Out of Pod Experience

Why Statistics Are Pseudoscience



For your consideration and my own personal amusement, I will demonstrate to you an alternative version of statistical theory. First, I would like to address the supposed gamblers fallacy and in order to keep it as simple as possible we will use a coin with only 2 sides. If the gambler gets heads he loses and if he gets tails he wins the pot.

Now, he watches the man in front of him get 9 heads in a row. So he throws in 100 dollars and bets tails. He loses because the streak of nine was really a streak of 10 heads in a row. He does it again but now he bets 200, and he loses again because this streak of 10 heads in a row was actually a rarer streak of 11.

What does he do now?

You guessed it... he bets on tails again and throws down 300 dollars. He wins. Not only did he win but he lost nothing at all. He used the gamblers fallacy to great effect.


How Did He Do This?

Because even though the statisticians insist that each coin flip has a static 50:50 chance of coming up heads or tails with each toss (with no other factors involved) the gambler knows that if you flip a coin 12 times then 4,095 out of every 4,096 flips it will not come up 12 heads in a row. That is called playing the odds and that is by no means a fallacy.

If the gambler saw a 12 heads streak then the odds of getting a streak of 13 is 1 in 8,192 flips. For 14 heads in a row it doubles to 1 in 16,384 and so on and so forth. Intuition trumps the static "50:50" math because the gambler has a far more complicated mechanism sitting atop his neck then a calculator. The human brain is capable of discerning probability all on it’s own intuitively and that intuition tells us that after 12 heads in a row getting another becomes increasingly unlikely despite the fact that the chances are fixed at 50:50.


Why is this? Why am I being so bold as to fly in the face of widely accepted mathematical theory? It is because I believe that the human mind knows something about the universe that the “art” of math does not. Here I will attempt to explain it.


The Status Quo

Statisticians give you 1 static equation to represent a coin and it is 50:50. They use this to convince the laymen that their equations prove that if you flipped a coin forever you can eventually flip heads 50 billion trillion trillion times in a row. Our gambler would be in trouble if that suddenly happened, followed shortly their after by a riot in the casino do to them using loaded coins.

Most people don’t have any idea what all of the statisticians important looking math means and so they find it hard to create a rational counter argument against such silliness as randomly flipping 50 billion trillion trillion heads in a row. But their instincts tell them that is not so… and then of course those same scientists reply by tell the laymen that their instincts are faulty. But are they really so faulty? They are the byproduct of 4 billion years of evolutionary processes and why should we presume to disregard them at a whim?



A Possible Solution (debate it with me if you will)

I suggest that the statisticians are missing a step or two in their mathematical representations of probability. Yes a coin has a static 50:50 probability of coming up as either heads or tails following any given flip, but is that all that there is to it? Perhaps their representation is being over simplified.


Static Probability Of A Coin

50:50 or 1:2


(Add) Theoretical Probability (any possible repeating pattern extending indefinitely)

11111111111111111111111
(or)
00000000000000000000000
(or)
010101010101010101010101

These are possible outcomes that are never actually observed in reality. They can occur but do they in physical actuality?


(Add) Consecutive Probability (or) “Patterned” Probability

11111111111111 (combo breaker)

A tendency for long streaks to be less likely to continue onward as the unit of time grows. Basically, long streaks result in a diminished probability of continuation per unit of time. This is ultimately caused by the very same 50:50 static probability that makes long streaks possible in the first place.



In Theory

1. As the unit of time increases the likelihood of longer streaks increases but never reaches 100% for any expected value. 2. The effect of static probability acts to diminish the occurrence of longer stings do to the very same 50:50 randomness that makes long streaks possible. 3. Consecutive values of (insert arbitrary large number: 30) or greater become exceedingly difficult to find as their value grows. Even when there are only 2 variables involved and given incredibly long stretches of time.



The 50:50 Threshold

An oscillation of any + and - value must come up opposite after a certain period of time or it is no longer an oscillation. Oscillations create movement and movement (or physical interactions in general) create observable chaos. So it is simply the nature of the beast to “flip” within a certain temporal threshold (or after a certain period of time) or what you are looking at is no longer an oscillation. These thresholds may vary depending on the nature of the oscillation.

A coin flipping through the air is an oscillation and the force of gravity creates a temporal value that will force the coin to stop. Everything from the force of the flip to the height of the man feeds into both variables and their output is indeed random. But what is randomness?

I'm not sure you have made any case at all for this.

IMO though anything outside of physics and chemistry is Pseudoscience. Since the the very basis of science
which is falsification, is absent.

The one thing you failed to mention though is this:

The Law of Averages

But yes this law only works with finite numbers.

When you start talking infinite numbers normal mathematics does in fact break down.

For instance: infinity + infinity = infinity. Of course this makes no sense in regards to finite mathematics.

Incorrect. The odds of rolling heads the first twelve times is 100% because the coin flips were all heads. In other words:
At zero flips, the odds of 13 heads is 1 in 8,192. If the first flip is heads, then the odds of 12 more heads is 100% (first flip) * 1 / 4096. If the 2nd flip is also heads, then the odds are 100% * 100% * 1 / 2048, etc..


A coin has no memory. If it did, then a coin wouldn't have a 50% of coming up heads.



And this is where the pseudoscience/make-believe/lack-of-anything provable comes in.


tl;dr - A coin has no memory. Test your coin flipping theory before spouting it as "fact". You'll see that that 13th flip really does only have a 50% chance to come up heads.

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http://en.wikipedia.org/wiki/Crank_%28person%29
What a posterchild the OP is of that, heh.


Except that he DIDN'T use the gambler's fallacy at all, it has absolutely nothing to do with it.
And he didn't NEED to wait until somebody threw 9 heads in a row first. Whether somebody did that or not is completely irrelevant. For all he knows, the next 9 throws might as well ALSO land heads. The fact a 9-heads streak just happened does not lower the chance of a 9-heads streak from happening right immediately after.

Also, you're doing it wrong. His third bet should not have been 300 dollars (he just broke even, he had already lost 300 which he won back), it should have been 400 dollars.
And if he lost that, his next bet would have been 800 dollars. Then 1600 dollars. And so on and so forth.
On each tails, he would win 100 dollars, and lose nothing on any streak of heads, if only he has AND IS ALLOWED to bet enough additional dollars.

Casinos have min/max betting limits for this exact reason, to prevent this system from actually working to the person's advantage even if he has enough money to place the ever-increasing bets on a losing streak.

The exact "patterns" you listed with that exact length WITHOUT infinite repetition actually do happen and ARE observed in reality.
It's only if you arbitrarily tack on the "repeated forever" qualifier when things become absurd.
If an actual pattern is REPEATING INDEFINITELY then the result you observe is by its very definition NOT random at all.

Let me put it another way. A simpler way. One which MAYBE you will understand.
Let's take a "pattern" of length 3.
There are only 8 possible "patterns" : 000, 001, 010, 011, 100, 101, 110, 111.

Having a string that ONLY repeats a SINGLE one of those "patterns" will obviously NOT be random.

But what do you know, given ANY particular random sequence of 1s and 0s, you can always break down the sequence in groups of 3, and somehow "miraculously" obtain only those 8 possible "patterns" !
Like, oh, say, 101100011101011000110001000010011001010001010010101101010011010 which I just typed by as randomly as possible hitting a place between the numpad 0 and 1 on my own keyboard.
Wow, it's 101 100 011 101 011 000 110 001 000 010 011 001 010 001 010 010 101 101 010 011 010 !!! That only contains those 8 "patterns" ! [sarcasm]What is this magic ?[/sarcasm]
I simply copypasted the sequence above and inserted spaces, of course. And well, it's not magic, obviously, there's only 8 possible ways for three 0s or 1s to be written, so of course you'll only get those eight "patterns".


By the way, calling them "patterns" is idiotic. They're not "patterns".
They're just all the possible ways in which you can arrange them.
They're simply freaking groups of 3 bits, nothing more, nothing less.
They're not magic, esoteric or supernatural in any way, shape or form.

There's no rule saying you HAVE to have all 8 groups, or that you have to have exactly as many groups of each type.
It just so happens that if you make the sequence long enough, the numbers of such groups will tend to get closer in percentage to eachother.
Just because they get closer in PERCENTAGE to eachother doesn't mean they need to get closer in ABSOLUTE NUMBERS to eachother however. They might very well diverge quite wildly from eachother in absolute counts. It's just the PERCENTAGES that get closer, because the increase in absolute count difference always grows slower (if not getting smaller) compared to the total number of groups (you can't have more groups of one type than you can have groups total, it's pretty straightforward).


You're pretty much missing the entire point of the "law of large numbers", which is an ACTUAL mathematical theorem.
The so-called "law of averages" is a misconception, a logical fallacy, closely related to the gambler's fallacy.

There is absolutely no place in the laws of large numbers that says that the number of tail throws minus number of heads throws has to be zero, not even that it should trend towards zero, and certainly NOT that the universe somehow resists a ridiculous number of heads or tails in succession.

If you have coin flips, the RATIO that is [ (Tails - Heads) / TotalThrows ] tends to get closer to 0, BUT ONLY because (tails-heads) generally remains a relatively small finite number while total throws keeps on getting larger, making the difference lower and lower as a percentage.

There's nothing saying that after 1 million throws you shouldn't ever have more than 501000 heads and less than 499000 tails (or a 2000 heads difference).
It only says that it's more likely for that difference to go down as a PERCENTAGE as you make more throws.
So you might as well get 1001900 heads and 998100 tails (3800 heads difference) or exactly the opposite, 998100 heads and 1001900 tails (a 3800 tails advantage) after an additional million throws, and the law of average says it's business as usual as far as the law in concerned, but even if you got 1002100 heads and 997900 tails (4200 heads difference) the law is just fine with that - it doesn't predict the future, it just says what's more likely to happen.

The "law of averages" does not actually reflect reality, never has, never will, not THIS reality anyway.
The "law of average" is wishful thinking, misunderstood statistics and more likely to predict events inaccurately rather than accurately, because it has a bias against what's likely to actually happen the more "unusual" the recent past was.

The "law of large numbers" however does reflect reality.
The "law of large numbers" is pure math and does NOT attempt to make any predictions of the exact events in the future, only describe the most likely overall trend.

Ok well... and there we have our first parrot dealing ad Ad hominem and all




Instead of trying to counter your epic pyramid quoting, I think that it would be better if I addressed each false statement that you just made one at a time. First, and most importantly, you said that the man in my example did not commit the gamblers fallacy. You said that I do not know what it is? Do you even know what it is?

I mean you type a good game of debate but that right there brings into question your true knowledge of even the most basic ideas of mathematics, not to mention whatever else. The gamblers fallacy is defined as:



(or)



(or)



Linkage:http://www.investopedia.com/terms/g/gamblersfallacy.asp#axzz22fUCRg9H



And in the example the gambler was not trying to earn more money from his own money, he was trying to win the pot without taking a loss. I never specified the pot but I did say it was there. I mean, are you in actuality one of these people who use big words but just make **** up as they go along or what? lol





So the gambler in my example did not commit the gamblers fallacy hmmm?
R U sure about that?

75% of all statistics are made up on the spot.

Actually, in your exact example, he used whatever the heck he used just to end up exactly where he started, with no wins and no gains.
Any person can use the martingale betting system to gain money as long as they have access to a large enough pool of cash and there's no limit to the upper size of the bet, and you do not require any prior knowledge of throws made before you start playing.



The problem is that you're using different premises for these two people.
In your example, person A believes that there's some cheating involved (that either the coin is biased or that the thrower makes it flip heads more often than it should) and thus concludes the next throw is more likely to be heads, whereas person B believes the coin is fair and the thrower is not cheating but suffers from the gambler's fallacy in believing a tails is more likely.
In reality, if the coin is perfectly fair and the one tossing it does not cheat, the chance of the coin landing heads or tails should be pretty much the same.
(If you want to get technical, in reality, whichever side is up when you start has a slightly higher chance to win, but let's ignore THAT one for now).




The odds WERE 1:4096 before the first toss. The odds NOW after 11 tosses are precisely 1:2.


Except that you can't change the result of the first 11 tosses with your 12th throw and nothing else.
The first 11 tosses become completely irrelevant for the 12th throw, unless you suspect a biased coin or cheating thrower, in which case you have a different problem.


Using YOUR logic, isolated streaks of 3 heads should happen far less than half of the time compared to streaks of 2 heads, and streaks of 4 heads should happen far less than half of the time compared to streaks of 3 heads, and so on and so forth, with every streak of X heads happening far less often than half of the numbers of streaks of X-1 heads.
In reality, you get ON AVERAGE and after a LONG SERIES OF TOSSES one independent streak of X heads for every 2 independent streaks of X-1 heads (including the first X-1 streak of ones inside the one of length X).

http://www.random.org/cgi-bin/randbyte?nbytes=200&format=b

There you go, count how many independent streaks of each length of 1s you find in there.
If you find a streak of six ones, for instance, that should count as exactly one streak of each two, three, four, five, and six ones in a row - you're only counting independent streaks (so a streak of six ones bordered by zeroes should not count as five streaks of twos, but just as one streak of twos).
Feel free to skip streaks of two or even three ones and only record streaks of four or more ones in a row bounded by zeroes.

Do it a few times, just to be through. At least 10 times. Preferably 50. Record all your results.
Heck, if you prefer, do it with this:
http://www.random.org/cgi-bin/randbyte?nbytes=15000&format=b

See if you really do get far less than half of each, or if there's roughly a halfing of streak incidence with each added 1 to the streak lenghth instead.
I'll wait.
I already am pretty sure of the results you'll be getting, and the more tries you run, the closer to what I said your results will get.

Except that there is absolutely no gambling game where winning any ADDITIONAL pot except matching the cash you just put down would work in any form the way you describe it. How about you describe the exact rules of that particular game ? How much is the pot, who puts it up, when do you win it, and how many people have to share it with you ?

For the following I will assume that the only "pot" is simply matching your own bet. So if you bet 300 dollars, the "pot" is your 300 dollars plus 300 dollars from the "house".


Your gambler placed a 100 bet. Money in pocket, original-100. He lost. Total loss 100 dollars.
Your gambler then placed a 200 bet. Money in pocket, original-300. He lost. Total loss 300 dollars.
Your gambler then placed a 300 bet. Money in pocket, original-600. He won 600. Total gains, ZERO DOLLARS.

Your gambler broke the martingale betting system rules in that third bet. He should have bet 400, not 300. If he would, he would have walked away with 100, as opposed to breaking even.
Assuming he would have lost round 3 (total losses 700 dollars), he should have bet 800 dollars. If he wins, he walks off with 100. If he loses, his total losses are now 1500 and he bets 1600. If he wins, he walks off with 100. If he loses, his total losses are now 3100 and he bets 3200 next. And so on and so forth.

Notice how at absolutely no time was it relevant what the results of the first 9 throws he did not play in matter in any way, shape of form ?