The fallacy is an incorrect argument, but that in a superficial analysis is easy to be admitted as valid. The persuasive power of any fallacy lies in its persuasive nature: without a calm analysis it is difficult to identify the error in the argument. However, when carefully analyzed, it is possible to notice that the passage from premises to conclusions is not adequate. In games of chance, such errors in argumentation are common. Although these games are very much related to probability, the mind tends to bring out our most instinctive side in them. On several occasions, precisely to avoid dissonance and follow what instincts command, players reassure their rational side with erroneous arguments and conclusions.
In fact, the gambler's fallacy is a logical error in which it is believed that past random events affect future ones, in conditions where both are independent. This fallacy manifests itself mainly in two ways: In the belief that if an event occurred more frequently in the past, without there being a reason for it to be so, e.g., more heads than tails when flipping a coin, then it is less likely to occur again in the future. There is also the assumption that if an event happened less frequently in the past, it is more likely to happen in the future. In addition, reinforcing the previous idea, a player may think that he has not won for so long that in the next game it is very unlikely that he will not win.
In that sense, these two beliefs are supported by a logical error, since when events are independent of each other, their appearances in the future are not influenced by their past occurrences. Although people's intuition leads them to consider the opposite, the reality is that there is no connection between the two events. This is a very powerful illusion of control over events that are uncontrollable. Support for the susceptibility to illusory control is found in the fact that people can be led to believe that they can affect the outcome of random events. We can even observe it when we believe that, if a lottery number came up recently, then it is less likely to come up again, the probability of that number coming up twice in a row is miniscule, but once it has come up, in the next draw the probability is the same for the rest.
Another example of the fallacy is when we think that a woman will have a baby of a certain sex because she has previously had several of the opposite sex. As you can see, the fallacy does not only appear in games of chance, but also in other areas of life where chance and probability are present. Knowing about this fallacy is already a crucial step to avoid it, although it is not enough. Once you recognize the possible influence of the fallacy on your thoughts and decisions, try to emphasize the independence of the random events you are facing. Putting your beliefs through the filter of reflection is also necessary. Take the time to reflect on your thinking and you will see how false it may be. You may also find techniques to reduce cognitive bias helpful.
In conclusion, to avoid the gambler's fallacy there is nothing like having a good understanding of probability. When we use mathematics, that illusion that appears in the desert populated by defeats, and that invites the gambler to continue betting, disappears. Fallacies are defined as statements or ideas that have the appearance of truth, but in reality are not. Sometimes they are self-constructions, but at other times they become arguments that are collectively invoked and taken as true by all. Fallacies are not easy to detect, because they are not absurd or trivial statements, but maintain logic even if they are not true. This fallacy occurs in all circumstances in which you say "I can't" and attribute that can't to something external to you.
Did you have knowledge about the fallacy?
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