The Gambler's fallacy

In a world riddled with conflicts and disagreements, we all can wholeheartedly agree that the probability of my articles becoming viral and the Bitcoin price seeing a 1000% increase is not only independent but also extremely unlikely. If I claim that these two events are dependent in an attempt to gain engagement from the large crypto community, does it not make me a conman?

Or I could simply be a common man (or a conspiracy theorist) who mistakenly perceives independent events as somehow interconnected. Another group that commonly struggles with this issue is individuals with gambling addictions.

Don’t we all have those friends (or in a few cases, we were those friends) who experienced consecutive losses in gambling but persisted because they believed their turn to win was imminent? It could be portrayed as a tale of remarkable persistence and unwavering determination when that friend miraculously wins a significant sum of money, potentially bankrupting the casino. However, there is one glaring problem: your chances of winning in any casino game do not significantly increase after a prolonged streak of losses.

The outcome of each round in gambling games is not influenced by the results of previous rounds. The gods of probability, watching from above, are unconcerned with balancing a gambler’s prior losses by granting them royal flushes. They have more important tasks at hand, such as ensuring that a specific group of contestants on the game show “Let’s Make a Deal” emerges as winners, surpassing the others.

Now, if we revisit the tale of our tenacious gambling-addicted friend, we can observe that their addiction leads them to erroneously believe that two independent events are interconnected. It is akin to thinking that the probability of flipping heads in a coin toss significantly rises after encountering three consecutive tails.

I agree that flipping four tails in a row is a rare occurrence. It only happens once in every sixteen experiments, where an experiment involves sitting alone on your couch and flipping a coin four times. However, when you have already flipped three tails consecutively, you have traversed the sea of rarity and find yourself with a 50% chance of successfully completing that feat.

But why does gambling addiction lead to a misinterpretation of event dependency? I have no clue. I swear I read the neurological explanation of it somewhere, but I don’t seem to recall. However, I do have a theory that dates back to the late 19th century. It was the same era when a certain Charles Darwin challenged numerous religious beliefs with his theory of evolution.

Although the concept of natural selection seems to apply to various aspects of our lives, it is irrelevant to this discussion. Instead, let us briefly shift our focus to the research conducted by a renowned cousin of this father of evolution. You may recognize this cousin by the name of Francis Galton.

Like Darwin, Galton was heavily invested in researching genetics (maybe, it’s a family thing?). He conducted extensive research on the heights of parents and their offspring, making several insightful observations. Galton noted that the heights of parents tended to be similar to their children’s heights within the average range. However, when parents had extreme heights (either tall or short), the heights of their children tended to move closer to the population mean. Galton coined this phenomenon as “Regression toward the mean.”

In other words, regression toward the mean informs us that if we witness an extreme outcome in an experiment, the subsequent outcome from repeating that experiment is likely to be closer to the true mean of the random variable associated with it.

I noticed this phenomenon in my personal life when I scored higher than expected in one of my board exams, despite putting minimal effort into preparation. However, in the subsequent year’s board exam, I achieved a subpar score that accurately reflected my level of effort. It’s important to note that the difference in scores between the two exams was not due to a sudden decrease in my preparation effort; my effort remained consistent. Therefore, this observed difference can be attributed to random variation, which caused my scores to regress toward the true mean.

We all must have observed regression toward the mean occurring in our lives or careers at some point, which renders this concept strikingly familiar to us. There have likely been instances where we witnessed our initial “luck” wane, and our outcomes reverted to being average. At times, we may have experienced the reverse, starting with subpar results that gradually improved as they approached the average. Perhaps we have encountered this phenomenon repeatedly across various facets of life, leading us to employ it as a predictive tool in many situations causing us to lose all our money in the casinos of Las Vegas.

If we closely examine Galton’s description of this phenomenon, we will note that he presented it within an observational context rather than a predictive one. Regression toward the mean does not justify why the probability of this article receiving more than 50 views increases after my previous two articles garnered single-digit numbers in viewership. Regression toward the mean is just like going to the gym; it does not guarantee immediate results. Instead, it focuses on playing the long game. It certainly explains why the viewership of my articles dropped to single digits (which I assume is closer to the mean viewership of my blog) after an initial period of high interest.

Therefore, beware when your mind tricks you into thinking that you will win in a game of pure chance just because you failed miserably in the previous attempt. The probability of success for that trial is most likely unaffected by the previous results. So, when you can, I hope you pack your bags and run far away from that game.

And by the way, there’s a name for a gambler mistakenly interpreting that the outcome of the previous game has an effect on the result of the subsequent game. It’s called the Gambler’s fallacy.