What is Gambler's Fallacy?

Referring to a dictionary, the first definition of the word fallacy is: ‘mistaken belief, especially one based on unsound arguments’. An example of this definition is given as follows: ‘the notion that the camera never lies is a fallacy’.

Indeed the camera is more than capable of lying. In this day and age of digital photography, photographers are using the technology to edit any undesirable blemishes of once beautiful, but now aging, pop stars to reverse the natural process of aging.
Even long before the digital age photographers had mastered the art of deceptive photography as means of playful, and sometimes sinister, trickery.

Formal Fallacy

There are many different types of fallacies; anti-dotal fallacy, being one example, where an individual is guilty of letting personal experiences, not sound reasoning, dictate and obscure their otherwise logical decision making. Even the world’s most logical minds have surely been victim to this type of fallacy.

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Gambler’s Fallacy

This Gambler’s Fallacy, known also as the Monte Carlo Fallacy, is best described as when a person is guilty of believing that randomly occurring future events are somehow determined by an event, or series of events, that took place at some point in the past.
For example, the belief that a pair of socks, worn on the day of a big victory, are somehow lucky is not the basis of a world-beating football team.

Even if the lucky socks are worn to every game, the fate of the game is unlikely to be dictated by the socks. World-beating qualities are often attributed to skill and determination, and it is not possible to say that events that happened in the past decide the events happening in the present or events that will happen in the future.

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The Coin Toss

The classic example, everyone has been there. There is a stalemate and both parties involved in the coin toss desperately wants the coin to land favorably. A simple toss of the coin is capable of determining many, many things. Who will be awarded first possession in sporting matches? Who will answer the door when it knocks on a lazy Sunday morning during the soap opera marathon on the TV set but all are too lazy to move to see who is knocking?

Only a coin toss is capable of determining who is to answer the door. A coin toss is even responsible for the naming of Portland, Oregon when the name could not be reasonably decided on. When decisions are just too difficult to make a coin toss can always be relied upon to make those, all too often, tough decisions.

Probability

On a single toss of a coin, the probability of the coin landing on either side is 50% for heads and a 50% chance it will fall on the tails side of the coin. Increase the amount of coin flips and the probability of the coin landed the same side each time changes accordingly. There is a 25% chance of getting two heads in succession, the probability is cutting right in half. This holds true for more flips; to get three heads in succession, the chances are halved to 12.5% and the relationship between percentage and successful flips in a row continues.

If a coin is tossed 100 times and each the coin lands on tails, under gambler’s fallacy a person may think that the next toss is likely to land on heads. This process of thinking is incorrect and demonstrates a lack of probability understanding. No matter what has happened before the next coin toss it does not dictate what will happen. Each flip is an independent event having no bearing on what will happen, the chance of the coin landing on either side is always 50%.

 
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