## Human random numbers

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## Pick a number between 1 and 20

1
19
4%
2
18
4%
3
15
3%
4
15
3%
5
10
2%
6
16
4%
7
23
5%
8
17
4%
9
28
6%
10
18
4%
11
22
5%
12
43
10%
13
29
6%
14
36
8%
15
14
3%
16
21
5%
17
41
9%
18
21
5%
19
24
5%
20
18
4%

evilbeanfiend
Posts: 2650
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Location: the old world

### Human random numbers

lets do some science and see how good a human based RNG this fora is

(And no fair looking at the results before choosing a number.) - gm
in ur beanz makin u eveel

Technical Ben
Posts: 2986
Joined: Tue May 27, 2008 10:42 pm UTC

### Re: Human random numbers

Could we take this a step further and see if we can make other processes out of forumites? Then we can build a central processor, then some sort of program all run on forum posts... http://xkcd.com/505/
It's all physics and stamp collecting.
It's not a particle or a wave. It's just an exchange.

Blatm
Posts: 638
Joined: Mon Jun 04, 2007 1:43 am UTC

### Re: Human random numbers

I like these sorts of polls. I can't wait to see how it will turn out (if we ever get enough people to participate).

Velifer
Posts: 1132
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Location: 40ºN, 83ºW

### Re: Human random numbers

My hypothesis (pre-vote)
Spoiler:
bell-curve. Skewed toward a mean around 7.

My hypothesis (post-vote)
Spoiler:
I suck at guessing.
Time flies like an arrow, fruit flies have nothing to lose but their chains -Marx

Ptolom
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### Re: Human random numbers

Spoiler:
I predict a profusion of 17, 18, 19's people tend to pick a bigger number, not a "round" number like 1 ,5 ,10 or twenty, not an even number and possibly a prime. In an attempt to be more random, they do the very opposite.

Sana
Posts: 123
Joined: Wed Sep 26, 2007 3:53 am UTC

### Re: Human random numbers

The limited choices affect the results, and therefore the test is flawed.

itaibn
Posts: 142
Joined: Mon Dec 29, 2008 7:06 pm UTC

### Re: Human random numbers

After voting and looking at the results, I decided the majority of xkcd is too clever to fall for any of the usual tricks.
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gmalivuk
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### Re: Human random numbers

Sana wrote:The limited choices affect the results, and therefore the test is flawed.

It's not flawed. The test is to see if the general population of people taking this poll are capable of picking numbers randomly. If there is a strong preference for some numbers over others, it's strong evidence against that.

Personally, I think
Spoiler:
numbers like 7 and 17 that first seem "more random" to people will actually be picked less than average in this case, because people are consciously avoiding them.

This gives me an idea for a forum game...
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
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Charlie!
Posts: 2035
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### Re: Human random numbers

Spoiler:
13 is unlucky, apparently.
Some people tell me I laugh too much. To them I say, "ha ha ha!"

spdqbr
Posts: 171
Joined: Sat Mar 08, 2008 1:41 am UTC
Location: A shaker of salt

### Re: Human random numbers

I chose 14 as it's the closest to (pi %1), which is fun.
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual.

Galileo

Zeno's Pair of Ducks
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### Re: Human random numbers

yy2bggggs
Posts: 1261
Joined: Tue Oct 17, 2006 6:42 am UTC

### Re: Human random numbers

I picked 14 because in the word "STAN" using modulo 20 arithmetic, T is the additive identity and S and A are inverses, leaving N which is 14. "STAN" came from my makeshift entropy selection strategy.

evilbeanfiend
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Location: the old world

### Re: Human random numbers

itaibn wrote:After voting and looking at the results, I decided the majority of xkcd is too clever to fall for any of the usual tricks.

i don't know, there seems to be a slight bias towards numbers > 10. i was going to assume a model for error in each bin of the sqrt of the number in the bin, so the distribution is slightly flatter then it looks but still not flat within errors (feel free to suggest better error models btw)
in ur beanz makin u eveel

Knightshire
Posts: 19
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### Re: Human random numbers

I think there are too many choices with not enough people to do some real statistical analysis.
It would be more meaningful if there were only 5 choices.

Technical Ben
Posts: 2986
Joined: Tue May 27, 2008 10:42 pm UTC

### Re: Human random numbers

Spoiler:
Hmm. I chose 14. I was watching snooker, so that may have influenced me (scores on the tv and all that). Also 4 is my favourite number, but I thought that was too obvious a choice. It's great to see "my" number is winning currently!
It's all physics and stamp collecting.
It's not a particle or a wave. It's just an exchange.

evilbeanfiend
Posts: 2650
Joined: Tue Mar 13, 2007 7:05 am UTC
Location: the old world

### Re: Human random numbers

Knightshire wrote:I think there are too many choices with not enough people to do some real statistical analysis.
It would be more meaningful if there were only 5 choices.

well the results already look statistically significant to me, if it were flat we would expect with 100 votes every bin to contain 5 +/- sqrt(5), some bins are clearly way off this.
in ur beanz makin u eveel

d0nk3y_k0n9
Posts: 97
Joined: Sun May 03, 2009 4:27 pm UTC

### Re: Human random numbers

I'll vote as soon as I can find my d20... or a decent dicegen.

Lol it was sitting buried on my desk. That didn't take long.

quintopia
Posts: 2906
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Location: atlanta, ga

### Re: Human random numbers

2

Ieatsoap6
Posts: 204
Joined: Sat Dec 22, 2007 7:24 pm UTC
Location: Atlanta

### Re: Human random numbers

I find it interesting that 6 and 14 are winning since they're symmetric about 10.

I chose 16 because it was the right choice.

gmalivuk
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### Re: Human random numbers

evilbeanfiend wrote:well the results already look statistically significant to me, if it were flat we would expect with 100 votes every bin to contain 5 +/- sqrt(5), some bins are clearly way off this.

Yeah, but isn't that only one standard deviation? Being outside of one sigma is not exactly significant, I don't think.
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
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evilbeanfiend
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Location: the old world

### Re: Human random numbers

yes its not amazing, and since then it already looks flatter.
in ur beanz makin u eveel

BlackSails
Posts: 5315
Joined: Thu Dec 20, 2007 5:48 am UTC

### Re: Human random numbers

I actually chose mine randomly, by closing my eyes and scrolling up and down. My mouse landed on 12, so thats what I chose

scikidus
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### Re: Human random numbers

1. Because I can.
Happy hollandaise!

"The universe is a figment of its own imagination" -Douglas Adams

Yakk
Poster with most posts but no title.
Posts: 11129
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### Re: Human random numbers

If you rolled a d20 100 times, the 95% conf. interval would be about:
2 * sqrt(.95*.05*n) = 4.35889894
with an expected value of 5.

So for a given random digit, you'd expect somewhere between 0.85 and 9.35 votes on it.

However, the problem is we are looking at all 20, and searching for one that is outside that range. It is perfectly reasonable for 1 or more attempts, out of 20, to be outside the 95% confidence interval, even if the results where uniformly selected. That is what the 95% confidence interval means.

The fact we have only 2 outside of that interval is a sign that we aren't being that crappy of a RNG, using this naive test.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

megabnx
Posts: 50
Joined: Tue Aug 19, 2008 1:30 am UTC

### Re: Human random numbers

Interesting. As of the time that I voted (randomly by scrolling mouse without looking) I voted for 14, giving 14 a lead with 14 votes. Now if it were the mean and median too I would be really spooked...Its not...

fwlbg
Posts: 40
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### Re: Human random numbers

Get about 20480 poll answers for this one, then you can analyse it quite well.

I answered, but I'm not saying what I put.

Bassoon
Posts: 476
Joined: Wed Nov 28, 2007 10:58 pm UTC
Location: Wisconsin

### Re: Human random numbers

3. Prime number FTW.

yy2bggggs
Posts: 1261
Joined: Tue Oct 17, 2006 6:42 am UTC

### Re: Human random numbers

This is simple, so I did it.

Each column but the first represents a tabulation of 127 "votes" for the number in the first column, using random.org to generate the numbers.

Code: Select all

`1 | 3| 4| 3| 5| 4|2 | 9| 8| 4| 5| 4|3 | 9| 7| 5| 9| 3|4 | 7| 6| 7|10| 5|5 | 4| 8| 3| 8|11|6 | 5| 8| 5| 1| 8|7 |10|10| 7| 6| 9|8 | 6| 6| 8| 7| 7|9 | 4| 6| 8| 3| 4|10| 5| 6| 9| 1| 1|11| 3| 8| 9| 7| 8|12| 5| 6| 8| 6| 8|13| 4| 1| 8| 6| 3|14| 8| 7| 8| 7| 7|15|10| 1| 9| 7| 3|16|17|11| 8| 6|13|17| 4| 4| 4|10| 3|18| 4| 4| 3| 4| 9|19| 6| 7| 5| 9| 8|20| 4| 9| 6|10| 9|`

Enjoy!

Iv
Posts: 1207
Joined: Thu Sep 13, 2007 1:08 pm UTC
Location: Lyon, France

### Re: Human random numbers

import random

random.choice(range(20))+1

It told me 16.

gmalivuk
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### Re: Human random numbers

Yakk wrote:If you rolled a d20 100 times, the 95% conf. interval would be about:
2 * sqrt(.95*.05*n) = 4.35889894
with an expected value of 5.

So for a given random digit, you'd expect somewhere between 0.85 and 9.35 votes on it.

Why the 2, if this is one-sided as implied by your last sentence?
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
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Yakk
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### Re: Human random numbers

The 95% confidence interval is about 1.96 or so (or was it 1.97? I forget), IIRC. I find using 2 (as in within 2 SD) to be easier, and (in any case) less bound to the arbitrary 95% number. And only off by 2%.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

gmalivuk
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### Re: Human random numbers

Ah, right. I just saw twice the standard deviation and was thinking, well, one on each side of the mean. (Forgot temporarily what a confidence interval even is, it seems.)
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
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Yakk
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### Re: Human random numbers

So there are 2^20 subsets of the above. Minus 1, because we don't care about the empty subset. That is about 1 million subsets.

So we want on the order of an all but 1 in a million confidence interval for an arbitrary subset.

To be quick about it, this the SD is maximal at 1/2 of the entries (or 10 sides), at which the SD is about 1/2 * sqrt(1/N) in percentage terms.

Being strict about it, we have Chebyshev's inequality, which states at last (1 - 1/k^2) fraction of observations are within k standard deviations of the mean. Which places it at ~1000 standard deviations. (I kid!)

Assuming normally distributed data (which at the scales involved, we'll have hit), 5 sigma is enough for 1 in a million or so (actually 1 in 2 million, but who is counting).

So that is 5/2 * sqrt(1/N) is an (overly generous) standard. If you can find many subsets that are more than 5/2 * sqrt(1/N) standard deviations away from the expected value of that subset (given a random population), you have some strong evidence that the results aren't random.

With 1 million subsets and a 1 in 2 million chance that a given subset would randomly lie outside the 5 sigma range, call it a 1 in 3 chance that a given set of random numbers has an element outside of the 5 sigma range. Sadly, these correlate (sigh).

So... how about a single subset more than 6 sigma away. That's 3 * sqrt(1/N).

On 200 elements, that means +/- 21%. Ie, find a subset of N die sides that is at least N*5%+21%, or less than N*5%-21%.

One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

theta4
Posts: 130
Joined: Wed Aug 27, 2008 5:16 am UTC

### Re: Human random numbers

It's a random number generator. If everybody picked 7, it would still be random.

And, lv:
Iv wrote:import random

random.choice(range(20))+1

It told me 16.

afaik, that doesn't qualify as a human random number
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Tass
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### Re: Human random numbers

I chose the wrong forum for my experiment I see. I should have tried to sell it as science, then I migth have gotten better statistics.

Interestingly it seems that people browsing the science forum is much more random than those in the silly games forum.

PM 2Ring
Posts: 3715
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Location: Sydney, Australia

### Re: Human random numbers

Allegedly, if you ask people to pick a random number between 10 & 20, you get a lot of 17s. But I don't think this works so well on a bunch of scientists, mathematicians & programmers. The idea is that odd numbers are considered more random than even ones, eleven is special because it has repeated digits, 13 is special because it's unlucky, 15 is too round, and so the first "non-special" number in the range is 17.

Velifer
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Location: 40ºN, 83ºW

### Re: Human random numbers

And people like "M" better than "Q". (The Pepsi Challenge, for those of you too young to remember the 8-track.)

There are some fun mentalism tricks that exploit these quirks. You're thinking of a carrot, aren't you?
Time flies like an arrow, fruit flies have nothing to lose but their chains -Marx

Simius
Posts: 89
Joined: Tue Nov 06, 2007 2:17 pm UTC
Location: Vancouver

### Re: Human random numbers

Maybe this should be made into a Global Announcement for a little while... for SCIENCE!

MarshyMarsh
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### Re: Human random numbers

I didn't choose my number randomly, I chose 9 because it is 9.

You're experiment is now void as not every number has been chosen by the being choosing them randomly due to me! I picked 9 because it is 9!

This also gives me an idea for a forum game, rather than team post racing. Number racing!

quintopia
Posts: 2906
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Location: atlanta, ga

### Re: Human random numbers

i think your non-randomness still ends up being pretty random in the scheme of things. on the other hand, the person who used a software RNG IS interfering with the test.

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