By definition, independent random events cannot be predicted with certainty. This way of thinking is wrong because past events do not change the likelihood of certain events that will occur in the future. [Sources: 2, 4]
Gambler delusion is best defined as the tendency to think that future probabilities are skewed by past events when they do not really change. The player’s mistake is that he erroneously evaluates whether the series of events is really random and independent, and erroneously concludes that the outcome of the next event will be the opposite of the outcome of the previous series of events. If we estimate the likelihood of an event based on past events, we will all be misleading the player. Player error stems from our tendency to assume that if a random event happened many times in the past, it will happen more or less often in the future. [Sources: 2, 3, 5, 6]
So we are trying to rationalize random events in order to create an explanation and make them predictable. When we are busy rationalizing random events, we do not think clearly. Because player error forces us to keep track of our experience or base future events on past performance; we do not make an informed choice. It also refocuses the question of “rationality” implied in the term “fallacy”, because then we can ask ourselves if it is illogical to behave as if past results helped us predict future outcomes. [Sources: 3, 4, 5]
The fact that past events will not change the possibility of future events is the reason why such ideas and decisions are wrong. Player error is a person who mistakenly believes that past events or a series of events will affect future events. This error occurs when a person mistakenly believes that a particular event may or may not occur, depending on the result of a series of previous events. [Sources: 5]
Therefore, an error occurs when a person believes that a particular event in the past will affect future events. The root of this error is that we tend to assume that an event has occurred based on the number of occurrences in the past. It is based on the misunderstanding that due to previous events, events are more or less likely to happen. When an event occurs more frequently than usual, it is less likely to happen in the future. [Sources: 5]
There are also potentially unique issues that can be associated with sequential events. This could plausibly reflect a different process from the gambler’s delusion observed while gambling, however, it would be interesting to see if the similarities show up even in the investment scenario when decisions are made regularly based on consistent information such as daily performance or hourly. One possible approach would be to use a developmental paradigm to test if anything similar to the player’s fallacy arises before developing an understanding of the properties of chance. In this light, the phenomena described here are easy to understand; Beliefs about a relationship with previous results can provide a valuable (or, in the case of random events, the only) possible source of information about what might happen in the future and increase our sense of predictability. [Sources: 4]
We often select past experiences that we believe should be similar to future events or that we believe should reflect an ideal outcome. However, once a base rate is established, or at least a fair estimate, we can predict when certain events will return to the average. We see regression towards the mean because each individual event can bring us closer to our original baseline (assuming the baseline remains the same). [Sources: 1, 3]
In fact, the same is true for the frequency domain and probability domain. Heads-up with LeBron James will not change the results, while playing with someone with your skill level will make the results more or less random. Unless you think your mindset and processes are actually changing every week, the most likely outcome for any given week is a long-term return on investment. [Sources: 1, 8]
I find that the error of the players is so strong because it is difficult for people to understand how the mean reversion occurs. Player error can be so severe that it influences decision making because people tend to “act” after peripheral events. [Sources: 1]
This can be explained by the tendency of traders to judge a decision based on the outcome rather than the quality of the decision at the time it was made. To illustrate the bias in the outcome, we can use the example of a trader trading a system that relies primarily on Fibonacci retracements and extensions. To avoid skewing the result, the trader must think of his trading as a package of many skills. [Sources: 6]
This can be explained by a tendency to seek, interpret, focus, and memorize information in a way that confirms a preconceived notion. Distortions – After generalizations, people agree to distortions in order to adapt the information to their beliefs. The framing effect (cognitive bias) People respond differently to certain choices depending on how they are presented. [Sources: 0, 6]
This can be defined as the tendency to rely on or reinforce a trait or piece of information in making decisions (usually the first piece learned on the topic). Cognitive bias is best explained as a thinking bias that influences people’s decisions and judgments. They arise as a result of our brains trying to simplify information processing. [Sources: 6]
Hindsight bias This is sometimes called the “knew it all” effect — the tendency to view past events as predictably as they happened. Retrospective bias (cognitive bias) The tendency, after an event has occurred, to view the event as predictable, even though there is little objective basis for predicting it. Player error. The tendency to think that future probabilities are distorted by past events when they have not really changed. [Sources: 0, 7]
Focusing effect. The tendency to attach too much importance to one aspect of an event. The illusion of control. The tendency to overestimate the degree of their influence on other external events. [Sources: 7]
connection error. Tend to assume that certain conditions are more likely than general conditions. Information Bias The tendency to seek information, even if it cannot influence action. Basic rate error (cognitive error). Tend to ignore information about the basic interest rate (general, general information) and focus on specific information (information only relevant to specific cases). Basic bet error or basic bet lost. Tend to ignore information about basic rates (general and general information) and focus on specific information (information related to specific cases only). [Sources: 0, 7]
Availability heuristic. The tendency to overestimate the likelihood of events with increased “availability” in memory, which may depend on how recent the memories are or how unusual or emotionally charged they may be. Player error, also known as Monte Carlo error, occurs when a person mistakenly believes that a certain random event is less or more likely to occur based on the outcome of a previous event or series of events. Hot Hand Bug Hot Hand Bug (also known as the Hot Hand Phenomenon or Hot Hand) is the belief that a person who succeeds in a random event is more likely to succeed in further attempts. The error occurs due to the erroneous concept of the law of large numbers. [Sources: 1, 2, 7]
— Slimane Zouggari
##### Sources #####
[0]: https://www.studystack.com/flashcard-2548692
[1]: https://www.actionnetwork.com/education/jonathan-bales-endowment-effect-gamblers-fallacy-betting-fantasy-sports
[2]: https://www.investopedia.com/terms/g/gamblersfallacy.asp
[3]: https://thedecisionlab.com/biases/gamblers-fallacy/
[4]: https://www.nature.com/articles/palcomms201650
[5]: https://bizzbucket.co/gamblers-fallacy-why-it-matters-in-business/
[6]: https://tgfx-academy.com/lessons/lesson-2-psychological-biases/
[7]: https://uxinlux.github.io/cognitive-biases/
[8]: https://marro.io/bias/interpretation/probability.html