What Is the Gambler’s Fallacy (And What Does It Mean to You)?


The gambler’s fallacy is one of several gambling myths. It is based on the assumption that a series of random events follows a pattern. If such a pattern exists, then it follows that the pattern should reverse trends at some point.

But if there’s a pattern, then the events are not random. By definition, a random event cannot be predicted.

And if it’s unpredictable, then there cannot be a true pattern. Mathematicians say that long series of random events include “local patterns” that don’t predict anything about future events.

Randomness is sometimes described as independence. The independence of two random events means that neither influences the other. Coin tossing is often used to illustrate how randomness affects statistics and probability.

If a person tosses a coin 1,000 times and records the results, that person can compute a probability distribution describing the percentages of “heads” and “tails” results.

That probability distribution makes no prediction about how many of the next 1,000 coin tosses will result in “heads” or “tails.”

On the other hand, given the knowledge that there are only two sides to a coin, the rules of statistics and probability say there’s an approximately even chance (probability) that any future coin toss results in either “heads” or “tails.”

For me, a simple way to explain this apparent contradiction is to say, “probability in the past is fixed and certain, but probability in the future is not fixed.” That is why philosophers and everyday people say “the future is what you make of it.”

Why Is It Called “The Gambler’s Fallacy?”

The concept has a more scholarly name in “fallacy of the maturity of chances.” The earliest credited use of this phrase is Hoyle’s Games, 1907 edition. The text used roulette to illustrate the principle. The 1907 edition included the following paragraph in the section on probabilities:

“Some persons imagine that because the odds are so great against any event happening a certain number of times in succession, that when it has happened so many times it is very unlikely to happen again. If the ball in the roulette wheel has not fallen in the red for ten rolls, they think it must come red next time. This is called the ‘maturity of the chances’ and by betting on this fallacy, many millions have been lost.”

Hoyle didn’t invent the phrase. Several journals and books referred to “maturity of the chances” in the 1800s. An 1877 novel, A Woman-Hater, describes the principle using roulette.

The scenario played out in real life in Monte Carlo, 1913. After that time, the phrase “Monte Carlo fallacy” became popular.

A 1963 paper published in The Journal of Psychology titled “The Maturity of the Chances: A Gambler’s Fallacy” introduced the modern name by which the concept is now known. The name caught on in popular literature and has been used ever since.

Some Random-Seeming Things Really Are Parts of Patterns

Card games provide good of examples of how randomness affects a limited set of probabilities. There are only 52 cards in a standard playing deck. The probability of any 1 card being drawn from a full deck is 1 in 52.

As cards are dealt, the probability for any one remaining card being drawn improves. The ratio comes down on the right side to 1 in 51, 1 in 50, etc.

This is why advantage players are able to count cards in blackjack. The remaining possibilities may be unpredictable, but each one becomes more likely as the deck or shoe loses cards to the table.

True randomness is not achieved in any kind of card game. The limited number of cards always have some order when kept together as a deck. The players are simply unaware of the order of the cards.

Gaming machines use random number generator chips to simulate random sequences. Research in the field of computer science continues to improve the algorithms these chips use. Older chips’ algorithms can be reverse-engineered with a supercomputer.

The randomness that most casino games count on depends on players being unaware of the RNG algorithms or the shuffled order of playing cards.

Among the well-known casino games, the most random games are craps and roulette. Craps is random because players take turns throwing the dice. Roulette is random because the wheels are designed to minimize wear and tear from friction with the ball.

Casinos also change out dice, balls, and wheels as necessary to ensure the games remain as fair and random as possible.

Slot Machine Games Are Considered to Be “Random Enough”


The only documented case of slot machine RNG chips being reverse-engineered occurred a few years ago. A Russian gang acquired older slot machines from several casinos. They hired computer experts to tear the machines’ computers apart.

Using a super-computer, the Russians sent operatives into casinos around the world. The operatives played slot machine games similar to those that had been studied by the gang’s experts.

The players used their smartphones to transmit live video of the games back to the super-computer, which determined how to beat the games. The players stole a lot of money before the casinos caught them.

Land-based casinos have changed their security procedures to protect against this kind of cheating. It’s not clear if online casinos have been compromised in the same way. To do so, criminals would have to possess one of the gaming platforms that online casinos lease from software companies.

Hopefully, the data centers are well-protected and the software companies do a good job of vetting who leases their systems.

Because it’s so hard to reverse-engineer a slot game, the casinos make most of their profits from slots. Serious players advise people not to play slots with any hope of making money. People should only play slots for fun, if at all.

The Gambler’s Fallacy Is Less Likely to Happen in Sports Betting

Although honest bettors remain ignorant of the outcomes of all competitions, a thorough knowledge of team skills and performance statistics is leveraged to weight bets.

A team that has lost every game in the first half of the season is not likely to make a dramatic comeback, although it occasionally happens. Usually, there is a change in the roster, coaching, or the team’s schedule. Sports analysts sometimes argue that a mediocre team can achieve a winning record against weaker rivals.

Horse racing enthusiasts rely on handicappers to estimate which horses are most likely to win. The handicapping process looks at a horse’s record on each type of track.

Bookies and racetracks offer odds based on two factors: which competitor they deem more likely to win and how many bets they receive at the offered odds. Racetracks and bookies must adjust their payout odds as the weight of bets shifts one way or another.

A naive bettor might go against the odds on the assumption that something has to change. But more experienced bettors take every available fact into consideration. Consistently losing competitors do tend to lose more often than not.

Betting Systems Based on the Gambler’s Fallacy May Still Be Useful

Despite the fact that a system wrongly assumes a series of random events is more likely to change going forward, some betting systems make good recommendations for sizing wagers.

If a betting system recommends using modest bets, that’s prudent. The system’s assumptions may be invalid but the betting limits could be worth following.

There is also the psychological factor. If a betting system teaches you to change what you bet on, that may make the game more interesting. Ignoring the predictive factor, players can gamify the game by waiting to see what happens.

As long as the player maintains a true perspective, it’s fun to see a false prediction come true. Just don’t count on it happening again.


Some players run simulations of games into millions or billions of iterations. They do this to estimate the “true probabilities” of results.

These simulations don’t ever predict the future. They are as guilty of the gambler’s fallacy as any betting system that assumes the next ball must be red or odd.

If you’re not just gambling for fun, never lose sight of the fact that the casino is counting on you not knowing what happens next. They’ll do whatever is necessary and legal to ensure the next event is a surprise.

At best, you can leverage your knowledge of a game to make wiser choices. At worst, you could fall for the gambler’s fallacy without realizing it, even though you’re aware of what it is.