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WHY THE ‘BALANCING FORCE OF THE UNIVERSE’ IS
BALONEY
Gambler’s Fallacy
In the summer of 1913, something incredible happened in Monte Carlo. Crowds
gathered around a roulette table and could not believe their eyes. The ball had
landed on black twenty times in a row. Many players
took advantage of the
opportunity and immediately put their money on red. But the ball continued to
come to rest on black. Even more people flocked to the table to bet on red. It had
to change eventually! But it was black yet again – and again and again. It was not
until the twenty-seventh spin that the ball eventually landed on red. By that time,
the players had bet millions on the table. In a few spins of the wheel, they were
bankrupt.
The average IQ of pupils in a big city is 100.
To investigate this, you take a
random sample of 50 students. The first child tested has an IQ of 150. What will
the average IQ of your 50 students be? Most people guess 100. Somehow, they
think that the super-smart student will be balanced out – perhaps by a dismal
student with an IQ of 50 or by two below-average students with IQs of 75. But with
such a small sample, that is very unlikely. We must expect that the remaining 49
students will represent the average of the population, so they will each have an
average IQ of 100. Forty-nine times 100 plus one IQ of 150 gives us an average
of 101 in the sample.
The Monte Carlo example and the IQ experiment show that people believe in
the ‘balancing force of the universe’. This is the
gambler’s fallacy
. However, with
independent events, there is no harmonising force at work:
a ball cannot
remember how many times it has landed on black. Despite this, one of my friends
enters the weekly Mega Millions numbers into a spreadsheet,
and then plays
those that have appeared the least. All this work is for naught. He is another
victim of the
gambler’s fallacy
.
The following joke illustrates this phenomenon:
a mathematician is afraid of
flying due to the small risk of a terrorist attack. So, on every flight he takes a bomb
with him in his hand luggage. ‘The probability of having a bomb on the plane is
very low,’ he reasons, ‘and the probability of having two bombs on the same
plane is virtually zero!’
A coin is flipped three times and lands on heads on each occasion. Suppose
someone forces you to spend thousands of dollars of your own money betting on
the next toss. Would you bet on heads or tails? If you think like most people, you
will choose tails, although heads is just as likely. The
gambler’s fallacy
leads us
to believe that something must change.
A coin is tossed 50 times, and each time it lands on heads. Again, with
someone forcing you to bet, do you pick heads or tails? Now that you’ve seen an
example or two, you’re wise to the game: you know that it could go either way.
But we’ve just come across another pitfall:
the classic
déformation
professionnelle
(professional oversight) of mathematicians: common sense would
tell you that heads is the wiser choice, since the coin is obviously loaded.
Previously, we looked at
regression to mean
. An example: if you are
experiencing record cold where you live, it is likely that the temperature will return
to normal values over the next few days. If the weather functioned like a casino,
there would be a 50% chance that the temperature would rise and a 50% chance
that it would drop. But the weather is not like a casino.
Complex feedback
mechanisms in the atmosphere ensure that extremes balance themselves out. In
other cases, however, extremes intensify. For example, the rich tend to get richer.
A stock that shoots up creates its own demand to a certain extent, simply because
it stands out so much – a sort of reverse compensation effect.
So, take a closer look at the independent and interdependent events around
you. Purely independent events really only exist at the casino, in the lottery and in
theory. In real life, in the financial markets and in business, with the weather and
your health, events are often interrelated. What
has already happened has an
influence on what will happen. As comforting an idea as it is, there is simply no
balancing force out there for independent events. ‘What goes around, comes
around’ simply does not exist.
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