research on gambling has found that throwing the dice

September 21, 2018

“Gambling Brain” Studies Make Clear Why It’s Hard to Stop Rolling the Dice

Neural regions underlying risk-taking and regret may one day point toward treatments for compulsive betting

By Bret Stetka

Getty Images

More often than not a trip to Las Vegas is not a financially sound decision. And yet every year over 40 million people hand over their cash to the city’s many towering casinos, hoping the roulette ball rattles to a stop on black.

Gambling and other forms of risk-taking appear to be hardwired into our psyche. Humans at least as far back as Mesopotamia have rolled the dice, laying their barley, bronze and silver on the line, often against miserable odds. According to gambling industry consulting company H2 Gambling Capital, Americans alone lose nearly $120 billion a year to games of chance.

Now a set of neuroscience findings is closer than ever to figuring out why. Ongoing research is helping illuminate the biology of risky behaviors—studies that may one day lead to interventions for vices like compulsive gambling. The recent results show an explanation is more complex than looking at dysfunctional reward circuitry, the network of brain regions that fire in response to pleasing stimuli like sex and drugs. Risking loss on a slim chance of thrill or reward involves a complex dance of decision-making and emotion.

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A new study by a team from Johns Hopkins University appears to have identified a region of the brain that plays a critical role in risky decisions. Published September 20 in Current Biology , the authors analyzed the behavior of rhesus monkeys, who share similar brain structure and function to our own. And like us, they are risk-takers, too.

First the authors trained two monkeys to “gamble” against a computer to win drinks of water. Then they had to choose between a 20 percent chance of receiving 10 milliliters of water versus a far more reliable 80 percent chance of getting only three milliliters. The monkeys overwhelmingly took the gamble, even when they were no longer thirsty.

Previous work has shown a brain region called the supplementary eye field (SEF) is, along with regulating eye movements, also involved in decision-making. When the authors suppressed SEF activity by cooling the region with an external metal plate—a process that is harmless and reversible—the monkeys were 30 to 40 percent less likely to make risky bets.

Johns Hopkins neuroscientist and study co-author Veit Stuphorn says the findings were not entirely unanticipated, given the role the SEF and its neighboring areas play in decisions. Yet he is intrigued that an area of the brain is so tied in with processing the risk associated with a particular behavior without actually causing the behavior itself. “The specificity of the contribution of SEF to risky decisions was surprising to us,” he says. “We interpret this as a sign that SEF mainly reflects the contribution of higher-order cognitive areas…, such areas build a model of the environment and use it to predict opportunities and dangers.” In other words, the SEF appears to shape the attitude toward a particular risky behavior. It also, Stuphorn suggests, represents a possible treatment target for those prone to excessively risky pursuits like problem gambling.

But not just yet. “We do not understand the risk-taking network in the brain well enough to think about therapeutic implications,” he says. “But as our understanding increases, there is hope for better behavioral interventions based on a better understanding of the factors that drive risky decisions. And in the long run possibly direct interventions in the form of brain stimulation.”

Yale University neuroscientist Daeyeol Lee, who was not involved in the new research, is also optimistic. “Finding that excessive risk-taking might be influenced by the function of a specific brain area might be an important step in treating humans with severe risk-taking tendencies,” he says, adding that certain drug treatments for Parkinson’s disease and other neurological disorders can also cause risky behaviors. “The findings in this study might also have implications in reducing such unwanted side effects,” he says.

Typically, the brain’s “reward center” or “reward circuitry,” have not included the SEF but rather other brain regions that drive pleasurable responses via the neurotransmitter dopamine. Yet, as Daeyeol points out, reward is complex. The SEF is likely to be involved in the anticipation of reward and helping control dopamine activity in a reward area called the basal ganglia.

Another study published last week, also in Current Biology , adds an additional layer to the neuroscience of gambling risk—the feeling of regret. In 10 neurosurgical patients the authors measured electrical activity in a brain region called the orbitofrontal cortex—part of the prefrontal cortex near the SEF—while presenting them with gambling scenarios. They used electrodes to analyze brain activity as each study subject decided whether or not to make a bet, right after a bet and when—a half a second later—they learned the outcome.

By comparing the findings to previous brain recordings associated with regret, they deduced that during the split second between placing a bet and learning the outcome our brains frantically replay previous betting decisions. We recall the regret we felt from losing prior bets and from not betting more on those we won.

Senior author Ming Hsu, an associate professor in the Haas School of Business and the Helen Wills Neuroscience Institute, both at the University of California, Berkeley, notes this rumination on past choices is probably an evolutionarily means of improving future decision-making. “This type of replay is particularly prevalent during the lull after one makes a decision and before finding out about the outcome,” he says. “But what we see is that the [orbitofrontal cortex] is incredibly active, and in particular processing how much regret the subject experienced on the previous decision.”

Scientists have long known the prefrontal cortex is involved in complex decision-making. An early clue was the case of Phineas Gage, a 19th-century railroad foreman who, in some accounts, become wildly impulsive after an explosion drove an iron bar through the front of his brain. Hsu thinks the rapid replay of past decisions could explain why the prefrontal cortex is implicated in conditions like depression and addiction, both of which involve a willful neglect of negative consequences, an apathy toward risk.

Washington University School of Medicine in Saint Louis neuroscientist Camillo Padoa-Schioppa, who did not take part in either new study, comments, “Many monkey studies, including work from my lab, have found that decision computations [involve] the orbitofrontal cortex.” The fact this study showed the same thing in humans, he notes, is an important step toward understanding our own decision-making process.

As researchers like Hsu and Stuphorn gradually unravel the neurocircuitry of risk and reward, perhaps we will one day see better treatments for such conditions, most likely behavioral interventions or brain-stimulating technologies.

We may also see treatments that quell the thrill and compulsion of problem gambling and other risky behaviors and encourage a bit more fiscal prudence. If so, perhaps those at risk of draining their bank accounts on the Vegas Strip will find themselves cashing in their chips, not squandering them.

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Expressing gambling-related cognitive biases in motor behaviour: rolling dice to win prizes

Affiliation.

• 1 Department of Psychiatry, Warneford Hospital, University of Oxford, Oxford, OX3 7JX, UK.
• PMID: 23620161
• DOI: 10.1007/s10899-013-9381-x

Cognitive perspectives on gambling propose that biased thinking plays a significant role in sustaining gambling participation and, in vulnerable individuals, gambling problems. One prominent set of cognitive biases include illusions of control involving beliefs that it is possible to influence random gaming events. Sociologists have reported that (some) gamblers believe that it is possible to throw dice in different ways to achieve gaming outcomes (e.g., 'dice-setting' in craps). However, experimental demonstrations of these phenomena are lacking. Here, we asked regular gamblers to roll a computer-simulated, but fair, 6 sided die for monetary prizes. Gamblers allowed the die to roll for longer when attempting to win higher value bets, and when attempting to hit high winning numbers. This behaviour was exaggerated in gamblers motivated to keep gambling following the experience of almost-winning in gambling games. These results suggest that gambling cognitive biases find expression in the motor behaviour of rolling dice for monetary prizes, possibly reflecting embodied substrates.

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How gambling affects the brain and who is most vulnerable to addiction

Once confined mostly to casinos concentrated in Las Vegas and Atlantic City, access to gambling has expanded dramatically, including among children

Vol. 54 No. 5 Print version: page 62

• Personality
• Video Games

It has never been easier to place a bet. Once confined mostly to casinos concentrated in Las Vegas and Atlantic City, gambling has expanded to include ready access to lotteries and online games and video games with gambling elements for adults and children.

Sports betting is now legal in 37 states plus Washington, DC, with six more considering legislation, according to American Gaming Association data from early 2023. People can gamble around the clock from anywhere and, increasingly, at many ages, including teenagers and even young children who are well below the legal age for gambling.

As access to gambling has expanded, psychologists and other experts have become concerned not just that more people will give it a try, but that more will develop gambling problems. And while it is still too soon to know what the long-term effects will be, evidence is growing to suggest that young people, especially boys and men, are among those particularly vulnerable to gambling addiction—the same demographic most often participating in the newest forms of gambling: sports betting and video game-based gambling.

People in their early 20s are the fastest-growing group of gamblers, according to recent research. And many kids are starting younger than that. Nearly two-thirds of adolescents, ages 12 to 18, said they had gambled or played gambling-like games in the previous year, according to a 2018 Canadian survey of more than 38,000 youth funded by the government of British Columbia ( Understanding the Odds , McCreary Centre Society, 2021 [PDF, 1.1MB] ). Starting young carries a relatively high burden of psychological distress and increased chances of developing problems.

Researchers are now working to refine their understanding of the psychological principles that underlie the drive to gamble and the neurological underpinnings of what happens in the brains of gamblers who struggle to stop. Counter to simplistic assumptions about the role that the neurotransmitter dopamine plays in addictions ( Nutt, D. J., et al., Nature Reviews Neuroscience , Vol. 16, No. 5, 2015 ), research is showing variations in the volume and activity of certain areas of the brain related to learning, stress management, and rewards processing that might contribute to problematic gambling.

Understanding what makes certain people vulnerable to developing problems could ultimately lead to better strategies for prevention and treatment, and also elucidate the evolving health impacts of gambling, the consequences of starting young, and even the role that the government should play in addressing those issues.

As it stands, the National Institutes of Health has agencies dedicated to problem alcohol use and drug use, but there are no official efforts aimed at problem gambling, and there are no federal regulations against advertisements for sports betting, said social worker Lia Nower, JD, PhD, director of the Center for Gambling Studies at Rutgers University in New Jersey. That means kids can see ads, often featuring their sports heroes promoting gambling, at any time of day or night. “It’s the wild, wild west with regard to gambling,” Nower said.

Examining the risks

Most adults and adolescents in the United States have placed some type of bet, and most do it without problems. But a significant subset of people who start gambling go on to develop gambling disorder, defined in the Diagnostic and Statistical Manual of Mental Disorders (Fifth Edition) as a persistent, recurrent pattern of gambling that is associated with substantial distress or impairment.

Gambling problems, previously called pathological gambling, were considered an impulse control disorder until 2013, when the DSM-5 classified them as an addictive disorder. That made gambling addiction the first, and so far the only, defined behavioral addiction in the clinical section of DSM-5 (with some hints that video gaming disorder might ultimately follow, experts say). Like addictions to alcohol and drugs, gambling addictions are characterized by an increasing tolerance that requires more gambling as time goes on to feel satisfied. People with the disorder can also experience withdrawal that causes irritability when they try to quit.

Over the last 20 years or so, researchers have refined their understanding of how common gambling addictions are and who is most vulnerable. Among adults, the estimated proportion of people with a problem ranges from 0.4% to 2%, depending on the study and country. Rates rise for people with other addictions and conditions. About 4% of people being treated for substance use also have gambling disorder, as do nearly 7% of psychiatric inpatients and up to 7% of people with Parkinson’s disease. An estimated 96% of people with gambling problems have at least one other psychiatric disorder. Substance use disorders, impulse-control disorders, mood disorders, and anxiety disorders are particularly common among people with gambling problems ( Potenza, M. N., et al., Nature Reviews Disease Primers , Vol. 5, No. 51, 2019 ).

Vulnerability is high in people with low incomes who have more to gain with a big win, added psychologist Shane Kraus, PhD, director of the Behavioral Addictions Lab at the University of Nevada, Las Vegas. Young people, especially boys and men, are another susceptible group. Up to 5% of adolescents and young adults who gamble develop a disorder. And men outnumber women at a ratio of about 2 to 1 among people with gambling addictions, although there are a growing number of women with the disorder.

Despite concerns, scientists have yet to document a consistent rise in the rates of gambling problems in recent years, said Jeffrey Derevensky, PhD, a psychologist and director of the International Centre for Youth Gambling Problems and High-Risk Behaviours at McGill University. Still, because more people now have access to gambling, evidence suggests that overall numbers of problems appear to have risen, Derevensky said. After Ohio legalized sports betting, for example, the number of daily calls to the state’s gambling helpline rose from 20 to 48, according to the Ohio Casino Control Commission. Other states have reported similar trends.

As evidence accumulates, it is important to examine the risks without overreacting before the data are in, said Marc Potenza, PhD, MD, director of Yale University’s Center of Excellence in Gambling Research. When casinos enter a region, he said, the area may experience a transient bump in gambling problems followed by a return to normal. Given how quickly gambling is evolving with digital technologies, only time will tell what their impact will be. “We don’t want to be overly sensationalistic, but we do wish to be proactive in understanding and addressing possible consequences of legalized gambling expansion,” he said.

From gaming to gambling

After years of studying the psychological effects of video game violence, psychologist James Sauer, PhD, a senior lecturer at the University of Tasmania in Australia, took notice when Belgium became the first country to ban a feature called loot boxes in video games in 2018. Loot boxes are digital containers that players can buy for a small amount of money. Once purchased, the box might reveal a special skin or weapon that enhances a character’s looks or gives a player a competitive advantage. Or it might be worthless.

On a Skype call after the news broke, Sauer, a psychological scientist and coexecutive director of the International Media Psychology Laboratory, talked with his collaborator, psychological scientist Aaron Drummond, PhD, of Massey University in New Zealand, about Belgium’s decision. Because loot boxes represent a financial risk with an unknown reward, Belgian policymakers had categorized them as a form of gambling, and those policymakers were not the only ones. Countries and states that have passed or considered regulations on loot boxes include Australia, the Netherlands, and Hawaii. But those regulations were contentious.

Sauer and Drummond discussed the need for more science to guide the debate. “We were trying to think about how we might contribute something sensible to a discussion about whether these in-game reward mechanisms should or should not be viewed as a form of gambling,” Sauer said.

To fill the evidence gap, the researchers watched online videos of players opening loot boxes in 22 popular and recently released games that had been rated by the Entertainment Software Ratings Board as appropriate for people ages 17 and younger. Nearly half of the games met the definition for gambling, the researchers reported in 2018, including Madden NFL 18 , Assassin’s Creed Origins , FIFA 18 , and Call of Duty: Infinite Warfare ( Nature Human Behaviour , Vol. 2, 2018 ). Among the criteria for qualifying as gambling was an exchange of real money for valuable goods with an unknown outcome determined at least partly by chance. Purchased objects had value that gave an advantage in the game and sometimes could be sold or traded to others for real money.

Loot boxes tap into the same psychological principles that draw people to slot machines, Sauer said. They may deliver a big payoff, but payoffs come at random intervals. Unlike rewards given after every repetition of a behavior, this type of variable ratio reinforcement, or intermittent reinforcement, exploits a cognitive distortion that makes a player or gambler view each loss as one step closer to a win and can lead to very rapid adoption of a behavior that can then be hard to extinguish, Sauer said. Animals exhibit the same patterns. “They feel sure that the reward is coming, but they can’t know when, so they keep repeating the behavior,” he said. “They continue even as rewards become less and less frequent and even stop entirely.”

After establishing that loot boxes, which generate billions of dollars in revenue for video game companies, are often in fact a type of gambling, studies by Sauer’s group and others since then have shown that people who spend more on loot boxes are often at higher risk of developing gambling problems, and that the connection is strongest in adolescence. Scientists are now working to untangle the question of whether buying loot boxes can cause gambling addictions, and at least some evidence supports this kind of gateway idea.

In one survey of 1,102 adults in the United Kingdom, about 20% of gamblers said that loot boxes were their first introduction to gambling and that their experiences with the game rewards made them think that other forms of gambling could be fun, according to a 2022 study ( Spicer, S. G., et al., Addictive Behaviors , Vol. 131, No. 107327, 2022 ). More than 80% of them had started buying loot boxes before they were 18. More recently, Canadian researchers surveyed hundreds of young adult video gamers at two time points, 6 months apart. Among those who were not gamblers when the study started, dozens went on to gamble over the course of the study, they reported in 2023, suggesting that loot boxes had opened the gambling floodgates ( Brooks, G. A., & Clark, L., Computers in Human Behavior , Vol. 141, No. 107605, 2023 ).

But the relationship can also go the other way. People who already gambled, the Canadian researchers found, spent more on loot boxes. And in the U.K. research, about 20% of people who started out with other types of gambling migrated to loot boxes—the same proportion that went in the other direction. Figuring out how loot boxes and gambling behavior influence each other remains a work in progress. “We just don’t have the data yet to understand the long-term consequences,” Sauer said.

Also contentious is the question of how loot boxes affect mental health. Sauer’s group has found a link between spending on loot boxes and severe psychological distress ( Scientific Reports , Vol. 12, No. 16128, 2022 ), while other research has failed to find the same association. Because kids are increasingly being exposed to gambling, it is an important question to sort through. “Some researchers have argued,” Sauer said, “that if we don’t want kids engaging with bona fide gambling behaviors, maybe we want to be wary about kids engaging with these...gambling-like reward mechanisms.”

Early exposure

Loot boxes are not the only avenue to gambling for kids. Online games that simulate gambling without financial risk are often available to very young children, said Derevensky, who once watched a young girl play a slot machine game on a tablet installed in an airport waiting area. She was earning points, not real money, and loving it. “She’s winning, and she’s saying to her dad, ‘I can’t wait until I play it for real,’” he said. “She must’ve been no more than 6 years old.”

By adolescence, about 40% of people have played simulated gambling games, studies show. These games often involve more winning than their real-world equivalents, Derevensky said. And that playful introduction without financial stakes can spark an interest. Work by his group and others has shown that teens who play simulated gambling games for points are at higher risk of having gambling problems later on ( Hing, N., et al., International Journal of Environmental Research and Public Health , Vol. 19, No. 17, 2022 ).

Seeing parents, siblings, or other members of the household gamble also normalizes gambling for kids, making them more likely to engage in gambling and other risky behaviors, including alcohol and drug use, Nower has found in her research ( Addictive Behaviors , Vol. 135, No. 107460, 2022 ). And the earlier kids get exposed to gambling through online games and other avenues, studies suggest, the more severe their gambling problems are likely to be later on ( Rahman, A. S., et al., Journal of Psychiatric Research , Vol. 46, No. 5, 2012 ).

“Kids as young as preschool are being bombarded with requests to buy things in video games,” Nower said. “A lot of kids move from betting on loot boxes in video games to playing social casino games that are free and then triage them to pay sites. You can’t really tell gambling from video gaming anymore. There’s so much overlap.”

The brain of a problem gambler

To understand why early exposure makes a difference, and why a subset of people develop gambling addictions, some scientists have been looking to the brain.

Studies have linked gambling disorders to variations in a variety of brain regions, particularly the striatum and prefrontal cortex, which are involved in reward processing, social and emotional problems, stress, and more. Some of these differences may be attributable to genetics. Twin studies and modeling work suggest that genes explain half or more of individual differences with gambling problems, specifically.

In people with gambling disorders as well as substance use disorders, a meta-analysis found that several studies showed less activity in the ventral striatum while anticipating monetary rewards ( Luijten, M., et al., JAMA Psychiatry , Vol. 74, No. 4, 2017 ). Along with other findings, those results suggest that this part of the brain contributes to impulsive behaviors for people with gambling problems.

Among other emerging insights, people with gambling problems also have smaller volumes in their amygdala and hippocampus, two regions related to emotional learning and stress regulation. Brain research might help explain why teenagers are particularly susceptible to gambling, Potenza said, including the observation that different parts of the brain mature at different rates in ways that predispose teenagers to gambling and other risk-taking behaviors. The prefrontal cortex, which regulates impulsivity and decision-making, is particularly late to develop, especially in boys.

Parsing out the details could lead to new treatments, Potenza said. For example, he and colleagues stimulated the prefrontal cortex of people with problematic gaming behavior and found improvements in their ability to regulate cravings and emotions ( European Neuropsychopharmacology , Vol. 36, 2020 ). The U.S. Food and Drug Administration has begun approving neuromodulatory approaches for using targeted brain stimulation to treat psychiatric conditions, including addictions, that could eventually help people with gambling problems, Potenza said.

New strategies for treatment would be welcome, experts say, as gambling is a particularly tricky addiction to treat, in part because it is easy to hide. As many as 90% or more of people with gambling problems never seek help ( Bijker, R., et al., Addiction , Vol. 117, No. 12, 2022 ).

For now, cognitive behavioral therapy is the most common form of treatment for gambling addiction, Nower said, and identifying pathways can tailor therapy to particular needs. She has proposed three main pathways that can lead to gambling problems ( Addiction , Vol. 117, No. 7, 2022 ). For one group of people, habitual gambling pushes them to chase wins until they develop a problem. A second group comes from a history of trauma, abuse, or neglect, and gambling offers an escape from stress, depression, and anxiety. A third group may have antisocial or impulsive personalities with risk-taking behaviors.

Betting on the game

For young adults who have grown up with video games and online gambling games, sports betting is the newest frontier—for both gamblers and researchers interested in understanding the consequences of early exposure to gambling.

Now legal in many states, the activity has exploded in popularity. An estimated 50 million people were expected to bet some $16 billion on the Super Bowl this year, according to the American Gaming Association, more than double the amount wagered the year before. (Official numbers are not yet available and are usually an underestimate because of “off the books” betting, Nower said.) At its peak, according to news reports, the betting platform FanDuel reported taking 50,000 bets per minute. Billions more were expected to be bet on March Madness.

Sports bettors trend young: The fastest-growing group of sports gamblers are between 21 and 24 years old, according to an analysis by Nower’s group of data from New Jersey, which legalized sports gambling in 2018. Compared with other kinds of gambling, the in-game betting offered during sports games is highly dependent on impulsivity, Nower said. There are opportunities to place bets during the game on everything from who will win the coin toss to which quarterback will throw 100 yards first to how long the national anthem will last. And impulsivity is particularly common in younger people and among sports fans caught up in the emotion of a game, Nower said.

Researchers are still collecting data to see if sports betting is causing a true surge in gambling problems, said Kraus, who is working on a longitudinal study of sports bettors that is following about 4,000 people over a year to see who is most likely to go from betting on a game to having problems with gambling. His group just collected their third wave of data and will be writing up a paper on their results in the coming months. “We’re going to be riding on this issue for years,” he said.

Early signs from Nower’s research in New Jersey suggest that people who engage in sports betting appear to develop gambling problems at particularly high rates and are at higher risk for mental health and substance use problems compared with other kinds of gamblers. About 14% of sports bettors reported thoughts of suicide and 10% said they had made a suicide attempt, she and colleagues found in one New Jersey study.

“Risk-takers who like action can get really involved in sports wagering,” Nower said. “Because of gambling on mobile phones and tablets, there’s no real way to keep children from gambling on their parents’, friends’, or siblings’ accounts. And they’re being bombarded with all these advertisements. This is a recipe for problems among a lot of young people.”

It takes time for a gambling problem to develop, and simple steps can interrupt the progression for many people, Kraus said. That might include placing a limit on how much they are going to spend or setting an alarm to remind them how long they have been gambling.

Education before people try gambling would help, Derevensky said, and plenty of prevention programs exist, including interactive video games designed by his group. But kids do not often get access to them. Teachers are not monitoring lunch tables for gambling activity, Nower said. And administrators are not screening for problems. Derevensky recommends that parents talk with kids about loot boxes and other gambling games and explain the powerful psychological phenomena that make them appealing.

“We educate our kids in our school systems about alcohol use, drug use, drinking and driving, and unprotected sex,” Derevensky said. “It’s very difficult to find jurisdictions and school boards that have gambling prevention programs.”

Further reading

Sports betting around the world: A systematic review Etuk, R., et al., Journal of Behavioral Addictions , 2022

The migration between gaming and gambling: Our current knowledge Derevensky, J. L., et al., Pediatric Research and Child Health , 2021

The intergenerational transmission of gambling and other addictive behaviors: Implications of the mediating effects of cross-addiction frequency and problems Nower, L., et al., Addictive Behaviors , 2022

National Problem Gambling Helpline

Gamblers Anonymous

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Rolling the dice: a comprehensive review of the new forms of gambling and psychological clinical recommendations.

1. Introduction

1.1. gambling disorder world prevalence, 1.2. online gambling disorder world prevalence, 1.3. problematic gamblers demographic characteristics, 1.4. government regulations towards online gambling worldwide, 1.5. aim of the study, 2. materials and methods, 2.1. search strategies, 2.2. eligibility criteria, 3.1. characteristics of the included studies, 3.2. gambling disorder, gambling disorder and personality, 3.3. internet gaming disorder, 3.4. gambling disorder, internet gaming disorder, and online gambling disorder, 3.5. online gambling, 3.5.1. childhood and adolescence, 3.5.2. young adulthood, 3.5.3. adults, 3.5.4. late-life, 3.6. mobile gaming and loot boxes, loot boxes in adolescence and young adulthood, 3.7. social media gambling: twitch.tv, 3.7.1. demographic characteristics of twitch users, 3.7.2. relationship between content creator and viewer, 3.7.3. the “slotstreams”, 3.7.4. online gambling and slotstream viewing, 3.8. electronic gaming machines, race betting, and sports betting, 3.9. psychological clinical recommendations to diagnose and treat problem gambling.

• Screen for problem gambling using validated tools such as the Problem Gambling Severity Index (PGSI) and the Online Gambling Disorder Questionnaire (OGD-Q). These tools can help identify individuals who may require further assessment and interventions [ 87 ].
• Consider online self-directed interventions as a potential treatment option for problem gambling. These interventions have been shown to be effective in reducing gambling severity and increasing treatment-seeking behavior [ 88 ].
• Examine online psychological interventions as a potential solution for addressing problem gambling and gambling disorder. Meta-analytic evidence suggests that such interventions can lead to a significant reduction in gambling severity and psychological distress [ 89 ].
• Assess for comorbid mental health conditions, as problem gambling is often associated with depression and anxiety [ 85 ].
• Address risk factors associated with specific gambling activities. For example, sports betting has been associated with higher levels of problem gambling in men, while electronic gaming machines are associated with higher levels of problem gambling in women [ 86 ].
• Consider incorporating quality-of-life assessments into treatment plans, as problem gambling can have a negative impact on an individual’s quality of life [ 90 ].

4. Discussion

4.1. previous research, 4.2. limitations, 5. conclusions, supplementary materials, author contributions, institutional review board statement, informed consent statement, data availability statement, conflicts of interest.

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Casu, M.; Belfiore, C.I.; Caponnetto, P. Rolling the Dice: A Comprehensive Review of the New Forms of Gambling and Psychological Clinical Recommendations. Psychiatry Int. 2023 , 4 , 105-125. https://doi.org/10.3390/psychiatryint4020014

Casu M, Belfiore CI, Caponnetto P. Rolling the Dice: A Comprehensive Review of the New Forms of Gambling and Psychological Clinical Recommendations. Psychiatry International . 2023; 4(2):105-125. https://doi.org/10.3390/psychiatryint4020014

Casu, Mirko, Cecilia Ilaria Belfiore, and Pasquale Caponnetto. 2023. "Rolling the Dice: A Comprehensive Review of the New Forms of Gambling and Psychological Clinical Recommendations" Psychiatry International 4, no. 2: 105-125. https://doi.org/10.3390/psychiatryint4020014

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Before putting $20 down on the table, audit your mental health, researchers from the Institute of Behavioral Science suggest.

Gambling activities are more readily available than ever, but the availability could play into potential problem gambling and addiction based off one’s genetics, according to new research from the University of Colorado Boulder. 

In a study published in Addictive Behaviors , the researchers found that individual’s genetics, psychiatric diagnoses and behaviors influence the frequency in which a they gamble, the specific activities they participate in, and the probability that they will develop problems with gambling.

Gambling addiction affects roughly two million people per year and yet much about what causes the addiction to arise is relatively unknown given the complexity of the data. This new research, though, provides some insight on the relationship of genetics and addiction.

"The types of gambling that you do and your current mental health matters, and how much you gamble all depends on whether you develop problematic outcomes from it," Spencer Huggett, (PhDPsych’19), a postdoctoral fellow at Emory University and an author on the paper, said.

“Certain people are more prone to develop problems gambling and/or to engage in certain types of gambling than others,” he said.

Huggett and Evan Winiger (PhDPsych’21), the study’s co-author and a postdoctoral fellow at Anschutz Medical Campus, were roommates as they both pursued their doctorates in behavioral, psychiatric and statistical genetics. Winiger studied cannabis and Huggett, studied cocaine. Through living under the same roof, scientific, technical and philosophical conversations on addiction and genetics ensued. One of these conversations led them to asking questions about gambling and its addictive properties. 

“We hypothesized that there’s going to be some common feature to all types of gambling from playing poker and betting on slot machines to buying lottery tickets and day trading in the stock market. Although we did not think this would fully recapitulate the complexities and nuances across all forms of gambling,”. Huggett said. “We thus set out to study clusters of gambling behavior — particularly those involving an element of ‘skill’ — to investigate and characterize the developmental pathways of gambling behavior.” 

Evan Winiger is the study’s co-author and a postdoctoral fellow at Anschutz Medical Campus researching cannabis and sleep.

To assess these potential phenomena, they utilized the Institute of Behavioral Genetics’ library of complex datasets and pulled the large twin and sibling sets. The sibling sample was selected based on externalizing behaviors, and the twin sample provided a general population overview. They used multi-dimensional statistical techniques on a sample of 2,116 twins and 619 siblings to understand the structure, typology and etiology of gambling frequency.

“This study is a genetically informed evaluation of different gambling profiles,” Winiger said. “There’s some research out there trying to categorize different kinds of gamblers, and our study is kind of another approach showing this might be a different way to look at these different subgroups as well as how certain classes or subgroups might correlate with various mental health or substance use.”

Their study identifies four gambling subtypes distinguished by their gambling behavioral profiles (or how often they gambled). According to the study, the gambling subtypes with the highest rates of psychiatric disorders had approximately two to six times higher rates of problem gambling than those with lower rates of mental illness. Genetics play an important role in the development of gambling behavior, the researchers said, noting that the gambling subtypes with highest rates of problem gambling were strongly predicted by genetic factors. The individual’s mental health, genetic risk plus their gambling behavioral profiles determined whether or not problematic gambling behaviors would arise, the researchers found. 

The study also found that individuals participating in common gambling activities such as betting on slots, playing dice and buying lottery tickets were more likely to lead to problem gambling than gambling with a perceived element of skill gambling such as day trading and playing pool for money.

Huggett and Winiger applied the Pathways Model, an established model within gambling research that determines problem and pathological gamblers, which defines three possible pathways that individuals begin to experience problems with gambling. The three pathways are behaviorally conditioned problem gamblers, emotionally vulnerable problem gamblers, and antisocial impulsivity problem gamblers. 

“What we really wanted to understand was, ‘is there a profile of certain gambling activities that clusters into broader mental health subtypes?’” Huggett said “We did find evidence that this was the case. Certain types of gamblers based off of the activities that they prefer tended to mimic some of these more popular pathways to gambling addiction.” 

In the discussion of the study, the researchers mention that their examination of personality disorders and gambling should be approached with caution due to the wide spectrum of gambling activities and behaviors. This study does, though, supports the connection between genetics to personality disorders and gambling addiction.

“This is an extremely big pie of mental illness and gambling and the thing that we did was the smallest little sliver,” Huggett said. “We wanted to shed light in that pie so we can have a better understanding and hopefully use this information to tailor more proactive approaches and potentially tailored treatment profiles to the individual.”

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• v.365(1538); 2010 Jan 27

Decision-making during gambling: an integration of cognitive and psychobiological approaches

Gambling is a widespread form of entertainment that may afford unique insights into the interaction between cognition and emotion in human decision-making. It is also a behaviour that can become harmful, and potentially addictive, in a minority of individuals. This article considers the status of two dominant approaches to gambling behaviour. The cognitive approach has identified a number of erroneous beliefs held by gamblers, which cause them to over-estimate their chances of winning. The psychobiological approach has examined case-control differences between groups of pathological gamblers and healthy controls, and has identified dysregulation of brain areas linked to reward and emotion, including the ventromedial prefrontal cortex (vmPFC) and striatum, as well as alterations in dopamine neurotransmission. In integrating these two approaches, recent data are discussed that reveal anomalous recruitment of the brain reward system (including the vmPFC and ventral striatum) during two common cognitive distortions in gambling games: the near-miss effect and the effect of personal control. In games of chance, near-misses and the presence of control have no objective influence on the likelihood of winning. These manipulations appear to harness a reward system that evolved to learn skill-oriented behaviours, and by modulating activity in this system, these cognitive distortions may promote continued, and potentially excessive, gambling.

1. Introduction

The term gambling refers to a form of entertainment where a wager, typically a sum of money, is placed on the uncertain prospect of a larger monetary outcome. As a form of recreation, gambling has been widespread for several centuries, and across many cultures ( Raylu & Oei 2004 b ). The 2007 British Gambling Prevalence Survey found that 68 per cent of respondents reported gambling at least once in the past year, and 48 per cent reported gambling on games other than the state lottery ( Wardle et al . 2007 ). To economists and psychologists, the popularity of gambling represents an enduring paradox, as the vast majority of gamblers are well aware of the popular saying ‘the house always wins’. This refers to the fact that gambling odds are carefully arranged to ensure a steady profit for the bookmaker, casino or slot machine; something that can only be achieved at the expense of the gambler. In economic terms, the expected value of gambling is negative, such that an accumulating debt is inevitable over a large number of trials. Thus, the widespread tendency to accept such gambles may provide some useful insights into the mechanisms of human irrationality. However, in addition to the financial considerations, it is probable that gambling is also motivated by cognitive and emotional factors. Unpredictable monetary wins are a potent form of positive reinforcement that strengthen the instrumental response. Gambling is associated with physiological arousal that is manifested in heart rate increases and elevated cortisol levels ( Anderson & Brown 1984 ; Meyer et al . 2004 ). Environmental cues (e.g. flashing lights, the chime of coins) that are associated with this arousal become conditioned stimuli via Pavlovian processes. Gambling may also serve to alleviate unpleasant states of boredom, anxiety or low mood (i.e. negative reinforcement). These emotional learning mechanisms will play a key role in shaping gambling behaviour ( Blaszczynski & Nower 2002 ).

Gambling is also a behaviour that can spiral out of control in some individuals. As gambling becomes excessive, there are observable harms including debt, illegal activity and interpersonal conflict. In its most extreme form, pathological gambling is a recognized psychiatric diagnosis in the Diagnostic and statistical manual , version 4 (text revision) (DSM-IV-TR; American Psychiatric Association 2000 ), with a prevalence of around 1 per cent ( Petry et al . 2005 ). The severity of gambling involvement is thought to lie on a continuum, and the label of ‘problem gambling’ is used to denote the less severe form. The US prevalence of problem gambling is estimated between 1 and 4 per cent ( Shaffer et al . 1999 ; Welte et al . 2002 ).

The current psychiatric system places pathological gambling within the impulse control disorders, a heterogeneous ‘rag-bag’ of conditions that also includes kleptomania (compulsive stealing) and trichotillomania (compulsive hair-pulling). Accumulating data point to a re-alignment of pathological gambling within the addictions ( Potenza 2006 ). The diagnostic criteria themselves were closely modelled on the features of substance dependence, and there is evidence of cravings ( Tavares et al . 2005 ), withdrawal symptoms ( Wray & Dickerson 1981 ) and tolerance ( Griffiths 1993 b ) in severe gamblers. In addition to clinical phenomenology, several other lines of evidence indicate aetiological overlap between problem gambling and drug addiction: there is substantial comorbidity between the conditions ( Petry et al . 2005 ), shared genetic liability ( Slutske et al . 2000 ), and prospective data identify personality traits that predict the development of both problem gambling and substance use disorders ( Vitaro et al . 1999 ; Slutske et al . 2005 ). The critical difference is that problem gambling does not involve the ingestion of a psychoactive substance. Long-term drug administration causes an array of changes in the brain, so that in current users, it is difficult to disentangle the mechanisms by which the addiction developed. As a putative ‘behavioural addiction’, problem gambling may represent a model for studying addiction vulnerability, in brains that are not confounded by the damaging effects of drugs ( Bechara 2003 ).

Research into gambling behaviour can therefore address two broad issues. First, given the general prevalence of this behaviour, what does gambling tell us about the fallibility of decision-making mechanisms in the healthy human brain? Second, from a clinical perspective, how does this common recreational behaviour become dysfunctional? An overarching theory of gambling should be able to explain both its general popularity, and its potential to become pathological. The aim of the present article is to integrate two approaches to gambling behaviour that have gained considerable popularity in recent years, but which are rarely linked and command quite separate research literatures. The cognitive approach emphasizes thought content and a distorted appraisal of control during gambling. The psychobiological approach assumes a disease model of problem gambling, and has sought to identify group differences between pathological gamblers and healthy controls on measures of brain chemistry and brain function. I will provide an overview of the current status of each approach, before reviewing recent findings that suggest a synthesis of the two approaches may be warranted.

2. The cognitive approach

The cognitive formulation of gambling argues that the problem gambler continues to play because they possess distorted beliefs about gambling that cause them to over-estimate their chances of winning ( Ladouceur & Walker 1996 ). Several kinds of erroneous beliefs have been identified ( Toneatto et al . 1997 ; Raylu & Oei 2004 a ), which ultimately give rise to an ‘illusion of control’ where the gambler confuses a game of chance with a game of skill ( Langer 1975 ; Thompson et al . 1998 ). In games where there is some genuine skill involvement, such as blackjack, the gambler comes to believe that skill is excessively influential ( Ladouceur & Walker 1996 ). In believing that they are acquiring the necessary skills to win (or even that such skills exist in principle), the gambler is able to justify continued play.

Much of the evidence for the cognitive approach has used the ‘think aloud’ procedure developed by Gaboury & Ladouceur (1989) . In this paradigm, the gambler is asked to verbalize all thoughts during a brief period of gambling in a naturalistic setting, such as a casino. They are encouraged to speak continuously and to avoid censoring their speech. Their speech output is recorded by the experimenter, and statements are categorized subsequently as accurate (e.g. ‘It's a machine, we have no control over it, it's all luck’) or erroneous (‘I'm getting good at this game. I think I've mastered it’; Ladouceur & Walker 1996 ). In regular gamblers, around 70–80% of strategic statements about the game were erroneous, with similar figures obtained in slot-machine players and roulette players ( Gaboury & Ladouceur 1989 ; Walker 1992 ). High rates of erroneous thoughts were even present in players who were clearly aware that the outcomes were determined by chance, given their responses on a questionnaire administered before and after the gambling session.

While these erroneous thoughts are evident in infrequent and controlled gamblers, one tenet of the cognitive approach is that cognitive distortions are exacerbated in problem gamblers, and are used to justify ongoing excessive play ( Ladouceur & Walker 1996 ). A number of studies support this ( Walker 1992 ; Griffiths 1994 ; Baboushkin et al . 2001 ; Joukhador et al . 2003 ). Using the think-aloud procedure, Griffiths (1994) found that regular (at least once per week) fruit machine players reported more erroneous thoughts than non-regular players (less than once per month). Baboushkin et al . (2001) found that university students classified as probable pathological gamblers on the widely used South Oaks gambling screen (SOGS; Lesieur & Blume 1987 ) reported more erroneous thoughts during computerized games of roulette, blackjack and a slot machine. In addition, a programme of research by Ladouceur et al . (2002) has shown efficacy of a form of cognitive therapy for pathological gambling that aims to correct these erroneous beliefs.

At a psychological level, it is important to understand how these faulty beliefs develop, in both occasional and problem gamblers. There appear to be at least two mechanisms at work. On the one hand, humans are generally poor at processing probability and judging randomness. On the other hand, various features of gambling games directly foster these distorted beliefs. It is widely accepted that humans are highly error-prone at judging probabilities ( Gigerenzer 2002 ). Classic studies from experimental psychology show that people are poor at generating, and recognising, random sequences, such as the outcomes of a series of coin tosses ( Tversky & Kahneman 1971 ; Wagenaar 1972 ). Subjects prefer sequences without long runs of the same outcome, and with balanced overall frequencies of heads and tails. This may arise because subjects fail to appreciate the independence of turns, and expect small samples to be representative of the populations from which they are drawn ( Wagenaar 1988 ). Impaired processing of randomness may give rise to the ‘Gambler's Fallacy’, where the gambler believes that a win is ‘due’ after a series of losses. Cohen (1972; cited in Ladouceur & Walker 1996 ) looked at betting strategies in roulette players as a function of the previous outcome. Players were more likely to bet on black if the previous outcome was red (75%) than if the previous outcome was black (50%). In a study of university students choosing lottery tickets, it was shown that players preferred tickets of apparently random numbers over tickets containing consecutive numbers (14–19), clusters of numbers (e.g. six numbers between 20 and 30), and numbers involving patterns (16–21–26–31–36–41; Hardoon et al . 2001 ). Recent work in sport fans has also looked at winning and losing ‘streaks’, arguing that most people perceive a ‘streak’ on the third consecutive win or loss event ( Carlson & Shu 2007 ).

In addition to these generic difficulties in processing chance, various features of gambling games (referred to as ‘structural characteristics’) promote gambling ( Griffiths 1993 a ), potentially via the promotion of cognitive distortions. As a simple example, slot-machine wins are routinely accompanied by bright flashing lights and loud noises. Wagenaar (1988) suggested that this sensory stimulation fuels an ‘availability heuristic’, where the gambler can more easily recall past wins than past losses. By distorting their memory of past outcomes, this may bias the decision to continue play. In the next sections, we focus on two further structural characteristics that appear to manipulate the player's perceptions of winning in a particularly profound manner.

(a) Personal control

Personal control refers to the gambler's level of involvement in arranging their gamble. On a game of chance, the gambler is equally likely to win if they arrange their gamble, or if another agent places the gamble for them. For example, in a lottery, one's favourite numbers are as equally likely to win as a ‘lucky dip’ ticket. However, it has been reliably observed across many forms of gambling that players have inflated confidence when they are given the opportunity to arrange the gamble themselves. In a seminal study by Langer (1975) , subjects were invited to buy a lottery ticket, and the experimenter later asked to buy back their ticket. Subjects who were initially able to choose their ticket from a bag demanded more money ($9) to exchange compared with a group who were allocated a ticket at random ($2). In a follow-up experiment, subjects who had chosen their ticket were more likely to refuse a swap for a ticket in a second lottery with a higher chance of winning. This illustrates how perceived control can actually cause subjects to reject a genuine opportunity to increase their chances of winning.

Similar findings have been reported in craps and roulette. In craps, gamblers play in a team where they take turns to throw the dice (‘shooting the dice’) onto the craps table. They can place bets on certain numbers being rolled, on any player's throw including their own. Regular craps players display a range of superstitious behaviours when throwing the dice, such as blowing on the dice, and using more force in their hand movements when trying to throw a high number ( Henslin 1967 ). Consistent with an effect of personal control, when it is a player's turn to shoot the dice, they are more likely to place a bet, place higher bets, and place more risky bets compared with when other players are shooting ( Davis et al . 2000 ). Similarly, a study of roulette players found that higher bets were placed when the player was given the opportunity to throw the roulette ball, compared with trials where the experimenter acted as a croupier and threw the ball ( Ladouceur & Mayrand 1987 ). In each of these examples, the presence of personal control has no effect whatsoever on the likelihood of winning.

(b) The near-miss effect

Near-misses occur when an unsuccessful outcome is proximal to a win. They occur across all forms of gambling, such as when a slot-machine payline displays two cherries with the third cherry just coming into view. Near-misses are salient events to the gambler. Reid (1986) found that in student volunteers watching a computerized horse-race, races with a close neck-to-neck finish were rated as ‘better’ than races with a clear winner from early on. Gamblers often interpret near-misses as evidence that they are mastering the game, and in this sense, near-misses appear to foster an illusion of control. As a consequence of the near-misses, the gambler feels that he is ‘not constantly losing but constantly nearly winning’ ( Griffiths 1991 ).

A number of research studies have investigated the behavioural effects of near-miss outcomes on gambling play. In the first study of its kind, Strickland & Grote (1967) used a slot-machine simulation where the three reels stopped sequentially. The reels contained red and green stimuli, and wins were awarded for three reds. One group of subjects played a game where the chances of a red icon appearing on reels 1–3 was 70, 50 and 30 per cent, and hence there was a high likelihood of a near-miss. A second group played the same game but with reels 1 and 3 reversed, so that it was evident early on that the trial was a loss. The actual proportion of wins was matched across the two groups. Subjects in group 1 were seen to play for significantly longer than subjects in group 2. More recent studies have begun to systematically manipulate the frequencies of near-misses. Cote et al . (2003) assigned two groups of subjects to play a slot machine that either delivered no near-misses or a moderate (27%) frequency of near- misses. Subjects in the near-miss condition played significantly more trials on the game. A similar study compared three machines with 15, 30 and 45 per cent frequencies of near-misses, and reported an ‘inverted U’ effect with maximal persistence in the intermediate group ( Kassinove & Schare 2001 ). Clearly, the potency of near-misses is diminished if they are over-represented, rather like ‘crying wolf’.

(c) Summary

The cognitive approach argues that gambling behaviour is maintained by erroneous beliefs and cognitive distortions about the true chances of winning, such that gamblers perceive the expected value of gambling as positive, when in fact, the objective expected value is negative. The approach is not without its critics, who have argued that the think-aloud procedure is overly intrusive, that flippant verbalizations do not necessarily reflect cognitions held with conviction, and that there are only a limited number of ways that subjects can express accurate cognitions about chance and randomness during a period of gambling play ( Dickerson & O'Connor 2006 ). Nevertheless, the cognitive approach has considerable explanatory power: this framework can capably explain the general prevalence of gambling as erroneous cognitions and inaccurate perceptions of randomness are common in infrequent gamblers. The cognitive framework can also explain the process by which gambling becomes pathological as problem gamblers are hypothesized to make more erroneous cognitions (or to have greater conviction in those beliefs, or to be more inclined to use their faulty beliefs to justify continued gambling). There is some evidence for this hypothesis using the think-aloud procedure ( Walker 1992 ; Griffiths 1994 ; Baboushkin et al . 2001 ), although there is minimal work specifically comparing personal control or near-miss effects between problem and non-problem gamblers. In testing these ideas, one complexity is that cognitive distortions in regular gamblers can be highly idiosyncratic ( Delfabbro 2004 ), such that a gambler may view many outcomes as ‘near-misses’ that would appear ‘full-misses’ to a non-gambler.

3. The psychobiological approach

The psychobiological approach attempts to identify differences in aspects of brain function between groups of individuals with and without gambling problems. Studies can be divided into those measuring neurotransmitter function, and those measuring the activity or integrity of different brain areas. The latter approach can be subdivided into neuropsychological studies, which measure brain function indirectly using tasks validated in patients with brain injury, and functional imaging studies, which measure brain activity directly during task performance, typically with functional magnetic resonance imaging (fMRI).

(a) Neurochemical studies

Studies of neurotransmitter function in gamblers have focussed on the monoamines, dopamine, serotonin and noradrenaline, which are known to play key roles in arousal, motivation and higher cognitive functions (see Robbins 2000 for a review). It is difficult to measure neurotransmitter levels directly in the human brain. Instead, a number of studies have measured peripheral markers in urine, plasma or cerebrospinal fluid (CSF). These studies reported increases in markers of noradrenaline function ( Roy et al . 1988 ; Bergh et al . 1997 ), reductions in markers of serotonin function ( Nordin & Eklundh 1999 ) and alterations in dopamine function ( Bergh et al . 1997 ; Meyer et al . 2004 ). The study by Bergh et al . (1997) reported a decrease in CSF dopamine, coupled with increased levels of the dopamine metabolite, homovanillic acid, from CSF samples obtained in the clinic. The study by Meyer et al . (2004) measured dopamine and noradrenaline levels in plasma during a period of casino gambling in problem and non-problem gamblers. Problem gamblers showed greater increases in both noradrenaline and dopamine levels during casino gambling for real money, compared with a laboratory gambling session for points reward. Thus, the direction of effect—for dopamine changes in particular—remains unclear, and findings from peripheral markers must be treated with caution as their relationship with central activity is complex.

Another indirect approach has been to study genetic variants that are thought to affect neurotransmitter function. For example, the dopamine D2 receptor gene displays a common polymorphism (TaqIA, occurring in A1 and A2 alleles) that influences D2 receptor density in the brain, and is linked to the prevalence of alcohol and stimulant addictions ( Noble 2000 ). Studies by Comings et al . ( 1996 , 1999 ) reported changes in DRD2 and DRD4 polymorphism frequencies in groups of pathological gamblers, compared with the age, gender and race-matched non-gamblers. The reported TaqIA association (increased prevalence of the A1 allele) is consistent with reduced D2 receptor binding in the striatum in pathological gamblers ( Pohjalainen et al . 1998 ). Genetic studies have also indicated effects on other genotypes affecting serotonin and noradrenaline function ( Comings et al . 2001 ). However, this field has been plagued by failures of replication, and a recent study in siblings discordant for pathological gambling (140 pairs) indicated a significant association with the DRD1 gene but failed to support the DRD2 association ( da Silva Lobo et al . 2007 ).

At least two other lines of evidence converge on the finding that dopamine transmission is altered in problem gambling. A number of case reports have described impulse control disorders, including problem gambling, in patients with Parkinson's disease, where the primary neuropathology is degeneration of the dopamine system. The emergence of these impulse control disorders appears to be linked to treatment with dopamine agonist medications ( Weintraub et al . 2006 ), and in particular, to two drugs, pramipexole and ropinirole, that have a relatively high affinity for the dopamine D3 receptor ( Dodd et al . 2005 ). The emergence of pathological gambling has been linked to earlier age of onset of the Parkinson's Disease, comorbid or familial alcoholism, and elevated trait impulsivity and sensation-seeking scores ( Voon et al . 2007 ). However, it is unclear how the primary pathology in Parkinson's Disease interacts with the action of the medication.

Second, studies by Zack & Poulos (2004 , 2007 ) have looked at the effects of dopamine challenge in problem gamblers, on aspects of gambling behaviour. Their first experiment used amphetamine, an indirect dopamine agonist that also increases noradrenaline transmission. Amphetamine increased motivation to gamble and facilitated the reading of gambling-relevant words in problem gamblers. Their follow-up study used the more selective dopamine D2 receptor antagonist haloperidol, but unexpectedly reported similar effects to amphetamine: haloperidol increased motivation to gamble and primed gambling-relevant words as well as increasing heart rate responses during a period of slot-machine play. While this study supports the role of the dopamine D2 receptor in gambling behaviour, the direction of effect is problematic from a treatment perspective, as both an indirect agonist (amphetamine) and a selective antagonist (haloperidol) increased gambling tendencies. It is possible that low doses of a dopamine receptor antagonist act preferentially on presynaptic autoreceptors to increase dopamine function ( Moghaddam & Bunney 1990 ; Frank & O'Reilly 2006 ), and that higher doses of the antagonist would be needed to reduce dopamine transmission.

In summary, neurochemical studies of problem gambling have taken a number of indirect approaches to the measurement of neurotransmitter function. There are preliminary indications of changes in serotonin and noradrenaline function (see also Potenza 2008 ), and indeed, much reason to think that other transmitters like glutamate may be dysregulated ( Grant et al . 2007 ). The most consistent finding at the current time is for dysregulation of dopamine function in problem gamblers, although the direction and precise mechanisms of this effect remain unclear.

(b) Neuropsychological studies

In a comprehensive review of studies that used clinical neuropsychological tests, Goudriaan et al . (2004) concluded that there was little evidence for impairment in language, perception, intellectual function, and memory in problem gamblers. In contrast, several studies have detected impairments on traditional tests of frontal lobe function; namely, the Wisconsin card sort test, which requires the subject to perform abstract rule shifts, and the Stroop test, which requires the subject to override the automatic tendency to read colour words in order to name the colour of the ink that the word is printed in ( Goudriaan et al . 2006 a ; Kalechstein et al . 2007 ; Forbush et al . 2008 ; Marazziti et al . 2008 ). At an anatomical level, these tasks are reasonably coarse, and performance on the Wisconsin card sort test may also be disrupted by posterior cortical lesions ( Anderson et al . 1991 ). Neuropsychological probes that are more selectively associated with the dorsal aspects of the prefrontal cortex, like self-ordered (strategic) working memory tests, are not reliably disrupted in problem gamblers ( Goudriaan et al . 2006 a ; Leiserson & Pihl 2007 ; Lawrence et al . 2009 ). Pathophysiology in the dorsal frontal region may only be present in the most severe pathological gamblers, such as Blaszczynski & Nower (2002) ‘antisocial impulsive’ gamblers.

Neuropsychological measures of impulsive or risky decision-making have revealed more consistent deficits, resembling the effects seen in patients with damage to the ventromedial prefrontal cortex (vmPFC), who often display real-life difficulties with financial decision-making. This syndrome was initially measured using the Iowa gambling task (IGT; Bechara et al . 1994 ), where subjects make a series of card choices from four decks (A, B, C, D) that win and lose sums of hypothetical money. Unbeknownst to the subject, decks A and B are ‘risky’, associated with large wins but larger losses that incur gradual debt. Decks C and D are safe decks that yield smaller wins but with negligible losses. While healthy subjects develop a preference for the safe decks over 100 trials, patients with vmPFC damage maintain a preference for the risky decks, accumulating considerable debt. Similar performance has been reported in at least five studies of pathological gamblers to date ( Petry 2001 b ; Cavedini et al . 2002 ; Goudriaan et al . 2006 a ; Forbush et al . 2008 ; Roca et al . 2008 ).

These findings have been corroborated using other tasks of risky decision-making ( Brand et al . 2005 ; Lawrence et al . 2009 ) and delay discounting ( Petry 2001 a ), which are also linked to vmPFC integrity ( Mobini et al . 2002 ; Clark et al . 2008 ). The studies by Cavedini et al . (2002) and Lawrence et al . (2009) report impairment in risky decision-making in problem gamblers in the presence of intact executive ability (on the Wisconsin card sort test and spatial working memory, respectively), supporting the assertion that vmPFC pathophysiology is a more consistent marker in problem gambling. There is a concern that gamblers’ performance on these tasks of risk-taking and decision-making may be distorted by their extensive experience with monetary rewards, judging probabilities, and by their erroneous cognitions related to gambling. This would compromise a strict neuropsychological account of their deficits in terms of underlying brain dysfunction. However, these concerns are mitigated in studies showing comparable neurocognitive effects across problem gamblers and substance addictions ( Petry 2001 a ; Lawrence et al . 2009 ; notably, patients with alcohol dependence were also impaired on tests of working memory function that were spared in the problem gamblers ( Lawrence et al . 2009 )). Nonetheless, there is a real need for studies looking at the impact of cognitive distortions upon these simplified neuropsychological tests of gambling behaviour, and to corroborate findings with psychophysiological measures of emotion and motivation, such as skin conductance responses ( Goudriaan et al . 2006 b ).

(c) Functional neuroimaging studies

In recent years, several studies have compared brain responses in groups of problem gamblers and healthy controls during various cognitive tasks. In the first studies of their kind, Potenza and colleagues scanned male pathological gamblers and male healthy controls during performance of the Stroop colour–word interference task ( Potenza et al . 2003 a ) and during presentation of videos of an actor-narrated gambling scenario ( Potenza et al . 2003 b ). This latter ‘cue-induction’ procedure reliably elicits cravings in drug users. In both studies, the gamblers displayed decreased activation in the vmPFC region compared with the controls. In the cue-induction study, the PG group showed additional decreases in the striatum and thalamus. This diminished neural response to cue-induction might be considered surprising, given the elevated subjective reports of craving in these subjects. A subsequent cue-induction study comparing casino videos against nature videos found increases in brain activity in pathological gamblers, in several regions including the right dorsolateral PFC ( Crockford et al . 2005 ). Differences in the exact cue-induction procedure or patient characteristics may underlie these discrepancies.

Blunted activity in the vmPFC and striatum has been reported in subsequent studies. Reuter et al . (2005) compared brain activity during a card-guessing task in male pathological gamblers and healthy controls. The contrast of monetary wins minus monetary losses revealed a robust response (detectable at the single-subject level) in the ventral striatum and vmPFC. This response was attenuated in the gamblers, and these reductions were significantly correlated with SOGS gambling severity. The authors interpret their finding as consistent with a ‘reward deficiency’ hypothesis that has been applied to drug addiction ( Bowirrat & Oscar-Berman 2005 ): gamblers may be motivated to gamble to stimulate a developmentally underactive brain reward system. This kind of hypothesis assumes that the monetary wins are reinforcing in pathological gambling, and a positron emission tomography study in seven pathological gamblers confirmed increases in striatal glucose metabolism following blackjack play for real money compared with scans performed after a blackjack session for points only ( Hollander et al . 2005 ). Unfortunately, this study did not include a healthy control group for comparison. Reduced vmPFC activity was also reported in a study of substance-dependent problem gamblers as well as in substance-dependent non-gamblers, performing the IGT in the scanner ( Tanabe et al . 2007 ). Pathological gamblers also showed diminished activity in the lateral sector of the ventral PFC, in response to both monetary wins and losses in a reversal learning task, in a recent study by de Ruiter et al . (2009) .

Thus, there is some consistency in the observation of blunted ventral frontal cortex and striatal activation, across tasks of reward processing and decision-making (see also Potenza 2008 ). However, these findings must be treated as preliminary due to the small sample sizes, ranging from seven gamblers in the Hollander et al . (2005) study, to 19 in the de Ruiter et al . (2009) study. Further targets for research in this area also represent issues for the neurochemical and neuropsychological studies. First, the psychobiological approach has predominantly used the case-control design to compare groups of severe pathological gamblers against healthy non-gamblers, but there is a large spectrum of gambling involvement (and gambling harm) that lies between these two groups, and it is necessary to systematically assess the impact of gambling severity on markers of brain function. Second, there has been minimal consideration of sources of variability such as gender, psychiatric comorbidities, or preferred forms of gambling. For example, motivations to gamble may differ between players of different games: casino and sports betting gamblers may be driven predominantly by the excitement of gambling (i.e. positive reinforcement) whereas slot-machine gamblers may play to alleviate negative mood states such as boredom, stress or depression (i.e. negative reinforcement; Cocco et al . 1995 ). These differences are likely to moderate the neural correlates of reinforcement processing in problem gamblers.

4. Anomalous recruitment of the brain reward system during cognitive distortions

The cognitive and psychobiological accounts are rarely linked in the research literature, partly because of some key differences in approach and methodology. Cognitive studies of gambling frequently use non-gamblers or infrequent players (often university students), and place considerable emphasis on testing in naturalistic settings (e.g. a casino). In contrast, the psychobiological studies derive from a medical model of problem gambling, and have compared pathological gamblers who are typically in treatment, against healthy non-gamblers. In neuropsychological and functional imaging studies, the testing procedures are inherently laboratory based, and some studies have called into question the ecological validity of laboratory gambling, particularly where hypothetical points are involved instead of real money ( Anderson & Brown 1984 ; Meyer et al . 2004 ). Nevertheless, the two approaches are not mutually exclusive: cognitive distortions must be instantiated at the neural level, and individual differences in brain function or neurochemistry may plausibly influence one's susceptibility to developing erroneous beliefs about gambling.

In linking the two positions, let us start by considering the role of money. At a psychological level, money is a potent reward. More precisely, money is a conditioned reinforcer, meaning that it is not innately rewarding, but that its value is acquired through extensive pairing with primary rewards and through vicarious, cultural learning. Neurobiological findings indicate the existence of a specialized brain reward system that processes reinforcers and uses reinforcement to guide future decision-making (‘reinforcement learning’). At an anatomical level, fMRI studies demonstrate the central roles of the ventral striatum and the mPFC in this brain reward system; these regions are activated by monetary wins ( Delgado et al . 2000 ; Breiter et al . 2001 ; Knutson et al . 2003 ) as well as primary rewards like fruit juice ( Berns et al . 2001 ) or chocolate ( Rolls & McCabe 2007 ).

At a neurochemical level, the mesolimbic dopamine projection from the midbrain to the striatum and PFC is also central to neurobiological accounts of reward processing ( Wise 2004 ). A dominant hypothesis is that dopamine cells code a reward prediction error: the difference between the obtained and the expected reward ( Schultz 2002 ; Montague et al . 2004 ). Electrophysiological recording from non-human primates has shown phasic bursts of dopamine cell activity in response to unexpected rewards (a positive prediction error). As the monkey learns to associate a conditioned stimulus (CS; e.g. a light) with later reward delivery, dopamine firing shifts to the onset of the CS, and disappears at the time of reward itself; as the reward is now predicted, the prediction error is minimal. Subsequently, if the CS is presented but the expected reward then withheld, the dopamine cells show a pause in firing at the expected time of reward delivery (i.e. a negative prediction error). These observations have fuelled sophisticated computational models of reinforcement learning and decision-making based on the calculation of prediction errors (e.g. McClure et al . 2003 ; Daw et al . 2006 ).

Real-world tasks such as gambling games are more complex than the Pavlovian and instrumental conditioning tasks performed by experimental animals. Recent work has begun to indicate that activity within the brain reward system is modulated by some of the psychological manipulations that affect gambling behaviour. Our own work has focussed on the near-miss effect, using a gambling task based on a two-reel slot machine (see figure 1 ; Clark et al . 2009 ). The right-hand reel is spun so that the volunteer can either win £0.50p (if the two reels align) or not win anything; there are no losses in the task. In a study in 15 healthy volunteers with minimal involvement in gambling, the fMRI contrast of wins minus non-wins identified brain responses across established parts of the brain reward system, including the ventral striatum, medial PFC, anterior insula, thalamus and the dopaminergic midbrain (see figure 2 a (i),(ii)).

The slot-machine task uses two-reels, with the same six icons displayed on each reel, and a horizontal ‘payline’ across the centre of the screen. On trials with a white screen background, the volunteer selects one ‘play icon’ on the left reel, using two buttons to scroll through the icons, and one button to select. On trials with a black screen background, the computer selects the play icon. Following icon selection, the right-hand reel spins for a variable duration (2.8–6 s), and decelerates to a standstill. During outcome (4 s), if the right reel stopped on the selected icon (i.e. matching icons displayed in the payline), the subject was awarded £0.50; all other outcomes won nothing. Following the outcome phase, there was an inter-trial interval of variable duration (2–7 s). In the fMRI version of the task, two ratings were taken on intermittent (1/3) trials: following selection, subjects were asked ‘How do you rate your chances of winning?’, and following outcome, subjects were asked ‘How much do you want to continue to play the game?’. Reprinted from Clark et al . (2009) .

Coronal sections through the brain showing ( a (i)(ii)) the contrast of monetary wins minus non-win outcomes, at y = 4 (ventral striatum) and y = 34 (medial prefrontal cortex), thresholded at p < 0.05 corrected with family-wise error. ( b ) The contrast of near-miss outcomes minus full-miss outcomes, within regions sensitive to monetary wins, at y = 4 (ventral striatum; thresholded at t = 3.0 to better display extent of activation). ( c ) the interaction between near-miss outcomes (i.e. near-misses minus full-misses) and personal control (participant-chosen trials minus computer-chosen trials), within regions sensitive to monetary wins, at y = 34 (medial prefrontal cortex; thresholded at t = 3.0 to better display extent of activation). Data redrawn from Clark et al . (2009) .

Critically, the non-win outcomes could be further distinguished as ‘near-misses’ (where the reel stopped one position either side of the payline) and ‘full-misses’ (where the reel stopped more than one position away from the payline). Within the network of win-sensitive areas, the direct contrast of near-misses and full-misses revealed significant and bilateral activation of the ventral striatum and anterior insula by near-miss outcomes (see figure 2 b ). Thus, although the objective outcomes were identical on these trial types (i.e. both non-wins), the brain responded to the near-misses in a way that was comparable to the response to a monetary win. This ‘anomalous’ activation may underlie the invigorating effects of near-miss outcomes on gambling play in the studies discussed above by Cote et al . (2003) and Kassinove & Schare (2001) .

The slot-machine task was also designed to elicit a second cognitive distortion, of personal control: on half the trials, the subject was required to choose one of six icons on the left-hand reel as a ‘play icon’. The subject won if the right-hand reel stopped on that chosen icon. On the remaining trials, the computer chose the play icon and the subjects made a motor response to confirm selection. Ratings data taken on a trial-by-trial basis revealed greater confidence (‘How do you rate your chances of winning?’) on subject-chosen trials compared with computer-chosen trials, consistent with an illusion of control.

Similar manipulations of personal control have been studied in previous neuroimaging experiments, and show a modulation of brain activity at the level of the dorsal striatum and medial PFC ( O'Doherty et al . 2004 ; Tricomi et al . 2004 ; Walton et al . 2004 ; Yeung et al . 2005 ). Notably, the ventral striatum appears to respond to reward regardless of the level of control ( O'Doherty et al . 2004 ). The experiment by Tricomi et al . (2004) used an oddball task, where in one condition, monetary wins and losses were delivered at a fixed delay after a predictive stimulus. In the second condition, the volunteer was told that a choice response (left or right) would influence whether they won or lost money (in fact, the outcomes were fixed). The dorsal striatum was selectively activated by monetary wins under the choice condition. The study by Yeung et al . (2005) measured event-related potentials during a similar task, and reported greater feedback negativities, which are thought to derive from a medial frontal locus, when outcomes appeared contingent upon the volunteer's choices, compared with when outcomes required no active choice (see also Walton et al . 2004 ).

In our fMRI study of the slot-machine task, we were unable to detect any differences between monetary wins arising from participant-chosen versus computer-chosen gambles. However, there was a significant interaction between the manipulation of personal control and the near-miss effect, in the medial PFC (specifically, in the rostral anterior cingulate cortex; see figure 2 c ). A similar interaction was evident in behavioural data from a larger group of university students ( n = 40): on participant-chosen trials, near-misses increased ratings of ‘How much do you want to continue to play the game?’ compared with full-misses. On computer-chosen trials, the opposite effect was observed. Why would near-misses be more potent in situations where personal control is present? Presumably, our volunteers appraised the near-misses as evidence that they were mastering the game; such appraisals of skill acquisition would be more likely on trials with direct control over gamble selection. The observation of this same interaction in the medial PFC response implicates this region in appraising illusory control. The differential roles of the medial PFC and dorsal striatum in these experiments remain unclear, but one possibility is that medial PFC is preferentially recruited when the task appears to require the identification of higher-order structure ( Hampton et al . 2006 ), such as identifying stimuli that are more likely to win in future. The dorsal striatum may signal lower-order associations of motor responses and outcomes.

The dorsal striatum is also known to be involved in the formation of habits, and this role has generated considerable interest in the context of drug addiction. For example, studies in experimental animals have given rise to the hypothesis that the neural regulation of drug taking progresses from the ventral striatum to the dorsal striatum as the initial recreational consumption of drugs (e.g. for their hedonic effects) develops into habitual and compulsive usage ( Everitt & Robbins 2005 ). As supporting evidence for this role of the dorsal striatum in drug addiction, rodent studies have shown that inactivation of the dorsolateral striatum (by infusion of gamma-aminobutyric acid agonists) prevented context-induced reinstatement of cocaine seeking in withdrawn animals ( Fuchs et al . 2006 ). Changes in dopamine function in the dorsal striatum are observed after chronic, but not acute, cocaine self-administration ( Porrino et al . 2004 ). Whether this progression would also occur in a form of ‘behavioural addiction’ like problem gambling, where there is no drug involved, is unknown. As such, processes of habit formation and dorsal striatal function in problem gamblers represent an important target for future research that may answer broader questions of relevance to drug addiction.

The neuroimaging findings reviewed above suggest that gambling games harness a brain reward system that has evolved to learn about skill-oriented behaviours: situations where response feedback can be used either to improve the precision of the motor response itself, or to improve the prediction of future outcomes. This system often responds inappropriately under conditions of chance. Using the example of the near-miss, in many real-world situations such as target practice or getting to the railway station two minutes late, it is advantageous for the brain to assign value to near-miss outcomes, as they are a valid and useful signal of future success. However, in gambling games, where winning outcomes are largely or purely determined by chance, near-misses provide no information on future success, and it is misleading for the brain to assign them value. Similarly, in the case of personal control, it is obviously adaptive for the brain to learn how to control its environment, and specialized and sophisticated processes have evolved to identify rewards that occur contingently upon behaviour. However, the random nature of gambling games means that the availability of personal control has no actual bearing on the likelihood of a win occurring.

These data showing modulation of striatal and medial PFC activity by near-misses and personal control are from studies in healthy volunteers, who had low levels of gambling involvement. The findings therefore suggest that the brain reward system is naturally susceptible to these cognitive distortions associated with gambling. Nonetheless, the neuropsychological and functional imaging data described in the previous sections indicate substantial changes in the functionality of this system in problem gamblers, along with alterations in dopamine transmission. By the reasoning I have outlined above, the observed reductions in ventral striatum and vmPFC activity ( Potenza et al . 2003 a ; Reuter et al . 2005 ) may be only part of the story. Under conditions of cognitive distortion, it is hypothesized that these regions would be excessively recruited in pathological gamblers. We are testing this prediction in ongoing work.

In conclusion, the data outlined above suggest that two of the better-established cognitive distortions in gambling behaviour, the near-miss effect and the effect of personal control, are associated with anomalous recruitment in components of the brain reward system. The term ‘anomalous’ is justified by the objective status of near-misses as loss events that do not signal future success, and the objective irrelevance of personal control to gambling success on games of chance. This mechanism is unlikely to represent the only interface between the cognitive and psychobiological approaches to gambling, and recent neuroimaging work has highlighted several other possible avenues. For example, there are emerging links between chasing behaviour, which is often viewed as the final common pathway in problem gambling, and impaired recruitment of cortical brain regions involved in conflict monitoring and inhibitory control ( Campbell-Meiklejohn et al . 2008 ; de Ruiter et al . 2008 ). The perception of patterns (or ‘streaks’) within random sequences, fuelling a Gambler's Fallacy, has received little attention in the neuroimaging field, but is also likely to involve interactions between the frontal lobes and the striatum ( Elliott et al . 2000 ). There is a need to develop better tasks to capture these cognitive distortions in the scanner, and it is encouraging that studies in irregular and non-gambler samples seem able to detect variability in these distortions at a neural level ( Campbell-Meiklejohn et al . 2008 ; Clark et al . 2009 ). The longer-term objective here is to understand how this neural circuitry changes in the transition from recreational gambling to problem gambling. In order to achieve this target, there is also an urgent need for longitudinal designs that follow gamblers as they move in and out of problematic levels of gambling involvement.

Acknowledgements

Supported by a project grant from the Economic and Social Research Council and Responsibility in Gambling Trust (RES-164-25-0010, L.C. and T.W. Robbins) and completed within the University of Cambridge Behavioural & Clinical Neuroscience Institute, supported by a consortium award from the Medical Research Council (UK) and the Wellcome Trust. I am grateful to Dr R. Cools for feedback on an earlier version of the manuscript.

One contribution of 12 to a Theme Issue ‘Rationality and emotions’ .

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The Ancient Origins of Dice

Gambling is one of humankind’s oldest activities. Elaborate technologies and customs have emerged around games of chance. Dice in particular have drawn attention from scholars.

Gambling is one of humankind’s oldest activities. Dice in particular have drawn attention from scholars, and a recent study of dice reveals that  truly balanced dice did not really exist until the Renaissance . How pre-Renaissance people viewed their games’ fairness is difficult to say, but dice themselves have a long and fascinating history.

In the pre-colonial Americas, dice were typically just two-sided , painted on each side. According to archaeologists Warren DeBoer and Barbara Voorhies, native people throughout North America and Mesoamerica constructed dice of a wide variety of materials , such as fruit pits, shells, or teeth, or even split reeds or sticks. The typical die was curved on one side and flatter on the other. Six-sided dice came into use later and may have been introduced by Europeans.

Archaeologist H.S. Darlington believed that many American dice games had origins in sacred Aztec rituals . As part of the process of correcting their calendar for things like leap years, priests engaged in a “game of chance” to see if they could summon fire in the body of a sacrificial victim. The sticks used to tally the weeks of the calendar were bundled up and tossed as part of the ritual. Unsurprisingly, the priests rigged the game by making sure the fire would start. The sun symbolism and sticks found in many precolonial American dice games suggest the games may have begun with this ritual.

Given the uneven shapes of many early dice, it is unclear whether or not the games were truly games of chance. Therefore, according to DeBoer, dice playing in the Americas involved not just luck, but a considerable degree of skill to achieve a desirable toss. Some gamblers tried a different tactic; cheating was apparently rampant in some native societies.

Across the Atlantic, Romans in the fort of Richborough, in the UK, apparently did view dice as controlled by chance, and took steps to ensure a fair outcome. To this end, some ancient Romans employed a device called a dice tower . About 7.5 inches tall, made of bone, and inscribed with elaborate designs, the dice tower was a structure enclosing a series of ramps. Dating from the 4th century C.E., the dice were tossed in to the top of the tower. Passage down the ramps was supposed to make the roll fair. Such towers appear in illustrations and mosaics across the Roman world, so they must have been in wide use. But nobody knows if they worked as intended.

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The exact symbolism and fairness of the games may have varied, but high stakes were common. European colonists noted games of chance with large amounts of trade goods, food, housing, or even people, as the pot. Mayans used precious stones or feathers as wagers. Games were raucous affairs. The racket surrounding one such game had a very descriptive word in the Algonquin language, that subsequently entered English: hubbub.

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MINI REVIEW article

How can implementation intentions be used to modify gambling behavior.

• School of Psychology and Therapeutic Studies, Faculty of Social and Health Sciences, Leeds Trinity University, Leeds, United Kingdom

Problem gambling can cause significant harm, yet rates of gambling continue to increase. Many individuals have the motivation to stop gambling but are unable to transfer these positive intentions into successful behavior change. Implementation intentions, which are goal-directed plans linking cues to behavioral responses, can help bridge the gap between intention and many health behaviors. However, despite the strategy demonstrating popularity in the field of health psychology, its use in the area of gambling research has been limited. This mini review illustrates how implementation intentions can be used to facilitate change in gambling behavior. Adopting the strategy could help reduce the number of people with gambling problems.

Introduction

Gambling disorders, problem gambling, and excessive gambling can be detrimental to a person’s health. It can lead to negative consequences such as depression, unemployment, financial distress, relationship problems, and criminal behavior ( Afifi et al., 2016 ; Bond et al., 2016 ; Adolphe et al., 2019 ; Muggleton et al., 2021 ). Problem gambling can co-occur with other behavioral addictions ( Kessler et al., 2008 ; Konkolÿ Thege et al., 2016 ), have considerable impact on close ones ( Goodwin et al., 2017 ), and potentially lead to suicide ideation and behavior ( Wardle and McManus, 2021 ). It is estimated that problem gamblers account for between 0.1 and 5.8% of the population ( Williams et al., 2012 ; Calado and Griffiths, 2016 ).

Problem gambling has been an issue in Western society for decades, though the availability and opportunity to gamble has increased significantly over the past few years ( Abbott, 2020 ). For example, the recent growth in internet and online gambling has had a major impact on the gambling experience ( Gainsbury, 2015 ). Among the many advantages, internet gambling is highly accessible, convenient to users, and can be undertaken anonymously ( Gainsbury et al., 2012 ). There has also been a rapid rise in gambling advertisements with gambling companies offering free bets, enhanced odds, sign up bonuses, and money back guarantees ( Clemens et al., 2017 ; Rawat et al., 2020 ). Due to the availability of gambling and the influence of promotional campaigns, it is predicted that gambling is not going to abate in the future ( Hodgins and Stevens, 2021 ). Thus, there is a need for interventions to successfully intervene on and reduce gambling behavior.

Motivation toward gambling

Understanding and explaining human behavior can be achieved using social cognition theories and models, such as the theory of planned behavior ( Ajzen, 1991 ), the theory of reasoned action ( Fishbein and Ajzen, 1975 ), and social cognitive theory ( Bandura, 1986 ). These approaches identify the mechanisms through which psychological beliefs and determinants influence behavior. As well as understanding behavior, these theories can also inform the development of behavior change interventions. Specifically, the theories can identify the important and modifiable psychological determinants that interventions should target. For illustrative purposes and due to its popularity in the health domain, the theory of planned behavior will be the focus of this paper.

The theory of planned behavior places intention as the proximal determinant of behavior. Intention represents a person’s motivation and willingness to engage in the behavior and is determined by attitude (i.e., behavioral evaluations), subjective norm (i.e., perceived approval of others), and perceived behavioral control (i.e., perceived control over the behavior). A large body of research has attested to the utility of the theory in understanding why people do or do not engage in health promoting or health risk behaviors. The theory has been found to account for between 40 and 45% of the variance in intention and 19–36% of the variance in behavior (e.g., Armitage and Conner, 2001 ; Hagger et al., 2002 ; McEachan et al., 2011 ). Although research applied to gambling has been limited, some studies have used the theory to understand gambling intentions and behavior (e.g., Martin et al., 2010 ; Wu and Tang, 2012 ; St-Pierre et al., 2015 ; St Quinton, 2021 ). Wu and Tang (2012) and Martin et al. (2010) found gambling intentions to be predicted by attitude, subjective norm, and perceived behavioral control. Similarly, St-Pierre et al. (2015) identified intention to be predicted by attitude and perceived behavioral control. In relation to gambling behavior, research has found intention to be a significant predictor ( Wu and Tang, 2012 ; St Quinton, 2021 ).

The intention-behavior gap

The theory of planned behavior has accounted for impressive variance in intention towards health behaviors, including gambling. However, there is a well-known gap between what people intend to do and what actually occurs ( Sheeran and Webb, 2016 ). Experimental evidence has demonstrated that medium-to-large changes in intention results in only small-to-medium changes in behavior ( Webb and Sheeran, 2006 ). The successful enaction of intention often involves overcoming setbacks, not giving in to temptations, and staying on track ( Heckhausen and Gollwitzer, 1987 ; Schwarzer and Luszczynska, 2008 ). In relation to gambling, individuals may have the intention to limit or abstain from the behavior but nevertheless proceed to gamble. Indeed, evidence has shown that a large proportion of those with the motivation or intention to stop gambling often relapse ( Hodgins and el-Guebaly, 2004 ; Smith et al., 2015 ), and a significant number drop out from gambling-related treatment ( Pfund et al., 2021 ). Given the theory of planned behavior specifies intention as the proximal determinant of behavior, the model has been suggested to be unable to account fully for behavior ( Sniehotta et al., 2014 ). The question remains as to how those intending to refrain or abstain from gambling can be facilitated in doing so.

Implementation intentions

To account for the gap between intention and behavior, various strategies and models have been developed. In health psychology, research has found the benefits of planning, specifically implementation intentions. Implementation intentions are goal-directed plans formed based on what , when , where , and how the behavior will be undertaken. To develop an implementation intention, two important aspects must be considered ( Gollwitzer, 2014 ). First, one must identify a cue or critical situation. These can be cues facilitating the behavior or cues related to barriers to be overcome. Second, an appropriate behavioral response must be linked to the situation. These behavioral responses are behaviors to be undertaken once the cue is encountered. Implementation intentions are effective because deliberately identifying cues improves perceptual readiness and once encountered, automatically elicits the behavioral response ( Webb and Sheeran, 2004 ; Gollwitzer, 2014 ). The effectiveness of these plans can be increased when an “if/then” format is used to link the cue to the response. For example, a person wishing to stop gambling may state “If I am asked to go to a casino, then I will remind myself of the money I will likely lose.” Here, encountering the proposition to attend the casino will automatically elicit a reminder of the potential negative consequences.

It is important to note that an implementation intention is not a motivational strategy, and its effectiveness is not due to increased motivation ( Webb and Sheeran, 2008 ). That is because planning focuses on increasing opportunities to undertake the behavior, not on increasing motivation toward the behavior. An individual without a positive intention is unlikely to strengthen their motivation due to developing a plan. However, the effectiveness of planning depends on the presence of motivation. That is, the extent to which planning is successful depends on a person’s willingness to either engage or not engage in the focal behavior. In fact, the effectiveness of implementation intentions can be improved in the presence of strong intentions ( Prestwich and Kellar, 2014 ). Thus, a pre-requisite to planning is a (strong) behavioral intention or (strong) motivation toward the behavior.

Implementation intentions can be self-generated where the researcher or health provider instructs the person to develop their own plans. Specifically, they are asked to identify situational cues and link with appropriate behavioral responses. Given the person develops their own cues and responses, commitment to the plans can be enhanced ( Sniehotta, 2009 ). Alternatively, implementation intentions can be provided by the researcher or health provider. Armitage (2008) developed volitional help sheets which include a number of situational cues and behavioral responses. The individual is instructed to make links between the cues and outcomes deemed most relevant or salient to them. Although this does not guarantee the cues and responses will be applicable to all, this does circumvent any difficulty the person may have in generating their own plans.

Evidence has demonstrated implementation intentions to be effective in promoting behavior ( Gollwitzer and Sheeran, 2006 ), including those related to health ( Prestwich et al., 2003 ; Gollwitzer and Sheeran, 2006 ; Hagger and Luszcynska, 2014 ; Presseau et al., 2017 ). Gollwitzer and Sheeran (2006) showed implementation intentions had moderate-to large effects on health behaviors. Presseau et al. (2017) identified planning had a small-to-medium effect on objectively measured health behavior and a medium effect on self-reported health behavior. Despite these considerable behavioral effects, the use of implementation intentions has been limited in gambling research ( Rodda et al., 2020 ). For example, a systematic review conducted by St Quinton et al. (2022) identified 18 strategies were used in interventions targeting adolescent gambling. However, planning was not included in any intervention. Furthermore, Rodda et al. (2018) did find action planning was used by problem gamblers during online forums. However, it is unclear whether the plans were developed and enacted in the form of implementation intentions. Finally, Rodda et al. (2017) found that despite the uptake of many behavioral strategies, including planning, their use in gambling prevention is often not maintained. Therefore, there is a gap for implementation intentions to be used in this area.

It is worth noting that implementation intentions share similarities with other treatments used to modify risky behavior, such as gambling. For example, therapeutic approaches such as cognitive-behavioral therapy and motivational interviewing often attempt relapse prevention by identifying triggers. However, there are important differences between these approaches and implementation intentions. For example, although clients undertaking cognitive behavioral therapy are often asked to specify when and where they will strive for their goals, therapists rarely prompt clients to link a critical cue with a goal-directed response ( Duhne et al., 2020 ). Moreover, unlike these treatment approaches, the adoption of implementation intentions does not necessitate communication between a client and interventionist ( Wittleder et al., 2019 ). Evidence has also shown implementation intentions can be more effective than these therapeutic approaches (e.g., Varley et al., 2011 ; Mutter et al., 2020 ).

Implementation intentions and gambling

Individuals intending to quit or limit their gambling often fail to follow through on these good intentions ( Hodgins, and el-Guebaly, N., 2004 ; Smith et al., 2015 ). There are many factors that can interfere with these intentions. However, adopting implementation intentions could prevent motivation to refrain from gambling being derailed. Examples of how implementation intentions could be used are described next, but additional situations and responses are presented in Table 1 .

Table 1 . Examples of situations, responses, and implementation intentions related to gambling prevention.

Gambling is often undertaken as a social activity and can be influenced by the behaviors and actions of others ( Zhai et al., 2017 ; Mazar et al., 2018 ). Such referents can include friends, work colleagues, and social groups (i.e., sports teams, book clubs, and gym classes). Although these referents can support gambling abstinence, they may also have a negative influence by encouraging it. However, the negative influence of these groups can be subsided through implementation intentions. Consider a person invited to a casino by a group of friends. Now, this person could develop a plan that responds to the invitation. For example, the individual may state “If my friends ask me to go to the casino, then I will politely decline and inform them of my motivation to stop gambling.” In this way, encountering the situation (the invitation) would automatically lead to a positive behavioral response (the polite refusal). The implementation intention therefore protects the motivation or intention to abstain from gambling without having the need for conscious deliberation. As another example, a colleague may frequently visit a bookmaker during lunchtime. When asked by the colleague whether they would like to accompany them one day, the implementation intention “If I am asked to go to the bookmakers by a colleague, then I will recall how much money I have saved through gambling abstinence” could facilitate a positive behavioral response. Again, the plan put in place means the response is guided automatically when the situation is encountered.

These examples use implementation intentions to avoid entering a gambling facility. However, this may not always be preferred or needed. For example, in example 1, the individual may believe that refusing to go along to the casino with friends is likely to cause upset or disappointment. However, an implementation intention could be developed to elicit positive behavioral responses in these locations (e.g., “When I am in a casino, I will ensure that I ask my friend to stop me from gambling”). Similarly, the person in example 2 may feel confident going into the bookmakers but have concerns about abstaining from the slot machines. To facilitate abstinence, a plan such as “When I am in the bookmakers, I will stand on the opposite side of the room to the slot machines” could be used. Additionally, these examples relate to intentions to abstain from gambling, but the same logic would apply to limiting gambling. For example, example one could be modified to “If I am asked to go to the bookmakers by a colleague, then I will accept but put no more than £5 into the machine” or “If I lose £5 on the slot machine, then I will stop gambling immediately.”

In addition to social influences, gambling can be triggered by specific negative emotions, such as stress, boredom, or anger ( Buchanan et al., 2020 ; Kılıç et al., 2020 ). Implementation intentions can be used overcome these emotions. An individual prone to gambling when angry could plan “If I am angry and have the urge to gamble, then I will go for a walk instead.” In addition to negative emotions, gambling can be influenced by positive emotions ( Rogier et al., 2022 ). A plan could be developed to prevent such feelings leading to gambling. For example, an implementation intention could state “If I am happy and contemplate gambling, then I will remind myself that gambling will negatively influence my mood.”

There may be specific times or days when gambling are more likely to occur ( Morasco et al., 2007 ). For example, an individual could be more susceptible to gambling during the evening or after finishing work on a particular day. Implementation intentions such as “If I have the urge to gamble after work on Fridays, then I will recall how quickly I can spiral and lose money” and “If I have the desire to bet during the evening, then I will remind myself of the importance of saving money for my upcoming family holiday” could protect motivation toward abstinence. Finally, planning could be used to limit the influence of gambling advertisements, promotions, and pop-ups. Consider a person sitting watching a football match on television and a gambling advert appears on the screen with various enhanced odds for the match. This could make the person want to have a bet on the match. However, the implementation intention “If a betting advert comes on the television, then I will leave the room” could deter them from doing so.

These examples and those provided in Table 1 are not exhaustive as there will be many other circumstances and situations associated with gambling. Additionally, variability will exist in the effect of eliciting cues. For example, one individual may be inclined to gamble when stressed whereas another person may not. Moreover, the automatic behavioral responses will not be pertinent for each person; two people may be tempted to gamble in the evening, but only one may be influenced by a reminder that they are saving for a family holiday. It is therefore important that plans are relevant to the person wishing to abstain from gambling. Specifically, the situation and cues need to be considered carefully to elicit positive behavioral change. Plan effectiveness is also likely to be determined by the severity of the gambling problem. For example, planning for what happens when entering the casino may not be effective those with a severe gambling problem.

Implications for gambling

Abstaining from or limiting gambling can be a difficult challenge, even in the presence of strong motivation. Planning how this is going to be achieved can produce effective behavior change. Several recommendations can be made for the use of implementation intentions.

It is important that people are motivated to either limit or refrain from future gambling. That is because without an intention to do so, planning is unlikely to be successful. In the absence of a positive intention, motivational models, such as the theory of planned behavior, should be sought. These models can identify why a person is lacking motivation to change, and interventions can be developed accordingly. For example, some individuals may perceive odds to be in their favor or believe roulette outcomes can be predicted. In these instances, education could be useful to modify these erroneous attitudes.

In the absence of an intention to change, focus should be given to motivation. But the ceiling of motivation means this is usually insufficient to modify gambling behavior. Interventions should therefore introduce planning strategies to facilitate positive intentions. Given the ease of which planning interventions or instructions can be delivered, there is vast potential for its use in the gambling domain. Research in health psychology has recently adopted the use of technology to deliver behavioral interventions. For example, popularity has risen in interventions adopting a mobile device ( Steinhubl et al., 2015 ). Given the number of people using mobile phones to gamble ( James et al., 2017 ); this could be an effective mode to prevent it. This may be especially useful given a large proportion of gamblers are unwilling to seek face-to-face help ( Gainsbury et al., 2014 ). Communication could be made through text messages, emails, or mobile applications. For example, a text message could notify the user to develop an implementation intention, or a mobile application could instruct on how gambling abstinence can be achieved through planning. Bi-directional communication could be adopted whereby the user responds to such requests, and the implementation intentions are checked by the provider.

The optimal effectiveness of implementation intentions depends on ensuring aspects of fidelity. Firstly, it is important that the planning instructions are delivered in accordance with the strategy. If recommending implementation intentions, clear instructions need to be provided related to the identification of situations and behavioral responses. If, however, cues and behavioral responses are provided, then careful consideration must be given to ensure these are prominently associated with gambling. Secondly, it is important that the person wishing to abstain from gambling adheres to the instructions given. For example, failure to pair risky situations with critical responses would undermine the psychology underlying the effectiveness of planning.

Abstaining from or limiting gambling behavior is difficult and motivation is often insufficient. A useful strategy facilitating motivation is implementation intentions, a specific type of planning. The importance of both motivation and implementation intentions can be illustrated by considering the following: there is one individual with strong motivation to stop gambling. Now, this individual does not plan for circumstances that may deter influence motivation to refrain from gambling. When encountering many unanticipated events, the individual fails to implement the intention by proceeding to gamble. There is a second individual with the same strong intention to refrain from gambling. Unlike the first individual, this person has also developed specific implementation intentions after considering potential barriers. When this person encounters the same unanticipated events as example 1, they are able overcome them and follow through on their intention to abstain from gambling. Therefore, those with a strong intention to refrain from gambling plus implementation intentions may be better placed to reduce or abstain from gambling. Consequently, implementation intentions should be utilized by those wishing to modify their gambling behavior.

Author contributions

The author confirms being the sole contributor of this work and has approved it for publication.

Conflict of interest

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

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Keywords: implementation intentions, motivation, gambling, planning, intention

Citation: St Quinton T (2022) How can implementation intentions be used to modify gambling behavior? Front. Psychol . 13:957120. doi: 10.3389/fpsyg.2022.957120

Received: 30 May 2022; Accepted: 25 October 2022; Published: 09 November 2022.

Reviewed by:

Copyright © 2022 St Quinton. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Tom St Quinton, [email protected]

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

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Rolling the Dice: What Gambling Can Teach Us About Probability

Tom chivers on the historical origins of the science of statistics.

Traditionally, the story of the study of probability begins in French gambling houses in the mid-seventeenth century. But we can start it earlier than that.

The Italian polymath Gerolamo Cardano had attempted to quantify the maths of dice gambling in the sixteenth century. What, for instance, would the odds be of rolling a six on four rolls of a die, or a double six on twenty-four rolls of a pair of dice?

His working went like this. The probability of rolling a six is one in six, or 1/6, or about 17 percent. Normally, in probability, we don’t give a figure as a percentage, but as a number between zero and one, which we call p. So the probability of rolling a six is p = 0.17. (Actually, 0.1666666… but I’m rounding it off.)

Cardano, reasonably enough, assumed that if you roll the die four times, your probability is four times as high: 4/6, or about 0.67. But if you stop and think about it for a moment, that can’t be right, because it would imply that if you rolled the die six times, your chance of getting a six would be one-sixth times six, or one: that is, certainty. But obviously it’s possible to roll six times and have none of the dice come up six.

What threw Cardano is that the average number of sixes you’ll see on four dice is 0.67. But sometimes you’ll see three, sometimes you’ll see none. The odds of seeing a six (or, separately, at least one six) are different.

In the case of the one die rolled four times, you’d get it badly wrong—the real answer is about 0.52, not 0.67—but you’d still be right to bet, at even odds, on a six coming up. If you used Cardano’s reasoning for the second question, though, about how often you’d see a double six on twenty-four rolls, it would lead you seriously astray in a gambling house. His math would suggest that, since a double six comes up one time in thirty-six (p ≈ 0.03), then rolling the dice twenty-four times would give you twenty-four times that probability, twenty-four in thirty-six or two-thirds (p ≈ 0.67, again).

This time, though, his reasonable but misguided thinking would put you on the wrong side of the bet. The probability of seeing a double six in twenty-four rolls is 0.49, slightly less than half. You’d lose money betting on it. What’s gone wrong?

A century or so later, in 1654, Antoine Gombaud, a gambler and amateur philosopher who called himself the Chevalier de Méré, was interested in the same questions, for obvious professional reasons. He had noticed exactly what we’ve just said: that betting that you’ll see at least one six in four rolls of a die will make you money, whereas betting that you’ll see at least one double six in twenty-four rolls of two dice will not. Gombaud, through simple empirical observation, had got to a much more realistic position than Cardano. But he was confused. Why were the two outcomes different? After all, six is to four as thirty-six is to twenty-four. He recruited a friend, the mathematician Pierre de Carcavi, but together they were unable to work it out. So they asked a mutual friend, the great mathematician Blaise Pascal.

The solution to this problem isn’t actually that complicated. Cardano had got it exactly backward: the idea is not to look at the chances that something would happen by the number of goes you take, but to look at the chances it wouldn’t happen.

In the case of the four rolls of a single die, your chance of not seeing a six on any one throw is 5/6, or p ≈ 0.83. If you roll it again, your chance of not seeing a six on either throw is 0.83 times 0.83, or just shy of 0.7. Each time you roll the die, you reduce the chance of not seeing a six by 17 percent.

If you roll the die four times, your chance of not seeing a six is 0.83 × 0.83 × 0.83 × 0.83 ≈ 0.48. (To save time, we can say “0.83 to the power 4,” or “0.83 ^ 4.”) So your chance of seeing a six is 1 minus 0.48, or 0.52, or 52 percent. If you bet at even odds one hundred times, you’d expect to win fifty-two times, and you’d be in profit.

But look what happens when we do it with the two dice, looking for a double six. Your chance of seeing a double six on one roll of two dice is 1/36, or p ≈ 0.03, as we said earlier. So your chance of not seeing a double six is 35/36 or about 0.97.

If you roll your dice twenty-four times, your chance of not seeing a double six is 0.97 multiplied by itself twenty-four times (0.97 ^ 24). If you do that sum, you end up with 0.51. So the chance of seeing a double six is 0.49. If you bet at even odds, you’d expect to see it forty-nine times in a hundred, and you’d lose money.

(We should take a moment, here, to recognize the absolutely heroic amount of gambling that Gombaud must have been doing in order to be able to tell that his 52 percent bet was coming off, but his 49 percent bet wasn’t. Apparently, he had deduced, correctly, that you need twenty-five rolls of the dice, not twenty-four, for it to be a good bet. Gombaud was a man who enjoyed his dice-rolling.)

This led Gombaud to raise another question with Pascal. Imagine two people are playing a game of chance—cards or dice. Their game is interrupted halfway through, with one player in the lead. What’s the fairest way to divide the pot? It seems wrong to simply split it down the middle, since one person is winning; but it’s also unfair to give it all to the player in the lead, since they haven’t actually won yet.

Pascal found this fascinating, and exchanged a series of letters discussing the problem with his contemporary, Pierre de Fermat, of Last Theorem fame.

Again, this problem goes back a few centuries. The Italian monk Pacioli had a go at solving something like it in 1494, in his work Summa de arithmetica, geometrica, proportioni et proportionalità .

He imagines that two players are playing a ball game in which you win ten points for each goal, and the winner is the first person to get to sixty points. One of the players has reached fifty points, and the other has reached twenty, before the game is interrupted. How should the winnings be split?

Pacioli reasons that, since one player has scored five-sevenths of all the points so far scored, that player should win five-sevenths of the pot. Forty-five years later, the aforementioned Cardano—he who’d got the math backward on the dice problem, so could perhaps have shown a little more humility—scoffed that Pacioli’s solution was “absurd.” He imagined a slightly different scenario, where two players play a game of first to ten. One has seven points, and one has nine. In that situation, by Pacioli’s system, the first player should get nearly half the pot—seven-sixteenths—and the second player only slightly more, nine-sixteenths. But that seems obviously unfair, since one player only needs one point to win, while the other needs three.

Cardano suggested a better route. “His major insight,” writes Prakash Gorroochurn, “was that the division of stakes should depend on how many rounds each player had yet to win, not how many rounds they had already won.”

But Cardano didn’t get all the way there. He suggests using the ratio of the “progressions” of the two players’ still-required scores. The progression of a number, in his jargon, is that number, plus that number minus one, plus that number minus two, and so on down to one. So the progression of five would be 5 + 4 + 3 + 2 + 1 = 15.

In the example Cardano gave, the first player has three points still to win. The progression of three is six (3 + 2 + 1 = 6). The second player has one point still to win, and the progression of one is one (1 = 1). So, for Cardano, the pot should be divided six parts to one in favor of the second player.

This is better than Pacioli’s system, or at least gets you closer to the true answer. But it’s still wrong.

This is where Pascal and Fermat come into the picture. They realized the key point: It’s not how close to the finish you are, or how far from the start you’ve come, that matters. It’s the number of possible outcomes that remain , and how many of those outcomes favor one player over the other. Pascal, in a letter to Fermat, imagined a simple situation: two gamblers are playing a game of first to three points. They have each bet thirty-two pistoles (a gold coin used in currency at the time), so the total pot is sixty-four pistoles.

Let’s say it’s all square at two points each, and they suddenly have to end the game. In that case, reasons Pascal, it’s easy enough to divide. You just split it in half, thirty-two each.

But what if they’d had to end it one turn before, when one player had two points and the other player had one? Pascal extends the reasoning. They would have split it evenly had it gone to two rolls each, so the first player is sure of at least half the pot—even if that player were to lose the next throw, they would still have that. The other half is still a going concern. “Perhaps I will have them and perhaps you will have them,” Pascal imagines the first player saying. “The risk is equal. Therefore let us divide the thirty-two pistoles in half, and give the thirty-two of which I am certain besides.” So the first player will take 32 + 16 = 48, or three-quarters of the pot.

Another way to look at it is to say that there are four possible ways the game could have gone, had it continued. Player One could have won the first throw and the second; they could have won the first throw but lost the second; they could have lost the first throw but won the second; and they could have lost the first throw and lost the second.

Only in the fourth scenario does Player Two win the pot. If Player One wins the first throw, the second throw is irrelevant: Player One has made it to three points. So half the outcomes are wins for Player One without even going to the last throw. And even if they lose that first throw, they’re still in with a fifty-fifty chance of winning.

So the fair distribution of the pot, if the two players have to stop playing with one player up two to one, is three to one, just as Pascal said.

You can expand this, and Pascal does. Imagine that Player One was winning two–nil, not 2–1. If they win the next throw, they win. But if they lose, the other player is back to 2–1. And we’ve just seen that, from that point, their chance of winning the pot is 75 percent. In Pascal’s example, Player One would say: “If I win, I shall gain all; that is sixty-four. If I lose, forty-eight will legitimately belong to me. Therefore give me the forty-eight that are certain to be mine, even if I lose, and let us divide the other sixteen in half, because there is as much chance that you will gain them as that I will.”

So now Player One has a seven-eighths, or 87.5 percent, chance of winning, so the fair division is that Player One takes fifty-six pistoles out of sixty-four.

But how about if Player One only has one point, and Player Two zero? Then you extend it one further back, said Pascal. If Player Two wins the first throw, then it’s one–all, and an equal chance of winning. But if Player One wins the first throw, then it’s two–nil, and we know the situation: she has seven-eighths chance. Out of a possible sixteen outcomes, Player One wins in eleven, so she should win eleven-sixteenths of sixty-four pistoles, or forty-four.

This is the great insight of probability theory: that we should look at the possible outcomes from a given situation, not what has gone before. But laboriously counting out the number of possible outcomes as we have above takes quite a long time, so Pascal and Fermat worked on ways of making it quicker.

You can work it out as a sum, but it’s complicated if you have large numbers of rounds left to play. You need to work out the maximum possible number of remaining throws—that is, the number Player One needs to win, plus the number Player Two needs to win, minus one. If someone’s one–nil up in a first-to-three game, that’s four. (The highest score the game could reach is 3–2, five points in total.) Four remaining rounds means sixteen remaining possible outcomes—that is, two times itself four times. And then you need to work out which of the outcomes correlate to a win for Player One, which involves a lot of superscript and Greek letters and would just tire us all out.

Luckily, Pascal came up with a cheat. He wasn’t the first to use what we now call Pascal’s triangle—it was known in ancient China, where it is named after the mathematician Yang Hui, and in second-century India. But Pascal was the first to use it in problems of probability.

It starts with 1 at the top, and fills out each layer below with a simple rule: on every row, add the number above and to the left to the number above and to the right. If there is no number in one of those places, treat it as zero.

Pascal realized that he could use the triangle to solve the problem of points. Take our example. There are a maximum of four rounds left to play, so you count down four rows from the top (counting the very top row, the solitary 1, as row zero). Player One needs two more points to win, so take off the first two numbers from the left. Add the remaining numbers together, divide them by the total value of that row, and you get your chance of winning.

In this case, count down four rows from the 1, and you find you’re on a row that goes: 1 4 6 4 1. Take the first two numbers away, and you’re left with 6 4 1, which add up to 11. The whole row adds up to 16. That is, a 11/16, or a 68.75 percent chance: p = 0.6875.

Try it for the other examples we’ve looked at. If Player One has 2 points and Player Two has 1, then there are a maximum of two possible goes left, and Player One only needs to win one of them. So you count down two rows to the 1 2 1 row, you remove the 1, and you’re left with 3/4, or p = 0.75. It’s astonishingly neat, and saves you lots of time. It works for any event that has two equally likely outcomes, like coin-flipping or games between equally matched opponents. For a given number of goes, X, you look at row X (again, with the very top line being row zero). That gives you the total number of possible outcomes. So if you flipped a coin seven times, you’d count down to row seven, the one starting 1 7 21, add those outcomes up, and you find that it equals 128. So there are 128 possible outcomes.

Now, if you want to know what the possibility is of seeing exactly Y outcomes, say heads, on those seven flips:

It’s possible that you’ll see no heads at all. But it requires every single coin coming up tails. Of all the possible combinations of heads and tails that could come up, only one—tails on every single coin—gives you seven heads and zero tails.

There are seven combinations that give you one head and six tails. Of the seven coins, one needs to come up heads, but it doesn’t matter which one. There are twenty-one ways of getting two heads. (I won’t enumerate them all here; I’m afraid you’re going to have to trust me, or check.) And thirty-five of getting three.

You see the pattern? 1 7 21 35—it’s row seven of the triangle.

So if you want to know the chance of getting exactly Y heads on X flips, you count down X rows from row zero and look at the number that’s Y from the left (again, counting the 1 at the left as 0). Then you divide that second number by the first. Say you want to know the odds of getting exactly five heads, you look at row seven—that’s the 1 7 21 35 35 21 7 1—and starting from zero, you count five along. That’s the second twenty-one. So 21/128 ≈ 0.164, or about a one-in-six chance.

To find the chance of getting at least five heads, you just add the number of possible ways of getting six heads or seven heads to the ways of getting five heads: 21 + 7 + 1 = 29. Then you divide it by 128 as we did before. That’s what Pascal was doing to work out the fairest way to split the pot.

Pascal’s triangle is only one way of working out the probability of seeing some number of outcomes, although it’s a very neat way. In situations where there are two possible outcomes, like flipping a coin, it’s called a “binomial distribution.”

But the point is that when you’re trying to work out how likely something is, what we need to talk about is the number of outcomes— the number of outcomes that result in whatever it is you’re talking about, and the total number of possible outcomes. This was, I think it’s fair to say, the first real formalization of the idea of “probability.”

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Excerpted from Everything Is Predictable: How Bayesian Statistics Explain Our World by Tom Chivers. Copyright © 2024. Available from Atria/One Signal Publishers, an imprint of Simon & Schuster.

Tom Chivers

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