Gamblers' Fallacy

by Craig Shrives

What Is Gamblers' Fallacy?

The gamblers' fallacy, also known as the Monte Carlo fallacy, is a cognitive bias that occurs when individuals believe that the outcomes of future events are influenced by past events, even when the events are statistically independent. It involves the mistaken belief that if a certain event or outcome has occurred repeatedly in the past, it is less likely to happen in the future, or vice versa.

The gamblers' fallacy is commonly observed in situations involving chance or randomness, such as gambling or games of probability. Here is a quick example: So, the gamblers' fallacy arises from a misunderstanding of probability and randomness. Each event or outcome, whether past or future, is independent and unaffected by previous outcomes, assuming a fair and random process. The belief in the fallacy can lead individuals to make irrational decisions, such as placing larger bets based on the false assumption that a particular outcome is more or less likely due to recent outcomes.

To avoid falling into the gamblers' fallacy, it is important to understand and apply the principles of probability correctly. Each event should be evaluated independently, without being influenced by past outcomes, as long as the underlying process remains consistent and random.

An Example of Gamblers' Fallacy

It can't be a red again

The most common example of gamblers' fallacy is predicting that the ball on a roulette table will land on red next because the previous few numbers were black. The truth is that the next number is equally likely to be black. It's a 50/50 (if you don't include the green zero) at all stages of the game. The history is irrelevant.

A Practical Example of Gamblers' Fallacy

Don't try the old "keep betting on black" strategy

Hey, here's a plan. Let's go to the roulette table and keep betting on black. If it's red, we'll keep doubling our money until a black appears. We can't lose.

Actually, that's true. You can't. But, to make it work, you need a lot of nerve and a lot of money. This is because every time the ball spins, there's only a 50% chance of a win (actually, it's slightly less because of the green 0), and when you keep doubling a number you get to very large numbers very quickly.

Below is a legendary story that relates to that last idea.

Long, long ago, an Indian king challenged one of his subjects to a game of chess and lost. Prior to the game, the king had told his subject (who was also a good mathematician) he could have anything he wanted if he won. Having won, the subject asked for rice. More specifically, the subject wanted one grain of rice on the first square of the chessboard, two on the second, four on the third, eight on the fourth, etc.

The king was a little upset at the request because he had promised his subject "anything he wanted", and he thought the request would amount to less than a sack of rice as opposed to the bags of jewels and gold he had anticipated. [No, king, it actually amounts to 18,446,744,073,709,551,615 grains of rice.] However, the king soon learned that even if he sold all his national assets, he did not have enough money to buy the rice needed to fulfil the subject's request. [In fact, he would have needed about 210 billion tons of rice, enough to cover the whole territory of India with a metre-thick layer. What happened next is disputed. Some versions of this story say the subject was punished and some say he became king. Some cultures tell this story with wheat and not rice.]

Anyway, if you're planning to go to the casino with this "great" plan, remember, it's based on a gamblers' fallacy that has been committed by lots of people before you.

Critical Thinking Test

Are you good at spotting the biases, fallacies, and other cognitive effects? Can you spot when statistics have been manipulated? Can you read body language? Well, let's see! Show Instructions

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