What is Gambler’s Fallacy: Statistics are always surrounded by two kinds of events – dependent and independent events. While the dependent event’s calculations are governed by different approaches such as the Naïve Bayes theorem and full joint distribution tables, the calculations involving independent events are quite easy to follow.

New technology and data mining techniques are all about using past data in order to make predictions true about the future. However, is this always true? Does the future data always depend upon its correlated past data? Even statisticians were not too sure of this.

Gambler’s Fallacy is one such proof which states that a human mind often interprets the outcomes of a future event judging by its corresponding past events even if the two are completely independent of each other.

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Gambler’s Fallacy is inspired by the “failures of gamblers” due to their probabilistic illusions to make decisions in casino games. Also known as “Monte Carlo” fallacy, the gambler’s fallacy has been used a number of times for various conformances and inferences.

In this article, we are going to explain the basics of this fallacy and would also consider a few famous examples to understand the term and its context in a better way. Let’s start!

QUICK READ: The First Golden Rule of Investing -Avoid Herd Mentality.

The Coin Toss Example

Coin Toss Example - Gambler’s Fallacy

Gambler’s Fallacy can be very well explained with the help of a basic example involving a coin. For future reference, let’s suppose that the coin is fair with both sides (heads & tails) having an equal probability of landing on top.

Suppose a coin is flipped 10 times and the result of each event was “Heads”. What would you bet for the next coin flip?

Now, if a human bets on the outcome of the 11th flip of the coin to be “Tails” seeing the past events, there’s a 50% chance of him to fail. 

The above context does only imply a simple rule: The occurrence of an independent event is not dependent on the past events. In this example, the 11th flip of a coin would result in both heads and tails with a 50% chance of being associated with each one of them.

Therefore, the prediction of an event can’t be made seeing its past outcomes if the events are independent of each other.

Psychological Thinking & “The Gut Feeling”

Something which our brain is too good at is making inferences. A human brain is very quick at picking up things, assembling them, joining the pieces together, and making an inference. The probabilistic approach here is not always true, however.

A human brain is just incredible at churning out new patterns and associations that it might create illusions. To put it in plain and simple words:

Our brain can deduce patterns that even don’t exist in reality

That alone might cause problems and thus exist fallacies like “The Gambler’s fallacy”. In the coin toss example, our brain might work in two ways:

  1. It could think that on most of the coin flips, heads are turning up so, in the 11th flip, it might show a ‘head’ again. OR
  2. It could think that since most of the coin flips have shown “heads” on them, maybe it is going to show the “tails” now.

Both of them, however, are true BUT ONLY COLLECTIVELY.

In the coin toss example, the probability of the 11th flip showing “Heads” and “Tails” is equal and is exactly 50% for both of them.

Also read: Investing Psychology: Winner’s Curse

Gambler’s Fallacy and Investing

You would think what do these terms have to do with each other? However, you must know that it is a common practice in the investing domain as well. Investors tend to liquidate their positions (or their bet) over something which is long overdue – again, a classic example of the Gambler’s Fallacy.

For example, if a stock is continuously making new highs for the last 4 consecutive days, few may think that it will correct on the 5th day, so better to leave the position. On the other hand, the rest might argue that it will continue to rise because of the momentum.

An inaccurate understanding of basic terms related to probability can make one invest in the wrong places. Now, I would like to ask you the same question again!

In the coin toss problem mentioned above, how much would you like to bet on heads or tails or both?

The correct answer would be to bet half of your money on heads and half of it on tails – pretty simple, right? Not because tails is overdue, not because heads are on a streak but because both of them are having an exactly equal probability of landing on top.


Summing Up

If you pay heed to the name of this fallacy; the gambler’s fallacy, you would relate it to a casino game. The co-relation is justified!

Most of the games in a casino or gambling game have sequences that are randomly generated and are statistically independent. Making a prediction on the outcomes of the events involving the sequence of these games isn’t easy and sadly can’t be derived from the mathematics of probability. Therefore, one would find it purely random and “lucky” to get a winning sequence – the Gambler’s Fallacy is rolling its dice in the background.

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