start of the very next set, so in reality, the result we'll get is LOWER than the actual chance if we would have considered all the possibilities). Each of that separate set has a 1:128 chance to get what you want. So there's a 127:128 chance to NOT get what you want. With 10 separate sets, that's a (127/128)^10~=92% chance to NOT get what you want, so a ~8% chance to GET what you want. As previously mentioned, in reality, the chance to actually get those 7 heads in 70 throws is actually noticeably higher than 8%, because we only considered completely disjointed sets. Using THIS type of approximation, we would conclude that we'd be having only a ~1.55% chance to get 7 heads in a row out of 14 throws, when we already know that we already get a ~1.56% chance of that happening from as little as 9 throws.
Another inaccurate (and usually more generous than the reality) approximation would be to consider 64 possible sets of 7 heads (starting from position 1-7 to positions 64-70) each with 1:128 chance of happening, leading to a ~60.5% chance to NOT get what you want, and a ~39.5% chance to get at least 7 heads in a row out of just 70 throws. This is obviously incorrect (since we take into account overlapping sets), but it will be used to gather an upper cap for our estimates. Using THIS type of approximation would lead us to believe that out of 9 throws (3 sets) we would get as much as a ~2.3% chance of 7 heads in a row, when we know in reality it should only be ~1.56%.
So what we can quickly tell from those approximations ? That that the chance to get 7 heads in a row out of only 70 throws is higher than 8% but lower than 39%. In other words, not extremely likely, but quite plausible.
Quote:The odds of getting the unique sequence of 70 that I randomly flipped is 1:1,180,591,621,000,000,000,000 which seems really weird to me since any set that I randomly flipped would have the exact same odds. Thus making the whole thing meaningless outside of academic exercises. Can someone make sense of this? Because I thought this was connecting in my mind but now not so much. Are you just making allowances for these kind of uncertainties because statistics is "close enough" enough of the time? Yes, that EXACT sequence you flipped has infinitesimal odds of happening (out of all possible combinations of length 70), but it obviously DID happen, because you just got it By repeating 70 throws, your chance to get whatever sequence is also tiny, but again, it just happened. Things that seem highly improbable "at second sight" happen every time, it's nothing unusual The point however is that getting the EXACT SAME sequence both times, now THAT is something that's nearly impossible. http://wiki.eveonline.com/en/wiki/User:Akita_T http://eve-search.com/stats/Akita_T T2 BPO poll : https://forums.eveonline.com/default.aspx?g=posts&t=114789 |
Akita T
Caldari Navy Volunteer Task Force
1204
|
Posted - 2012.08.06 22:19:00 -
[78] - Quote
Whang'Lo wrote:Quote:The so-called "law of averages" is a misconception, a logical fallacy, closely related to the gambler's fallacy. This is actually pretty easy to prove, with a simple computer program. This was one of the very first things I ever programmed ages ago. So you write a program that randomly generates the numbers 1-10. Then you just add a simple counter for every time it hits one of the numbers. If you let it run for a few minutes, you will see that after awhile the counts for each number hit will average out. So it pretty much hits all the numbers equally over time. There are spikes here and there but they don't last long. This is my understanding of the law of averages. Also don't forget LUCK. Pretty well documented. The counts for each number will "average out" in the sense that the highest difference between the most common and the least common DIVIDED BY EITHER ONE OF THEM will be very small - and that's the "law of large numbers", which is accurate.
However, you can not guaranteed that at any time either of the ones that's slightly higher than the other will stay where it is while one of those that's smaller will get an extra hit - and the mistaken conception that it SHOULD USUALLY OR EVEN ALWAYS happen (when it obviously doesn't happen all that often at all) is "the law of averages", which is inaccurate.
http://wiki.eveonline.com/en/wiki/User:Akita_T http://eve-search.com/stats/Akita_T T2 BPO poll : https://forums.eveonline.com/default.aspx?g=posts&t=114789 |
Akita T
Caldari Navy Volunteer Task Force
1204
|
Posted - 2012.08.06 22:31:00 -
[79] - Quote
Eternum Praetorian wrote:can someone explain to me the meaning of "regression to the mean" It's more or less "the law of large numbers", in a slightly different form. When you take a single sample, that sample can be ANYWHERE in the sample set. Depending on the type of distribution of the variable being sampled (linear distribution, normal distribution a.k.a. bell curve, or any other type of distribution), that sample has certain chances of being closer to either of the extremes and other chances of being closer to the average. In time, the more samples you take, the closer the average of the samples will get to the average of all the actual possible values that exist in that particular distribution.
Take for instance a linear distribution between 0 and 1. Your first sample has an equal chance of being anywhere between 0 and 1, an equal chance for it to be 0.01457 or 0.97175 or even exactly 0.50000.
Now, if your FIRST sample was close to the extreme, like, say, under 0.1 or over 0.9 (total probability of being lower than 0.1 or over 0.9 being only 20%), your next sample has a much higher chance to be closer to the average (80% chance to get something between 0.1 and 0.9).
If your FIRST sample was somewhere closer to the average, like, say, between 0.4 and 0.6 (total probability to be between 0.4 and 0.6 being 20%), the chance of your next sample being farther away from the average is much higher (since the chance of getting something lower than 0.4 or higher than 0.6 is 80%).
It's only when you combine many independent samples that the average of your samples will tend to get closer and closer to 0.5 It won't always get closer to 0.5, but it USUALLY will.
http://wiki.eveonline.com/en/wiki/User:Akita_T http://eve-search.com/stats/Akita_T T2 BPO poll : https://forums.eveonline.com/default.aspx?g=posts&t=114789 |
Eternum Praetorian
True Creation
832
|
Posted - 2012.08.06 22:43:00 -
[80] - Quote
Quote:And why you think that it has nothing to do with how a sequence of heads and tails will play out over the course of large strings? I think this is what I was referring to as consecutive probability but I just didnGÇÖt know it.
As in... somehow effect how long of a string of heads, tails or any repeating sequence you will realistically achieve given pure randomness (without ever changing the static probability of each coin flip)
How does this idea not effect getting 100 heads in 100 flips--however many times in a row? It must have something to do with the fact that such things are never seen. No?
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Akita T
Caldari Navy Volunteer Task Force
1204
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Posted - 2012.08.06 23:09:00 -
[81] - Quote
100 (or more) in a row are unlikely to ever be seen by a single person due to the infinitesimal chance of it happening with a realistic number of flips.
1 : (1*1,267,650,600,228,229,401,496,703,205,376) = 1 : 2^100 odds for a single set of 100 flips 3 : (2*1,267,650,600,228,229,401,496,703,205,376) = 3 : 2^101 odds for a single set of 101 flips 8 : (4*1,267,650,600,228,229,401,496,703,205,376) = 8 : 2^102 odds for a single set of 102 flips 20 : (8*1,267,650,600,228,229,401,496,703,205,376) = 20 : 2^103 odds for a single set of 103 flips ...and so on and so forth.
Notice however how the first number in the odds of actually getting at least 100 heads in a row quickly increase with added flips, while the second number multiplier grows at a slower rate. The overall odds become better and keep getting better the more throws are made.
Eventually, the first number becomes more than 1,267,650,600,228,229,401,496,703,205,376 times larger than the second number used as the multiplier, and the odds become better than even to throw 100 or more heads in a row. Granted, the number of throws is a lot larger than the number of throws likely to be possible for a single person to ever make during his expected lifetime, but that's a different story (and one that explains why you don't see anybody claiming he made 100 heads in a row).
Then the odds keep going up afterwards. http://wiki.eveonline.com/en/wiki/User:Akita_T http://eve-search.com/stats/Akita_T T2 BPO poll : https://forums.eveonline.com/default.aspx?g=posts&t=114789 |
Eternum Praetorian
True Creation
832
|
Posted - 2012.08.06 23:49:00 -
[82] - Quote
Quote:The odds of getting 7 heads in a row if you throw it 7 times is 1:128 (0.78125%).
Isn't it 1:128 (.0078125)?
(1/2)^7 = .0078125
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Eternum Praetorian
True Creation
832
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Posted - 2012.08.07 00:27:00 -
[83] - Quote
After some consideration with regards to your explanation of regression to the mean, it seems like it is saying that after a streak of 10 in a row, there is an an inclination for the streak to end, although that is not definite. The static 50:50 does not change, but this principle of distribution will tend to apply.
Is this not so?
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Akita T
Caldari Navy Volunteer Task Force
1204
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Posted - 2012.08.07 01:03:00 -
[84] - Quote
Eternum Praetorian wrote:Quote:The odds of getting 7 heads in a row if you throw it 7 times is 1:128 (0.78125%). Isn't it 1:128 (.0078125)? (1/2)^7 = .0078125 0.0078125 = 0.78125 / 100 = 0.78125% 0.5 = 50 / 100 = 50% 1 = 100 / 100 = 100% That's what the % sign means - "percent", from the latin "per centum" meaning "from one hundred".
Eternum Praetorian wrote:After some consideration with regards to your explanation of regression to the mean, it seems like it is saying that after a streak of 10 in a row, there is an an inclination for the streak to end, although that is not definite. The static 50:50 does not change, but this principle of distribution will tend to apply. Is this not so? There's a 50% chance the streak will end on the next throw, a 25% chance it will end in two more throws, a 12.5% chance it will end in three more throws, a 6.25% chance it will end in 4 throws, a 3.125% chance it will end in 5 more throws, a 1.5625% chance it will end in 6 more throws and so on and so forth. That applies to the ending of a streak of ANY previous length, be it 2 or 10 or 20 or 30 throws. A streak of length 2 is not more likely nor less likely to end than a streak of length 30. http://wiki.eveonline.com/en/wiki/User:Akita_T http://eve-search.com/stats/Akita_T T2 BPO poll : https://forums.eveonline.com/default.aspx?g=posts&t=114789 |
Eternum Praetorian
True Creation
832
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Posted - 2012.08.07 01:16:00 -
[85] - Quote
Ok now this is what I mean by applying relativity to statistics. If I get this wrong I will just let it go so thx for bearing with me. You surely know your stuff.
ButGǪ
The odds of a streak ending in 3 more throws is 12.5 % from the perspective of the observer BEFORE he ever tosses the coin. This applies to the ending of a streak of any previous length, or any size and for any duration if you take into account general relativity before the coin is tossed. The static 50:50 of each toss does not have to change.
General Relativity being applied to statistical theory. I guess you explained my idea for me.
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Akita T
Caldari Navy Volunteer Task Force
1204
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Posted - 2012.08.07 01:26:00 -
[86] - Quote
Eternum Praetorian wrote:The odds of a streak ending in 3 more throws is 12.5 % from the perspective of the observer BEFORE he ever tosses the coin. Well, actually, if you want to be accurate, the total chance to end the streak in 3 throws or less is always 87.5% regardless of streak length. But as soon as he makes one extra throw, it either turns into 100% (if he just broke it) or into 75% to end it in 2 throws or less. Making the second throw (if he didn't break it earlier), it turns into 100% (if he broke it now) or into 50% to end it in the very next throw.
Similarly, the total chance to end any streak of any previous length anywhere in the next 4 throws is always 93.75%. Or the chance to end any streak in 5 throws or less, always 96.875%. And so on and so forth.
But as soon as you make a throw, it's either 100%=broken and you revise probabilities for breakage in the remaining X-1 tosses, or keep the probability and re-extend the toss count for the expected failure probability. The past has no relevance on future fixed probability events. It would only matter if the past could chance the odds of the very next coin toss, which it can't.
That's nothing new, that's old hat in statistics. It not statistic's fault you didn't know http://wiki.eveonline.com/en/wiki/User:Akita_T http://eve-search.com/stats/Akita_T T2 BPO poll : https://forums.eveonline.com/default.aspx?g=posts&t=114789 |
Eternum Praetorian
True Creation
832
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Posted - 2012.08.07 01:31:00 -
[87] - Quote
Your think about after you toss I am thinking about before you ever even started.
Maybe there is a reason we are not communicating. The past has no relevance to the future if you are still standing within it.
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Akita T
Caldari Navy Volunteer Task Force
1204
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Posted - 2012.08.07 01:32:00 -
[88] - Quote
I think about both before and after a toss at the same time. You think of either one or the other, never both at the same time. That's the reason we're not properly communicating. http://wiki.eveonline.com/en/wiki/User:Akita_T http://eve-search.com/stats/Akita_T T2 BPO poll : https://forums.eveonline.com/default.aspx?g=posts&t=114789 |
Eternum Praetorian
True Creation
832
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Posted - 2012.08.07 01:36:00 -
[89] - Quote
Let me put it another way, I am thinking about before you even tried to flip it X times (relative to the observer) you are thinking of it before and after each toss.
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Akita T
Caldari Navy Volunteer Task Force
1204
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Posted - 2012.08.07 01:37:00 -
[90] - Quote
Quick example, I give you one single coin toss.
BEFORE you make the toss, what's the chance that single toss you make is heads ? The correct answer assuming a perfectly unbiased coin is obviously 50:50. 50% heads, 50% tails. It didn't happen yet. Anything can still happen.
AFTER you make the toss and the toss came up heads, what's the chance the singe toss you make is heads ? Obviously, it's 100% heads, 0% tails. It already happened. You can't undo the past. You collapsed the wave function. You picked one of two alternate universes. Pick whichever explanation is more convenient, fact remains, for you, that particular toss changed from 50% heads before the toss to 100% heads after the toss was made. http://wiki.eveonline.com/en/wiki/User:Akita_T http://eve-search.com/stats/Akita_T T2 BPO poll : https://forums.eveonline.com/default.aspx?g=posts&t=114789 |
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