"melvin"  wrote
>
> The problem is, in a game show, every round a contestant is shown 3
> unopened doors, two have a goat and one has a car. The contestant then
> chooses a door that remains unopened and the host always opens one of
> the other two doors which always reveals goat. Should the contestant
> switch? The answer is yes with a success of 2/3 if the contestant
> always switches. Most people think the chances are 50/50 and it makes
> no difference and the problem leads to many heated debates. Many
> people never become convinced of the correctness of
> the solution and for many it remains counterintuative
>
> Some psychologists have studied in detail what leads people to the
> right or wrong conclusion and it would be interesting if one could do
> a study to tie in evolutionary pressures in intelligence to shed light
> on why the approaches to this problem are so divergent or if certain
> types of thinking though wrong still have an evolutionary benifit
> which outweighs the negative effects of incorrect reasoning.
>
This is really interesting. I initially assumed that the chance must remain
50:50 and that the problem was based on an error, until actually working it
out.

People are very bad at assessing probability. The gambler's fallacy (we
haven't had heads for three tosses now, so a head must be due), and the
Shakespearian monkey fallacy (with a large enough contingent of monkeys and
typewriters you will eventually get the works of Shakespeare), are both very
powerful. Together they support the entire gambling industry. For instance
there is no point buying a single ticket in the British National Lottery,
because the chance of winning is 1 in 14 million - the chance of dying
before the draw is made is much greater.

Why does the gambling scam work? I think that the reason is that in
evolutionary history it is very seldom possible to quantify a probablity
exactly. I will take a 50% chance of dying to save my sister from a
crocodile, but assessing the length of my spear, and the strength and hunger
of the crocodile, is not an exact art. One must make an intutive judgement
in a split second about whether it is better to attack the crocodile or to
run away.
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