Outsmart the Gambler’s Fallacy

Keeping Your Cool Online or at the Casino

A psychological phenomenon known as the ‘gambler’s fallacy’ (or the Monte Carlo Fallacy) is the mistaken belief that random events are related to future or past events. The theory generally applies to a random event like a fair coin toss, dice roll, or hot hand (hot hand fallacy).

The gambler’s fallacy is a negative autocorrelation established by mental shortcuts for cognitive processes (called the 'representativeness heuristic'). When a person believes a random process is related to a past experience or future occurrences, they engage in the gambler’s fallacy.

We’ll analyze the erroneous belief that random sequences can predict independent events and vice versa, including an inverse gambler’s fallacy of a person rolling a die in short sequences.

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What is the Gambler's Fallacy?

gambler's fallacy

The gambler’s fallacy derives from experimental psychology and a 19th-century philosophical essay called “Philosophical Essays on Probabilities.” French scholar and polymath Pierre-Simon Laplace described the mistaken belief of a future event relating to the anticipated gender of a newborn.

Laplace theorized about the supposed ‘increased probability’ associated with a previous event—a father having more than one baby boy “...judged that the boys already born would render more probable the births next of girls.”

Laplace claimed that the representative sequence of a chance process (having more than one baby boy) made people expect that a past event could predict future events.

A random event (such as having a boy or girl, a coin flip, or a lottery play) retains statistical independence regarding a future one when things happen based on chance. Like in random events, the gambler’s fallacy assumes that small samples of past events can predict the opposite outcome.

However, the probability of dice rolls or tossing heads or tails from a fair coin flip over an extended period is not a self-correcting process. Even if the next flip shows heads, which happens two or three times in a row, it’s a false and null hypothesis to assume flipping tails would then be more likely to occur.

How the Gambler's Fallacy Can Affect Your Decision Making

Rooted in social perception and cognitive bias (mental shortcuts), the gambler’s fallacy occurs when a person falsely assumes a random event can predict a future one based on a previous one. For example, the past events of 100 coin tosses from a fair coin might show heads or tails a few times.

However, it’s statistically incorrect to assume that heads or tails are more likely to occur in future coin tosses based on a past event (i.e., heads five times in a row during five coin flips doesn't mean there's a higher chance of tossing tails during the sixth).

A more representative sequence with empirical data shows the same chance (1 in 2) of tossing heads or tails on every one of 100 coin tosses.

Different outcomes happen based on the same number of independent events when a chance process unfolds with two outcomes (coin flips, having a boy or girl). If you toss five heads during a series of coin flips, it's the gambler's fallacy to suppose a certain event becomes more likely (tossing tails).

Gambler’s fallacy leads to poor decision-making, like “chasing” losses during a cold streak—with the most famous example being the Monte Carlo Fallacy.

Monte Carlo Casino

The gambler’s fallacy is also known as the Monte Carlo Fallacy. The most famous example of gambler’s fallacy occurred at the Monte Carlo Casino in 1913, when gamblers lost millions at the roulette wheel.

As the ball fell on black 26 times in a row, bettors used irrational behavioral decision-making (gambler's fallacy) to incorrectly predict the opposite outcome by placing the same bet on red.

The odds of the ball landing on black on the roulette wheel 26 times consecutively are about 1 in over 60 million, which is astronomically high. However, if the game represented a fair process, then each random event, or every spin, offered the same odds.

The Monte Carlo Fallacy became a prime example of the gambler’s fallacy, with bettors convinced that red would come up next every time. The two groups (red and black) offered the same odds on every spin, causing players to lose millions.

Bayesian Inference

Any example of the gambler’s fallacy often relates to different areas of mathematics and the psychology of human error. Thomas Bayes, an English philosopher and statistician, proved that probabilities were associated with the limits of what could determine an unknown event.

Laplace added to Bayes’ work in law, medicine, and science. Bayes' theorem offers statistical insight into the probability of an event occurring based on prior knowledge.

Bayesian statistical inference updates the probability of an event whenever more information becomes available (i.e., a player draws an Ace from a standard 52-card deck, and it doesn’t get placed back into the deck).

Bettors might use statistical inference in fantasy sports based on prior knowledge, while a mid-week injury report could deter their gambler’s fallacy. It’s best to remember that the first roll of the dice doesn’t represent what may or may not come next.

Cognitive Biases Related to the Gambler's Fallacy

Reverse Position Game Play

A common version of the gambler’s fallacy occurs in the inverse, with bettors making assumptions that a random event might be “due” to appear. For example, a coin flip showed heads three times in a row. Rather than choosing heads again (gambler’s fallacy), a bettor chooses the opposite outcome of tails.

Statistical analysis shows that retrospective gambler's fallacy, or assuming the outcome of a random event based on previous results, is incorrect.


The gambler’s fallacy, known as a ‘hot hand’ (or positive recency), refers to the belief that a person performing a positive action, like scoring or winning a lot in a short period, will repeat that action.

While human performance in sports or casino games might seem easy to judge, the probability of any action occurring does not derive from perceived performance.

Numerical Cognitive Bias and Probability Distribution

The two fallacies associated with the gambler’s fallacy often apply to the ‘law of small numbers.’ In the previous example of retrospective gambler’s fallacy, Laplace discussed how an expectant father might assume that, after having three boys, he may be “due” to have a baby girl.

As another example, loan officers might engage in RGF when declining a loan request after approving one beforehand.

An analysis of statistical inference based on social expectations in small numbers might influence perception; however, it does not determine the probability of an outcome.

Why does the Gambler's Fallacy Occur?

Cognitive bias in human perception may derive from a “fight or flight” response that generally helps to deal with high levels of emotion or anxiety.

With these intensely perceived emotions, the human brain often requires a quick solution for the problem to relieve the stress, which might cause the gambler’s fallacy to occur.

Here’s a look at various types of cognitive biases.

Cognitive Signs of Bias Associated with the Gambler's Fallacy

  • Immediately selecting information just because it aligns with a personal belief
  • Failing to adjust judgment or reassess when new information becomes available
  • Generalization-making or jumping to conclusions with little evidence (e.g., I always win on Tuesdays)
  • Blaming external factors for failures (e.g., The dice are rigged; the roulette wheel might be broken) but taking the credit for success (It must be my lucky socks)
  • Age is also a factor in cognitive bias activation as people erroneously equate life experiences with direct outcomes; thus, the more life you've lived, the more experiences you have to choose from that 'could happen' again

How Do You Avoid the Gambler's Fallacy?

Avoiding the gambler’s fallacy is essential to becoming a more disciplined and successful bettor. Players must learn to let go of the belief that the occurrence of a previous event determines a future outcome—that is statistically incorrect and provably false.

Strategies to get “back to reality” and remain grounded may include:

  • Taking a break
  • Establishing internal reminders (e.g., Dice don’t remember previous rolls)
  • Removing any distractions that could negatively influence your reasoning processes
  • Making clear decisions based on statistical accuracy and not your emotions

Problem Gambling Signs

To avoid problem gambling and bet responsibly, players should be aware of the signs to help stay in control. Routinely taking breaks is one of the easiest ways to reduce the chances of the gambler’s fallacy becoming a bad habit in your betting style.

If you or someone you know might have a gambling problem, there are always resources to help. Call or text 1-800-GAMBLER to contact the National Council on Problem Gambling.

Here are a few signs associated with problem gambling.

Common signs of problematic gaming

  • Frequently spending more money or time than planned
  • Gambling instead of engaging in other important things like work or spending time with others
  • Feelings of guilt after placing bets
  • Repetitive thinking that you have to keep playing to "turn things around"
  • Borrowing money, using a credit card, or stealing to gamble or pay off gambling debts
  • Lying about your gambling habits or hiding them from others

Ways to adjust your gaming practice

Players can adjust their gaming practices to avoid negative behaviors associated with the gambler’s fallacy.

Here are a few ways to “cool off” problem behaviors:

  • Use a problem gambling screener or fill out a relevant questionnaire online
  • Set daily time limits for gambling sessions
  • Set daily, weekly, or monthly limits on deposits, spending, and losses
  • Request a time-out for 72 hours to 12 months
  • Apply for a self-exclusion for a certain period (12 months to five years) in your state

Frequently Asked Questions about the Gambler's Fallacy

Do you have more questions about the gambler's fallacy, or are you wondering about responsible gambling practices? Read the common questions and answers we've compiled below.

What is the most common gambler's fallacy?

The most common gambler’s fallacy is assuming a future outcome based on a previous event(s). For example, bettors might believe that red is “due” to come next if the roulette ball lands on black five times in a row. However, every spin has the same odds for black and red.

Why do people believe the gambler's fallacy?

The gambler’s fallacy derives from a bias in the human brain associated with “mental shortcuts.” Inferring that a particular outcome should occur based on previous events is a false belief. Players should remind themselves of the gambler’s fallacy to avoid making irrational bets.

Can you avoid the gambler's fallacy?

Players should know house edge and randomness in casino games to avoid the gambler's fallacy. Craps and roulette games at land-based and online casinos in the U.S. get regulated by third-party companies and in-state agencies for accuracy and fairness. That means the odds for a particular outcome, including slots and other table games, remain independent on every hand, round, or spin.

Take breaks to avoid the gambler’s fallacy or establish internal reminders like “the dice don’t remember what they rolled beforehand.”

What causes the gambler's fallacy?

Cognitive processes influence a person’s brain to automatically engage in a psychological bias called the gambler’s fallacy. Suppose a person sees a specific result in a game or real-life situation. In that case, they might assume a particular outcome is “due” or that previous results impact a random event.

Is there an example of a famous gambler's fallacy?

The most famous example of the gambler’s fallacy comes from the Monte Carlo Fallacy. At the Monte Carlo Casino in 1913, a roulette ball landed on black 26 times in a row—with bettors making consecutive assumptions that the ball was “due” to land on red. Instead, they lost millions to the casino due to the randomness of the ball landing on black or red on every spin.

Are there specific activities that make you believe the gambler's fallacy?

Social expectations or influences may cause a person to believe in the gambler’s fallacy. For example, suppose many players are around a roulette table, and the ball lands on black in consecutive rounds. In that case, many players might influence each other by expecting red to occur and placing bets there.