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XKCD Comic where someone guesses a number and is right (https://xkcd.com/628/)

If you hover your mouse over the comic for a few second a small tool tip box says:

You can do a lot better than 1% if you start keeping track of the patterns in what numbers people pick.

Is there any evidence for this claim? What numbers do people choose?

  • Interestingly forensic accountants use Benford's Law to spot criminal accounting - people think that their fake financial data should be random when there is actually a non-uniform distribution it should follow given by Benford's Law. – user39339 Mar 22 '17 at 1:49
  • People also tend to think that there should not be long strings of similar events occurring when they need to make up data. For example, many people when told to make up 100 outcomes of flipping a coin - heads, tails, etc would not include long strings of the same outcome. Consequently, the absence of such long sequences of the same outcome indicates with high probability that the data is made up. – user39339 Mar 22 '17 at 1:51
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Yes, humans are more predictable than random chance. It is known as the "Blue-Seven Phenomena", because when asked for a colour and a number from one to nine, these perform beyond expectation.

This 2015 encyclopedia entry surveys the research. One large sample of Japanese university students found:

As for the preferred number, the subjects in Saito’s study selected “seven” most frequently (22.50 %), supporting Simon’s [13] finding of the “Blue-Seven Phenomenon.” The reasons given for the choice showed that “seven” was associated with “lucky seven” and was considered “a lucky number” and to “represent happiness” among Japanese students. Other highly preferred numbers were found to be “three” (16.24 %), “five” (13.03 %), and “one” (11.84 %). Odd numbers accounted for 68.35 % of the responses. Male students selected the number “one” more often (men, 15.67 %; women, 9.07 %), the main reason given being that it represented “number one” or “top.” Female students, on the other hand, preferred “five” (men, 9.66 %; women, 15.30 %), because they “just liked the number” or because it was “a birth date,” “a good cutoff point,” or “a shapely number.” A gender difference was also found in number selection. Numbers were sometimes preferred for their “visual appearance.”

Now the original claim referred to numbers from one to one hundred, not just one to nine. I haven't found research on that broad a range, but changing the range of the numbers was examined in this 1977 paper titled The "Blue Seven" Is Not A Phenomenon. [The title of the paper doesn't imply people don't pick blue and seven more frequently. It is that the people who pick blue aren't more likely to pick seven than the people who don't pick blue.]

They looked at the range 2-12 (to mimick dice games):

Changing the length of the range, and its beginning and end points, did not affect the choice of seven in the preference condition

They also looked at the range 0-20:

A value of chi square for preferred number could not be calculated since the expected frequency per cells was less than five. However, it is clear from the frequency distribution that seven is not the preferred number. This result holds for the favorite condition as well. [...] These results suggest that the choice of seven as the preferred or favorite number is contingent upon the range specified by the experimenter.

A statistically larger sample would help here.

The predictability of random choices transfers to more than just colours and numbers.

  • 9
    I don't have a citation, but I believe that from one to a hundred you're quite likely to pick thirty-seven. – Muzer Jan 10 '17 at 10:16
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    Reminds me of the Red Hammer mind trick: ask people to think of a tool (not telling you) then ask them to think of a color (not telling you) and tell them they were thinking about "Hammer" and "Red". Hammer is generally the first tool people think of, and the traditional hammer has a red band, influencing the following color choice... There are many tools and many colors, but humans are not that good at picking a "random" one. – Matthieu M. Jan 10 '17 at 11:37
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    ... @MatthieuM, I don't remember ever seeing a hammer with a red band, yet that was the colour I... wait, you called it "Red Hammer" before... never mind. :-/ – wizzwizz4 Jan 10 '17 at 17:18
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    @Muzer As I heard that trick explained to me, it was often given particular constraints: two-digit number where the digits are different and each odd. That limits choices to only 20 (13, 15, 17, 19, 31, 35, 37, 39, 51, 53, 57, 59, 71, 73, 75, 79, 91, 93, 95, 97), but it seems higher because the restrictions don’t seem onerous. For whatever reason, 37 (it was claimed) was chosen close to 50% of the time, with 35 a relatively close second and the rest quite infrequent—in general. A warning was included not to try it at MIT, since a major building’s number meets the criteria and becomes common. – KRyan Jan 10 '17 at 20:22
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    I find it slightly amusing that an answer about people thinking of odd numbers was answered by someone with the name @Oddthinking. – LeopardSkinPillBoxHat Jan 10 '17 at 23:06
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Human beings are really bad at picking random numbers. The reason is that we are hard-wired to identify patterns in nature -- even to the extent of seeing patterns where none exist. But while this helps us hunt (we are predators, after all, and the outline of an animal shape in the bushes means prey), we experience a cognitive dissonance when trying to emulate randomness.

In a true random sequence, it is perfectly normal for the results to be "clumpy" (i.e. lots of values that fall in a small range with only a few outliers). But we humans think of "randomness" as an equal distribution. We therefore subconsciously try to avoid patterns when trying to simulate randomness, and this pattern-avoidance can actually lead you to predict a person's "random" number with greater accuracy.

In other words, if you asked a person to name a random number between 1 and 100, and they say something like 37, then you can reliably predict that their next "random" number will probably be in the 60-80 range, giving you a 20% better chance of guessing their number correctly instead of the 1% chance you'd have otherwise.

You can also bias the person's response to a narrower range of choices by bringing a particular number into the foreground of their thought. "Give me a random number between 1 and 100, but you can't use the current day of the month." That will virtually guarantee a result between 1 and 30.

Some of the information contained in this post requires additional references. Please edit to add citations to reliable sources that support the assertions made here. Unsourced material may be disputed or deleted.

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    How is a Microsoft blog a reliable source on esp or bias phenomena? – Sklivvz Jan 10 '17 at 9:34
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    1.25% is "a 20% better chance than a 1% chance" – Johannes Pille Jan 10 '17 at 11:20
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    @Sklivvz That's not a Microsoft blog. It's just a blog of a Microsoft employee. Just a guy who works with random numbers and with how consistently the human perception of randomness favours other distributions than truly random. Sure, it's no peer reviewed journal, but it's a good, quick explanation of the basic problem. A good reference to such would definitely be worthwhile, though :) – Luaan Jan 10 '17 at 12:40
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    @Luaan it's still an argument from authority - while I don't dispute the accuracy of the content, this SE site is all about the quality of evidence presented. In this case, the evidence is not great. – Sklivvz Jan 10 '17 at 12:44
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    @Sklivvz Sure, I agree with that. But that doesn't make the link bad - the lack of references to reputable sources is. That's what I was trying to say :) – Luaan Jan 10 '17 at 12:47
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An other approach, less to answer the question about statistics, but more about how to pull of the Trick. There are 2 Methothds that you can do this.

One is trying to figure out, what number the other person is thinging based on tells (bodylanguage).

Example here and explained here.

The other one is more complicated, and needs a little preparation.

The second Method is called priming.

You can read about it here:

Priming is an implicit memory effect in which exposure to one stimulus (i.e., perceptual pattern) influences the response to another stimulus.

https://en.wikipedia.org/wiki/Priming_(psychology)

Suggestion is the psychological process by which one person guides the thoughts, feelings, or behavior of another person.

https://en.wikipedia.org/wiki/Suggestion

It means, that you can try to subconciously implant (in your case) an number in someones brain, that they are more likely to choose. It works with all kinds of things, for example forms or music songs.

It's a technique used by many magicians and mentalists. With this technique, you can not only guess with great accruracy, which number the other one will choose, but you can decide, which one it will be. This usually guarantees a mindblowing effect, because the suspect (mostly) didn't even notice, that you significly influenced his decision.

To answer your question: You can not only predict a number with great accuracy, but you can even (with some effort) decide which one it's most likely gonna be.

Some use suggestive methods. It's harder to read someones mind but easier to suggest what we should think of and make it seem as if they reading our mind. https://www.quora.com/Magic-illusion-How-does-David-Blaine-or-other-magicians-guess-the-number-card-that-you-are-thinking-of

You can see an example on the TV shows Cathrine Mills Mind Games (BBC) Breaking the Magician's Code: Magic's Biggest Secrets Finally Revealed or on various Appearances of Keith Barry. Usually Magicians don't admit how they do their tricks, so it's hard to give a good example on how they pull it of and (have the same person) explaining it. But Keith barry does this on the Show "Deception with Keith Barry", which you can find a link to the video when you click on his name.

This is a simple example of how it works:

Answer the following questions:

What color is snow?

A Zebra is Black and?

What color is Rice?

A Wedding dress?

What does a cow Drink?

Answer is in the comments :)

Some of the information contained in this post requires additional references. Please edit to add citations to reliable sources that support the assertions made here. Unsourced material may be disputed or deleted.

  • 3
    You've (or should have been) been fooled by the many "white" answers. – Frezzley Jan 10 '17 at 10:45
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    No, please don't give an example! Give a link to empirical evidence. – Oddthinking Jan 10 '17 at 13:45
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    That's exactly the sort of link that people normally give to Derren Brown, who is another magician who tells lies on-stage about how his tricks work. Magicians, on stage, talking about how their tricks work, are not reliable sources. They lie. They are paid to lie. They do it well. – Oddthinking Jan 10 '17 at 15:23
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    @Frezzley Uh, you realize that cows do drink milk, right? There's a reason they secrete it from their udders, and it's not because it's just so fun. Calves drink it. Most people would consider a calf a cow, informally speaking. – Nic Hartley Jan 11 '17 at 14:56
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    The thing I love about this is that I've seen that exact example at least twice before and when I got to the end I was like "Hah you didn't get me the answer is milk, not white!" :D – DRF Jan 12 '17 at 16:57
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If you asked 1000 people for a random number and lined that list up against 1000 actually random numbers, increasing the sample size to something meaningful, a statistician would be able to tell the difference. In the Radiolab episode Stochasticity (that is, something which is randomly determined) they do a very similar exercise. At about 9 minutes in they demonstrate how bad humans are at creating randomness, and how if you know what real randomness looks like you can tell the difference.

There's a class of students. Some flip a coin 100 times write down the results, "H" for "heads" and "T" for "tails". So something like "H H T H T T H T H H H T T H T H ...". The others write down what they think a simulation of flipping a coin 100 times would look like.

Then a statistician comes in, looks at their lists of flips, picks the fakes from the real lists. She does it immediately because she knows some things about randomness that most people don't.

The give away is runs like "H H H H H H". A human would look at that and go "well that's unlikely!" and not include it in their fake flips. "Those streaks just feel wrong... real randomness, when you see it, just doesn't feel random enough." A statistician looks at it and knows there's a 1 in 64 chance of a run of 6 (2 to the 6th power) so in 100 flips I expect to see at least one or two runs of 6 and a very good chance of a run of 7 (1 in 128). "Strange things do happen by chance."

So the one with a few runs of 5, 6 and even 7 identical flips is probably the real one. The ones without are probably made by humans. What humans think is random isn't. People's instincts about randomness and probability are generally mathematically incorrect (not necessarily wrong because they've served us for millions of years in the wild).

A similar principle is happening when you ask someone for a random number from 1 to 100. They'll give you their idea of a random number. So it gets personally influenced, culturally influenced, lucky numbers like 7 (if you're in the US), unlucky numbers like 13, culturally significant numbers like 23 or 42 or 69, personally significant numbers... but they're not actually picking from a list with a probability of 1 in 100. We can't do that without some device to do it for us.

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    Heard that episode as well. Its well worth listening to, if you've got an interest in this topic. – T.E.D. Jan 13 '17 at 19:12
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According to this, 17 and 7 were the most frequently chosen by people (a poll of blog readers) asked to pick a number from 1 to 20 -- those two numbers together accounted for 30% of respondents' picks, significantly higher than the expected value of 10%. And according to this, people most often choose 7 if asked to name a number between 1 and 10.

And according to MIT lore passed down in the Jargon File, "when groups of people are polled to pick a 'random number between 1 and 100,' the most commonly chosen number is 37."

(For what it's worth, Cueball's choice, 43, is 7 away from the midpoint of the range.)

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    Honestly, I think he picked 43 because 42 would have been too obvious - at least that is what would happen if you let a bunch of people who know the significance of 42 pick a random number 1-100 and ask them why they picked it. Source: personal experience. – Sumyrda Jan 10 '17 at 14:02
  • In fairness, if 347 people picked integers uniformly at random from 1 to 20, the top two choices would account for ~14.1% of the total, not the 10% you'd expect by determining two numbers ahead of time. – Charles Jan 11 '17 at 2:56
  • I'm wondering what the odds are in practice of a person picking a prime number when asked for a "random" number. That seems to be a common theme here. (Note there are only 25 of those < 100 and >1, and only 7 of them within 15% of the midpoint of the range) – T.E.D. Jan 11 '17 at 14:29
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    @Charles I'm interested to know how you figured that number out. Also, 3p% is still significantly more than that ;) – Nic Hartley Jan 11 '17 at 14:58
  • @QPaysTaxes 30% is definitely higher, but it's more like double the expected than triple and I thought that was worth pointing out. I didn't do any interesting probability calculation, just simulated the procedure a million times. – Charles Jan 11 '17 at 17:18

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