Probability is one of the most widely used concepts of mathematics, known for it universality and highly intuitive nature. Even before the theorems of probability were formally established, we were able to sense its presence and have appropriately applied in our daily lives. However, probability can be misleading. We systemically come to wrong conclusions
A classic example that reveals our limited understanding of this subject is something known as "Gambler's fallacy".
Consider a very simple example of six consecutive coin tosses. Say, all of the first outcomes land on heads. If a person were to bet a million dollars on the next outcome, what would he choose?
As an interesting study of the human psyche, a survey conducted using the above data produced results where majority chose tails as their outcome over heads. In addition to their choice, each of the participants were asked to justify why they came to such conclusions, which was extremely important for the experiment. The majority chose tails over heads, but almost none had a "correct" reason for making such choice.
Those who chose tails said something along the lines of "balancing forces at play", and those who said heads said that the coin was rigged. Despite being the correct answer, it was nothing more than a speculation.
The biggest shock for them, was when the answer was revealed. It was "none" which was understandably disappointing, not because the coin itself is unbiased, but because we lacked the data set. Theoretically, any one of the two choices would produce same results.
In both of the above answers, the candidates left out a very important aspect of the coin's outcome - the base rate. Gambler's fallacy is a special case of a larger psychological bias known as Base Rate neglect. The base rate is simply a large number of outcomes that reveals an object's true behavior. The larger this data, the more accurate the prediction becomes. For example, if we were to toss a coin 100 times and observe 52:48 heads to tail ratio, we don't know for a fact that the probability of heads is 52/100. Toss it a million times, and we get a closer understanding of it.
The worse answer is to consider "the balancing forces at play" - our belief that things balance out eventually, and this is simply not true. Next time, if anything happens more frequently than others, don't expect things to change just for things to balance out. A coins die or anything of that nature is unaware of its previous outcome. We should try and understand the causes or analyse the whole set of data in order to draw better conclusions.