<p>One strategy for ranges that are powers of 2 is to split the range in half and flip a coin. If it's heads, the upper half is your new range. If it's tails, the lower half is your new range. Repeat until you have a single number. This gives you a truly random number.</p>
<hr />
<p>Another strategy comes from George Marsaglia, on this Google Groups page: <a href="https://groups.google.com/forum/m/?hl=en#!msg/sci.math/6BIYd0cafQo/Ucipn_5T_TMJ" rel="nofollow noreferrer">https://groups.google.com/forum/m/?hl=en#!msg/sci.math/6BIYd0cafQo/Ucipn_5T_TMJ</a></p>
<blockquote>
<p>Choose a 2-digit number, say 23, your &quot;seed&quot;.</p>
<p>Form a new 2-digit number:
the 10's digit plus 6 times the units digit.</p>
<p>The example sequence is
23 --&gt; 20 --&gt; 02 --&gt; 12 --&gt; 13 --&gt; 19 --&gt; 55 --&gt; 35 --&gt; ...</p>
<p>and its period is the order of the multiplier, 6, in the group of residues relatively prime to the modulus, 10. (59 in this case).</p>
<p>The &quot;random digits&quot; are the units digits of the 2-digit numbers, ie, 3,0,2,2,3,9,5,...  the sequence mod 10.
The arithmetic is simple enough to carry out in your head.</p>
</blockquote>
<p>I don't know what the distribution is, but the numbers <em>look</em> random, at least to me. You could also concatenate digits to create larger numbers. You could then get a pseudo-random number for any specified length of number (i.e. 2 digits, 3 digits, etc).</p>
<hr />
<p>A similar question with many potential answers in the comments can be found at <a href="https://philosophy.stackexchange.com/questions/1961/are-people-capable-of-generating-a-random-number">https://philosophy.stackexchange.com/questions/1961/are-people-capable-of-generating-a-random-number</a>.</p>

CC BY-SA 3.0
2017-03-05T13:33:20.097Z
That doesn't give uniform distribution if your range is not an exponent of 2.
ghosts_in_the_code
CC BY-SA 3.0
2017-03-06T07:24:01.893Z
This does not provide an answer to the question. Once you have sufficient [reputation](http://cogsci.stackexchange.com/help/whats-reputation) you will be able to [comment on any post](http://cogsci.stackexchange.com/help/privileges/comment); instead, [provide answers that don't require clarification from the asker](http://meta.stackexchange.com/questions/214173/why-do-i-need-50-reputation-to-comment-what-can-i-do-instead). - [From Review](/review/low-quality-posts/13298)
Robin Kramer-ten Have
CC BY-SA 3.0
2017-03-06T07:26:00.260Z
@RobinKramer It does answer the question. I imagine there are better answers, but it does answer the question. The first part (the pseudo-comment) is completely separate from the answer.
Jacob
CC BY-SA 3.0
2017-03-06T07:31:29.230Z
I hope that one of the moderators can move your answer to the comments because the philosophical perspective is very interesting. The solution you gave is, in my opinion, not what is expected at CogSci. At CogSci, we seek to have answers that are grounded in psychological sciences with scientific references. Your answer seems to be more or less a life-hack.
Robin Kramer-ten Have
CC BY-SA 3.0
2017-03-06T07:35:14.803Z
The question was what strategies can a human use to find random numbers, correct? I'll edit my answer to make it more clear that the link to the philosophy question (which has many practical examples of how a human can generate random numbers) is not the point of my answer.
Jacob
CC BY-SA 3.0
2017-03-06T07:39:05.277Z
@RobinKramer And if you feel that my answer can be improved, feel free to edit it! Or post the link in the comments yourself, and I'll delete it from my answer. That's the beauty of the Stack Exchange system.
Jacob
CC BY-SA 3.0
2017-03-06T17:29:51.917Z
@RobinKramer His answer was exactly the kind of answer I was looking for. Maybe that makes it off-topic here, where should I post it then?
ghosts_in_the_code
CC BY-SA 3.0
2017-03-06T17:57:48.300Z
So, with the coin-flip strategy, your approach to generating a random number is... use a binary random number generator?
Nuclear Hoagie
CC BY-SA 3.0
2017-03-06T18:11:48.577Z
@Matt Haha, yeah, I'm cheating a bit on that one…
Jacob
CC BY-SA 3.0
2017-03-05T06:51:57.830Z
2017-03-06T17:50:46.263Z
2020-06-17T09:55:31.633Z
Jacob
<p>It is known that <a href="https://skeptics.stackexchange.com/q/36652/33071">humans are worse than computers</a> at random number generation, and that even computer's random numbers are often imperfect and predictable.</p>

<p>What strategies could a human employ to generate truly random numbers from a given range, and how uniformly distributed will they really be?</p>

<p>P.S. One trick I use, when generating a number from 1-9, is to select a random large number, say 2349, then find its <a href="https://en.m.wikipedia.org/wiki/Digital_root" rel="nofollow noreferrer">digital root</a> (2+3+4+7 = 16, 1+6=7, so digital root is 7). I don't know how random it truly is, but it's definitely better than just instinctively selecting a number from 1 to 10.</p>

CC BY-SA 3.0
2017-03-05T04:44:48.310Z
@RobertColumbia I know human-generated numbers are not random and hence predictable. I'm asking if there is a way humans can avoid this weakness.
ghosts_in_the_code
CC BY-SA 3.0
2017-03-05T14:13:10.757Z
So your random number between 1 and 10 will never be 1?
Shokhet
CC BY-SA 3.0
2017-03-05T14:27:18.307Z
@Shokhet you're right. My bad.
ghosts_in_the_code
CC BY-SA 3.0
2017-03-06T17:09:58.460Z
I am pretty sure [42](https://en.wikipedia.org/wiki/42_%28number%29#Popular_culture) and [pi/2](http://www.phdcomics.com/comics/archive.php?comicid=5) are random numbers
StrongBad
<mathematical-psychology><mathematical-ability><preferences>
Can a human select truly random numbers if he/she chose to?
ghosts_in_the_code
# Can a human select truly random numbers if he/she chose to?

(Asked by: username_0 on 2017-03-04)

It is known that [humans are worse than computers](https://skeptics.stackexchange.com/q/36652/33071) at random number generation, and that even computer's random numbers are often imperfect and predictable.

What strategies could a human employ to generate truly random numbers from a given range, and how uniformly distributed will they really be?

P.S. One trick I use, when generating a number from 1-9, is to select a random large number, say 2349, then find its [digital root](https://en.m.wikipedia.org/wiki/Digital_root) (2+3+4+7 = 16, 1+6=7, so digital root is 7). I don't know how random it truly is, but it's definitely better than just instinctively selecting a number from 1 to 10.

**Tags:** mathematical-psychology, mathematical-ability, preferences

> **Comments:**
> **username_0**: @RobertColumbia I know human-generated numbers are not random and hence predictable. I'm asking if there is a way humans can avoid this weakness.  
> **username_1**: So your random number between 1 and 10 will never be 1?  
> **username_0**: @username_1 you're right. My bad.  
> **username_2**: I am pretty sure [42](https://en.wikipedia.org/wiki/42_%28number%29#Popular_culture) and [pi/2](http://www.phdcomics.com/comics/archive.php?comicid=5) are random numbers  

---

## 1 answers

### Answer by username_3 on 2017-03-05. Score: 0

One strategy for ranges that are powers of 2 is to split the range in half and flip a coin. If it's heads, the upper half is your new range. If it's tails, the lower half is your new range. Repeat until you have a single number. This gives you a truly random number.

---

Another strategy comes from George Marsaglia, on this Google Groups page: <https://groups.google.com/forum/m/?hl=en#!msg/sci.math/6BIYd0cafQo/Ucipn_5T_TMJ>

> Choose a 2-digit number, say 23, your "seed".
>
> Form a new 2-digit number:
> the 10's digit plus 6 times the units digit.
>
> The example sequence is
> 23 --> 20 --> 02 --> 12 --> 13 --> 19 --> 55 --> 35 --> ...
>
> and its period is the order of the multiplier, 6, in the group of residues relatively prime to the modulus, 10. (59 in this case).
>
> The "random digits" are the units digits of the 2-digit numbers, ie, 3,0,2,2,3,9,5,... the sequence mod 10.
> The arithmetic is simple enough to carry out in your head.

I don't know what the distribution is, but the numbers *look* random, at least to me. You could also concatenate digits to create larger numbers. You could then get a pseudo-random number for any specified length of number (i.e. 2 digits, 3 digits, etc).

---

A similar question with many potential answers in the comments can be found at <https://philosophy.stackexchange.com/questions/1961/are-people-capable-of-generating-a-random-number>.

> **Comments:**
> **username_0**: That doesn't give uniform distribution if your range is not an exponent of 2.  
> **username_4**: This does not provide an answer to the question. Once you have sufficient [reputation](http://cogsci.stackexchange.com/help/whats-reputation) you will be able to [comment on any post](http://cogsci.stackexchange.com/help/privileges/comment); instead, [provide answers that don't require clarification from the asker](http://meta.stackexchange.com/questions/214173/why-do-i-need-50-reputation-to-comment-what-can-i-do-instead). - [From Review](/review/low-quality-posts/13298)  
> **username_3**: @RobinKramer It does answer the question. I imagine there are better answers, but it does answer the question. The first part (the pseudo-comment) is completely separate from the answer.  
> **username_4**: I hope that one of the moderators can move your answer to the comments because the philosophical perspective is very interesting. The solution you gave is, in my opinion, not what is expected at CogSci. At CogSci, we seek to have answers that are grounded in psychological sciences with scientific references. Your answer seems to be more or less a life-hack.  
> **username_3**: The question was what strategies can a human use to find random numbers, correct? I'll edit my answer to make it more clear that the link to the philosophy question (which has many practical examples of how a human can generate random numbers) is not the point of my answer.  
> **username_3**: @RobinKramer And if you feel that my answer can be improved, feel free to edit it! Or post the link in the comments yourself, and I'll delete it from my answer. That's the beauty of the Stack Exchange system.  
> **username_0**: @RobinKramer His answer was exactly the kind of answer I was looking for. Maybe that makes it off-topic here, where should I post it then?  
> **username_5**: So, with the coin-flip strategy, your approach to generating a random number is... use a binary random number generator?  
> **username_3**: @Matt Haha, yeah, I'm cheating a bit on that one…  

---

