An Introduction to Critical Thinking and Creativity - always yours

PROBABILITY 153
fact that lots of people make this mistake when they gamble. For example, the
probability of a fair coin landing on heads is V2. But suppose you toss the coin four
times and it landed on heads each time. Someone who thinks it is more likely to be
tails next time so that things will "balance out" is committing the gambler's fallacy.
This is because the probability of a fair coin landing heads is just the same as the
probability of landing tails, whatever the past results might have been. Similarly,
it is also a fallacy to think that a series of four tails is more likely to be followed by
yet another tail because the tail side is "hot."
A good real-life example of the gambler's fallacy might be when people choose
numbers for a lottery. Let's say the winning numbers of the last lottery are 2,4,18,
27, 29, 36. Most people would choose a different set of numbers when they play
the lottery, thinking that their combination is more likely to win than the previous
winning combination. But this is a fallacy, because if the lottery is a fair one, all
combinations are equally likely, or better, equally unlikely!
A very dangerous manifestation of the gambler's fallacy is the hot hand fallacy.
This happens when a gambler wins a few times in a row, and he thinks he is on a
lucky streak. As a result, he thinks he is more likely to win than lose if he continues
to gamble. But this is a fallacy because the probability of him winning the next
round is independent of his past record. It is a dangerous fallacy because very
often these gamblers start to feel they are invincible and so they increase their
wager and end up losing all their money.
17.4.2 Regression fallacy
Regression fallacy is a mistake of causal reasoning due to the failure to consider
how things fluctuate randomly, typically around some average condition. Intense
pain, exceptional sports performance, and high stock prices are likely to be followed
by more subdued conditions eventually due to natural fluctuation. Failure
to recognize this fact can lead to wrong conclusions about causation.
For example, someone might suffer from back pain now and then but nothing
seems to solve the problem completely. During a period of very intense pain,
the patient decided to try alternative therapy like putting a magnetic patch on his
back. He felt less pain afterward and concluded that the patch worked. But this
could just be the result of regression. If he sought treatment when the pain was
very intense, it is quite possible that the pain has already reached its peak and
would lessen in any case as part of the natural cycle. Inferring that the patch was
effective ignored a relevant alternative explanation.
Similarly, sometimes we are lucky in the sense that things go very well, and
other times we are unlucky and everything seems to go wrong. This is just an inevitable
fact of life. But if we read too much into it, we might think we need to
do something to improve our luck, and look for solutions where none is needed,
such as using crystals to boost our karma. Of course, it is important to reflect on
ourselves when things are not working well since it could be due to personal failings
such as not working hard enough. What is needed is a careful and objective
evaluation of the situation.