What is the Gambler’s Fallacy?

Imagine that you are just about to place a bet on your favorite football team. You decide to bet on whether the team will lose or win. You put a fortune for it to win, and they do. On the second match, you place another bet on your team to win, and as luck would have it, you’re right. This winning streak goes on for five more consecutive games, and as you would have it, your team is 7-0!

You start to think, what are the odds that my team wins seven consecutive straight games? The next match ‘Has’ to be the one where they lose, you assume, so you place a bet against your team. However, they win again.

Naturally, it is common to witness such a winning streak and perhaps reason that the streak will eventually be broken. This notion is known as the ‘Gambler’s Fallacy.’ Most online gamblers have likely heard and maybe even encountered the famed gambler’s fallacy. So what exactly is it? Here is everything you need to know about the gambler’s fallacy.

Definition: Gambler’s Fallacy

Equally called the famous ‘Monte Carlo’ fallacy, this concept was named after a remarkable occurrence in 1913 at the Le Grande’ Casino. This fallacy represents a belief in which the odds of something occurring with a fixed possibility grow lower or higher as the process repeats.

The notion is based on a concept of belief that random events are more or less likely to happen following a given activity or events series. In extension, the view is that something is likely to occur if it hasn’t happened in a long time like a coin flip coming up tails after a consecutive series of heads.

The gambler’s fallacy is connected to a broader ‘maturity of odds/chances’ doctrine that assumes that every play in a given game is associated with other events. As such, this appears to impose that a series of similar results of a given sort must be balanced with time by different outcomes.


Although it is still unclear about the real origins of the ‘Monte Carlo’ fallacy, it was, however, first proposed by Daniel Kahneman (Psychologist) and Amos Tversky (Mathematical Psychologist).

After assessing cognitive behaviors like a gambler’s psychology, the two attributed this fallacy to the erroneous belief that gambling is typically a fair process that somehow corrects itself mainly when a losing or winning streak happens.

How It Works: Example of Gambler’s Fallacy in Motion

This fallacy can best be explained using a coin toss challenge. In a typical coin toss event, the probability of the coin toss falling on either tails or heads is 1:1. This means that the likelihood of showing heads is the same as that of showing tails.

With the gambler’s fallacy in place, if you flip a coin ten times and they all fell heads up, you would subsequently predict your next flip as more likely to be tails. This prediction relies on the notion that since heads have appeared ten times, the streak will eventually break, and tails will land.

Nonetheless, the truth is that no matter the number of times your coin falls heads up, the odds of the next flip being tails or heads remains 50%. This is because every coin toss is uniquely a separate event and which is entirely independent of the previous toss, meaning that your last tosses have no bearing on your next ones.

When you use the gambler’s fallacy to roulette games, for instance, it is very easy to get sucked in. The odds of the ball falling on black, for example, are approximately 50 %. Therefore, in the event the ball dropped on black after 20 consecutive spins, applying the gambler’s fallacy would lead you to incorrectly assuming that the next turn will fall on the red. Conversely, just like with a coin toss, the odds of the outcome changing remains at 50%. Chances are it will land on the black as on red.

Why Is The Monte Carlo Casino Incident So Famous?

What is perhaps the most famous instance of the gambler’s fallacy in action is the 1913 events that happened in the globally-acclaimed Monte Carlo Casino-and primarily the reason behind the synonym ‘The Monte Carlo fallacy.’

Monte Carlo Casino

In a roulette game, the black color turned up 29 consecutive times! According to author David Darling, the probability as he calculated was at 1 in 136,823,184. Although this is striking for its relatively high improbability, gamblers at this casino heed the gambler’s fallacy. They bet multi-millions (in francs) against the black. The notion was that the string of consecutive black was creating an imbalance that would eventually lead to a streak of red. Unfortunately for them, it was never so!

The uniqueness of this particular roulette game and the vast amounts of money that gamblers lost that day is the primary reason for its iconic fame.

After black came up for the tenth time, gamblers started placing much more significant bets on the red, still under the misguided notion that an imbalance would shift the trend. But just like earlier outlined, the probability remains the same in each spin for black or red turning up as before: 18/37 (single zero wheel).

In the end, the Le Grande owners amassed approximately ten million francs in profits, with many gamblers going back home empty-handed.

The Gambler’s Fallacy and Online Betting Strategies

Regardless of it being a widely unsung notion, the gambler’s fallacy remains a significant factor in several casino betting strategies, particularly negative progressive systems. Perhaps the most famous example of its application is in the Martingale Strategy.

Commonly used in the roulette game, this strategy entails for a player to double his or her even money bet (black/red; low/high, etc.) each time you lose hope that you win your losses back once you finally succeed. The negative progression and Martingale strategies are based on the assumption that you will ultimately win after a massive streak of losses, just like with the gambler’s fallacy.

While this is not to say that these strategies are outright losing approaches (since they can be quite useful in some instances), while using them, don’t forget about the gambler’s fallacy, and don’t anticipate for any long-term profit!