The Gambler’s Fallacy

Updated on June 2, 2020
Rupert Taylor profile image

I've spent half a century (yikes) writing for radio and print—mostly print. I hope to be still tapping the keys as I take my last breath.

Each time a coin is tossed there is a fifty-fifty chance it will come down heads. It doesn’t matter how many times the coin came down heads before, the odds always remain fifty-fifty. The coin has no memory of previous outcomes, although the coin-flipper does. Believing that past events influence the probability of future ones causes a lot of trouble for gamblers; it also infects many other aspects of life.


The Roulette Wheel

The only way to consistently win in a casino is to own one, unless you are Donald Trump, but that’s another story. So it was that on the night of August 18, 1913, Le Grande Casino of Monte Carlo made an absolute killing.

Crowds gathered around the roulette table after word spread that the ball had dropped into a black slot 10 times in a row. Patrons started pushing bets onto red on the table, but still the ball fell on black.

Monte Carlo Casino in about 1900.
Monte Carlo Casino in about 1900. | Source

As play continued, the bets got larger, until millions were being wagered on each spin of the wheel. Black again! Gamblers were convinced that red must come up on the next go-round. But that belief defies logic. The odds of the result being black or red are exactly the same with each turn.

Eventually, on the 27th spin, the streak of blacks ended but, by then, fortunes in the neighbourhood of 10 million francs had been lost and handed over to the casino.

The gambler’s fallacy is “The mistaken belief that if a certain independent event occurs more frequently than normal during a certain time period, then it’s less likely to occur in the future.”


The Law of Small Numbers

On a roulette wheel there are 37 pockets; 18 are black, 18 are red, and one is green for the number zero (American-style wheels have two zero pockets). If the wheel is spun a billion times a fairly accurate level of probabilities will be produced. Not counting the zero slots, the outcome will be very close to 50-50 for black or red.

Back it up to 100 spins and the odds are probably going to be something like 48-52 either way. With just ten spins, as we’ve shown with the Monte Carlo incident, the probabilities can be wildly inaccurate.

This is where we meet a phenomenon that goes by several names: the law of small numbers, jumping to a conclusion, faulty generalization, or the fallacy of the lonely fact.

Professor Richard Nordquist on explains, “By definition, an argument based on a hasty generalization always proceeds from the particular to the general. It takes a small sample and tries to extrapolate an idea about that sample and apply it to a larger population, and it doesn’t work.”

Those gamblers in Monte Carlo were doing precisely this; they were taking a small sample and assuming past events would influence future ones. They can’t and don’t.

The Reverse Gambler’s Fallacy

Stepping aside from casino games, the illogical application of the gambler’s fallacy pops up in other places. Academics at the National Bureau of Economic Research (NBER) have found the phenomenon in the United States in such diverse fields as refugee asylum cases, major league baseball, and loan applications.

In the way that university professors like to write they refer to decision-makers exhibiting “negatively auto-correlated decision-making.” Simply stated, people making decisions unconsciously allow their earlier verdicts to influence later ones; this is the reverse of the gambler’s fallacy.

Judges in U.S. asylum-seeking cases are more likely to grant an application if it follows a case in which they denied asylum. The NBER report says “We estimate judges are up to 3.3 percentage points more likely to reject the current case if they approved the previous case. This translates into two percent of decisions being reversed purely due to the sequencing of past decisions, all else equal.”

Those don’t sound like big numbers, but the result can be catastrophic for those deported because a judge reflexively allowed a previous decision to impact a later case.

The researchers found the same phenomenon at play with bank loan officers, estimating that “five percent of loan decisions would have gone the other way if not for this type of bias.”

And, every baseball hitter knows for certain that umpires routinely make bad calls. The NBER team found there’s some truth to that, writing that major league baseball umpires “call the same pitches in the exact same location differently depending solely on the sequence of previous calls.”


Hot Hand Bias

Gamblers have a tendency to believe in lucky streaks; because I won my last bet, I’m more likely to win my next one. There’s no evidence to support this notion, and researchers found this idea exists in primates other than humans.

Tommy Blanchard has a PhD in brain and cognitive science. He and colleagues at the University of Rochester, New York studied the behaviour of monkeys. The primates were given two choices, one of which delivered a reward. The BBC reports that “When the correct option was random―the same 50:50 chance as a coin flip―the monkeys still had a tendency to select the previously winning option, as if luck should continue, clumping together in streaks.”


Of course, monkeys are not tutored in probability theory; they can’t harbour irrational beliefs in the likelihood of an event happening, so something else must be going on. Dr. Blanchard suggests the behaviour springs from an evolutionary advantage that developed as our ancestors foraged for food.

“If you find an apple lying around somewhere,” he told Wired, “chances are you’re going to find other apples nearby.” From this comes the knowledge that food tends to come in clusters, just as gamblers believe that luck comes in clusters.

Research shows that even though people are aware of the gambler’s fallacy many are still prey to it. One way to avoid falling into the trap is to apply disciplined, critical thinking to all decisions. Another approach is to not gamble.

People assume that streaks of outcomes will end up ‘evening out’ in order to be considered representative of what an ideal and fair random streak should look like, because they view chance as a fair and self-correcting process.”


  • The origin of roulette is a bit murky but it’s widely accepted the mathematician Blaise Pascal had a hand in the invention in the 17th century. Two similar games were called even-odd and roly-poly.
  • Only a player that bets on zero can win if the ball drops into the zero pocket. Anybody else who bet red or black, even or odd, or any other numbers loses. This gives the house a 2.6% edge. American roulette wheels have a double zero slot as well as a single zero one; this gives the house a 5.26% edge.
  • In the casino world, a “Whale” is a high-stakes gambler who bets millions of dollars in a single session. Casinos compete with lavish gifts to attract whales to their premises.
  • In 1992, Archie Karas was broke when he got a $10,000 loan from a friend. In Las Vegas, he used the loan to start a gambling run that, by the start of 1995, had netted him $40 million. By late 1995, he had lost everything playing craps at Binion’s Gambling Hall.


  • “Hasty Generalization (Fallacy).” Richard Nordquist,, September 7, 2019.
  • “The Gambler’s Fallacy – Explained.” Nick Valentine, The Calculator Site, June 23, 2019.
  • “Hot-Hand Bias in Rhesus Monkeys.” Tommy C. Blanchard et al., National Library of Medicine, July 2014.
  • “Monkeys, Like People, Believe in the Hot-Hand Phenomenon.” Mary Bates, Wired, July 10, 2014.
  • “Decision-Making under the Gambler’s Fallacy: Evidence from Asylum Judges, Loan Officers, and Baseball Umpires.” Daniel Chen et al., National Bureau of Economic Research, 2016.
  • “The Gambler’s Fallacy: On the Danger of Misunderstanding Simple Probabilities.”, undated.

© 2020 Rupert Taylor


    0 of 8192 characters used
    Post Comment
    • Miebakagh57 profile image

      Miebakagh Fiberesima 

      4 weeks ago from Port Harcourt, Rivers State, NIGERIA.

      Hi, I agreed. Thanks.

    • drylen profile image

      Charlie Halliday 

      4 weeks ago from Scotland

      Very interesting article Rupert

    • Miebakagh57 profile image

      Miebakagh Fiberesima 

      4 weeks ago from Port Harcourt, Rivers State, NIGERIA.

      Rupert, the best way to stop this sickness of gambling and the loss of money is to stop gambling with one's life. Gamlers did not win anything. Whatever their won soon lost all in re-gambling on the belief that a greater is ahead. Thanks.


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

    Show Details
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)
    ClickscoThis is a data management platform studying reader behavior (Privacy Policy)