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?
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.
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.
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 :)
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.
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.)
