Piattelli-Palmarini M. (1994). <Inevitable Illusions:
How Mistakes of Reason Rule Our Minds> John Wiley & Sons.
I got the book from the library this afternoon and
was drawn to Chapter 4: "Probability Illusions",
which begins with the following wager:
===============================================
I have just tossed a coin 7 times, and I ask you, who
have not seen the result, to guess which of the three
sequences below represents the sequence of my results.
I guarantee that one of the sequences is genuine. If
you don't get it right, you lose 10 dollars; if you
win, you get 30. H stands for heads, and T for Tails.
1. HHHHTTT
2. THHTHTT
3. TTTTTTT
On which would you bet? Let's think for a moment before
going on. <<If you think too much you'll lose ;-) --BH>>
Experiments with a great many subjects have shown that
the bets will be placed in the following order:2,1,3.
The preference for the second sequence is very strong.
But probability theory tells us that in seven tosses of
a coin the probabilities are totally even, and we rationally
should be quite indifferent to which of the three sequences
we choose. The person who chooses 2 is prey to one of the
most common cognitive illusions; she mistakes the most
<typical> for the most <probable>.
-- Piattelli-Palmarini, ibid p. 49-50.
=========================================================
Wow, if only I could get him to put his money where
his mouth is and actually make this wager with me.
First I would clarify what seems to be implied in
the above. Only one sequence is a real coin toss
event, the others are made up. Of course I would
also want an independent third party to verify
that he's really tossing a fair coin for one of
the sequences. With these stipulations I'm going
to make a lot of money until he figures out that
he better not put any pattern in the two sequences
he makes up, in which case we'll break even ;-).
I really can't help being amused by this, considering
the subtitle "How Mistakes of Reason Rule Our Minds".
His mistake of reason is to blindly trust his math
to the exclusion of common sense. But that this is
actually a mistake is not particularly clear since
it is common to obtain counter-intuitive results in
both math and science. I would be willing to make a
generous side-bet (if I were a betting man :) that
he would quickly abandon reason for common sense if
he actually had to make the above wager.
Brian Harper
Associate Professor
Applied Mechanics
The Ohio State University
"If cucumbers had anti-gravity,
sunsets would be more interesting"
-- Wesley Elsberry