
Perceptions of Randomness: Why Three Heads Are Better Than Four (2009) [pdf] - YeGoblynQueenne
http://psych.cf.ac.uk/home2/hahn/Psychological_Review_2009_Hahn.pdf
======
lqet
I always had the suspicion (which may be wrong) that in questions like "which
is a more likely outcome of 6 coin tosses, HHHHHH or HTHHTT", people tend to
understand this question as: "which is a more likely outcome of 6 coin tosses,
a sequence of 6 heads, or another sequence without any obvious regularity in
it", in which case the latter is clearly the correct answer.

I have an additional suspicion: in my experience, people with slight autistic
tendencies often have problems with sorting their impressions into broad,
general categories, but instead always analyze (even remember) the exact
impression (or "special case") they are confronted with. For people like this,
the question "HHHHHH or HTHHTT" is a completely different question than for
the majority of the population. So, the problem to me does not seem to be a
problem with human intuition for probability (or with System 1, in Kahneman's
words), but just one of semantics. If you go further and assume that
scientists have a higher percentage of people with autistic tendencies than
the general population, then the problem simply becomes one of communication
between the researcher and the subject.

I read Thinking: Fast and Slow a few years ago and remember many experiments
where it was clear to me that the subjects just answered a different question
than the one the researcher asked them. And I do not mean that they "anchored"
their answers on something else or they replaced the question with a different
question because they had no answer to the original question - they just had a
completely different understanding of the question itself, and their answers
to this question were correct, even in System 2.

~~~
FakeComments
I find a lot of psychology experiments about game theory have this problem,
for an example.

The common mistake is to analyze it as if people were in a prisoners’ dilemma
situation rather than an iterated prisoners’ dilemma situation: there’s no way
to fully detach lab participants from the fact that the people they’re
interacting with exist in society, which is a sort of large scale iteration of
all the social games.

Once you realize lab participants are treating each other as members of
society they’ll have to deal with in the future, instead of isolated lab rats
only existing for one round of experimentation, almost all of the “people
don’t understand game theory” results disappear.

It seems instead we have multiple papers confirming psychologists don’t
understand society.

~~~
jet_throw
Papers are published within an academic pretense. So you also have to account
for the brown nosing and sucking up to authority.

You pay tuition, but you don’t get your degree without conforming your
behavior to the expectations of faculty, and the institutional demands to
publish words that seem like a readable corpus of text.

This goes up the chain, as the expectation pervades a normative culture.

Academia eats Prestigious Institutions. Institutions eat Departments. Chair of
Department eats Professors. Professors eat Students. Students photosynthesize
Words pleasing to the ears of their parasitic herbivores.

You are what you eat.

------
nabla9
Consider the following three plots. In one of the plots each of the blue
points is sampled with equal probability from the entire square. Which one is
it?

1\. [http://norvig.com/plot1.png](http://norvig.com/plot1.png)

2\. [http://norvig.com/plot2.png](http://norvig.com/plot2.png)

3\. [http://norvig.com/plot3.png](http://norvig.com/plot3.png)

You can read the rest from [http://norvig.com/experiment-
design.html](http://norvig.com/experiment-design.html)

~~~
somebodythere
My stats professor said he used to have an assignment where he had students
flip a coin 100 times and record the results on a sheet of paper. He said he
could be reasonably confident who did and did not actually flip the coin
because the students who did not flip the coin would not have any runs longer
than 2 or 3.

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ccvannorman
The most interesting part of this paper to me is that "HHT" is more likely
than "HHH" to appear in a sub-set of tosses of length 4 or 12 (for example),
and that any sequence like HHH or HHT has a "wait time" calculated by
mathematicians. The wait times are how many flips on average you need to
produce the sequence and they are not equal -- HHHH has a wait time of 30 vs
HHHT has a wait time of 16 (not sure if I got the numbers exactly right.)

So the answer to the question "Which is more likely to be seen in a sequence
of 10 coin flips, HHH or HHT", the answer is surprisingly, "HHT".

This is the key point of the paper. People are shown a sequence and they
answer the question as if the sequence was pulled from a longer sequence
(though that isn't strictly what the question asks).

~~~
johnsimer
This is fascinating to me.

Do you have a link to the paper?

I can't quickly wrap my mind around why HHT would be have a shorter wait time
than HHH

~~~
fpalmans
Not having read the paper to which to parent referred, but I might be able to
shed some light on this...

Let us describe the state of the previous two tosses as XX, with X being
either H or T. If --(X)--> describes the next toss, we can describe the
transition between states as follows:

HH --(H)--> HH

HH --(T)--> HT

and

HT --(H)--> TH

HT --(T)--> TT

etc.

If we are waiting for HHT, starting from state HH

HH --(H)--> HH : or, we get back to state HH

HH --(T)--> "HHT" : HHT is found and we stop searching

as opposed to waiting for HHH

HH --(H)--> "HHH" : HHH is found, and we stop

HH --(T)--> HT : and we are in a new state which requires at least two more
--(H)--> in sequence before we return to state HH.

I hope this helps.

EDIT: reformatting & typo

------
reidacdc
There is a very accessible "numberphile" video which I think is closely
related to this, about playing the odds on predicting elements of a nominally-
random coin-flip sequence using the expected run length.

[https://www.youtube.com/watch?v=tP-
Ipsat90c](https://www.youtube.com/watch?v=tP-Ipsat90c)

