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Turning over a new belief: The psychology of superstition

According to Stuart Vyse in his book Believing in Magic: The Psychology of Superstition, the fallibility of human reason is the greatest single source of superstitious belief. Sometimes referred to as a belief in “magic”, superstition can cover many spheres such as lucky or unlucky actions, events, numbers, and/or sayings, as well as a belief in astrology, the occult, the paranormal, or ghosts. It was reported by Colin Campbell in the British Journal of Sociology, that approximately one third of the U.K. population are superstitious. The most often reported superstitious behaviours are (i) avoiding walking under ladders, (ii) touching wood, and (iii) throwing salt over one’s shoulder.

My background is in the gambling studies field, so as far as I am concerned, no superstitions are based on facts but are based on what I would call ‘illusory correlations’ (e.g., noticing that the last three winning visits to the casino were all when you wore a particular item of clothing or it was on a particular day of the week). While the observation may be fact-based (i.e., that you did indeed wear a particular piece of clothing), the relationship is spurious.

Superstition can cover many spheres such as lucky or unlucky actions, events, numbers, and/or sayings. A working definition within our Western society could be a belief that a given action can bring good luck or bad luck when there are no rational or generally acceptable grounds for such a belief. In short, the fundamental feature underlying superstitions is that they have no rational underpinnings.

There is also a stereotypical view that there are certain groups within society who tend to hold more superstitious beliefs than what may be considered the norm. These include those involved with sport, the acting profession, miners, fishermen, and gamblers – many of whom will have superstitions based on things that have personally happened to them or to those they know well. Again, these may well be fact-based but the associations they have experienced will again be illusory and spurious. Most individuals are basically rational and do not really believe in the effects of superstition. However, in times of uncertainty, stress, or perceived helplessness, they may seek to regain personal control over events by means of superstitious belief.

One explanation for how we learn these superstitious beliefs has been suggested by the psychologist B.F. Skinner and his research with pigeons. He noted in a 1948 issue of the Journal of Experimental Psychology, that while waiting to be fed, pigeons adopted some peculiar behaviours. The birds appeared to see a causal relationship between receiving the food and their own preceding behaviour. However, it was merely coincidental conditioning. There are many analogies in the human world – particularly among gamblers. For instance, if a gambler blows on the dice during a game of craps and subsequently wins, the superstitious belief is reinforced through the reward of winning. Another explanation is that as children we are socialized into believing in magic and superstitious beliefs. Although many of these beliefs dissipate over time, children also learn by watching and modelling their behaviour on that of others. Therefore, if their parents or peers touch wood, carry lucky charms, and do not walk under ladders, then children are more likely to imitate that behaviour, and some of these beliefs may be carried forward to later life.

In a paper published in Personality & Social Psychology Bulletin, Peter Darke and Jonathan Freedman (1997) suggested that lucky events are, by definition, determined entirely by chance. However, they go on to imply that, although most people would agree with this statement on an intellectual level, many do not appear to behave inaccordance with this belief. In his book Paradoxes of Gambling Behaviour, Willem Wagenaar (1988) proposed that in the absence of a known cause we tend to attribute events to abstract causes like luck and chance. He goes on to differentiate between luck and chance and suggests that luck is more related to an unexpected positive result whereas chance is related to surprising coincidences.

Bernard Weiner, in his book An Attributional Theory of Motivation and Emotion, suggests that luck may be thought of as the property of a person, whereas chance is thought to be concerned with unpredictability. Gamblers appear to exhibit a belief that they have control over their own luck. They may knock on wood to avoid bad luck or carry an object such as a rabbit’s foot for good luck. Ellen Langer argued in her book The Psychology of Control that a belief in luck and superstition cannot only account for causal explanations when playing games of chance, but may also provide the desired element of personal control.

In my own research (with Carolyn Bingham) into superstition among bingo players published in the Journal of Gambling Issues, it was clear that a large percentage of bingo players we surveyed reported beliefs in luck and superstition. However, the findings were varied, with a far greater percentage of players reporting everyday superstitious beliefs rather than beliefs concerned with bingo. Whether or not players genuinely believed they had control over luck is unknown. Having superstitious beliefs may be simply part of the thrill of playing.

Dr Mark Griffiths, Professor of Behavioural Addiction, International Gaming Research Unit, Nottingham Trent University, Nottingham, UK

Further reading

Campbell, C. (1996). Half-belief and the paradox of ritual instrumental activism: A theory of modern superstition. British Journal of Sociology, 47(1), 151–166.

Darke, P. R., & Freedman, J. L. (1997). Lucky events and beliefs in luck: Paradoxical effects on confidence and risk-taking. Personality & Social Psychology Bulletin, 23, 378–388.

Griffiths, M.D. & Bingham, C. (2005). A study of superstitious beliefs among bingo players. Journal of Gambling Issues, 13. Located at: http://jgi.camh.net/index.php/jgi/article/view/3680/3640

Langer, E. J. (1983). The psychology of control. London: Sage.

Skinner, B. F. (1948). “Superstition” in the pigeon. Journal of Experimental Psychology, 38, 168–172.

Thalbourne, M.A. (1997). Paranormal belief and superstition: How large is the association? Journal of the American Society for Psychical Research, 91, 221–226.

Vyse, S. A. (1997). Believing in magic: The psychology of superstition. New York: Oxford University Press.

Wagenaar, W. A. (1988). Paradoxes of gambling behaviour. London: Erlbaum.

Weiner, B. (1986). An attributional theory of motivation and emotion. New York: Springer-Verlag

Nag, nag, nag: The psychology of horse-race betting

All forms of gambling lie on a luckskill dimension. Neither games of pure skill nor games of pure chance are particularly attractive to serious gamblers. Games of chance (like lotteries) offer no significant edge to serious gamblers and are unlikely to be gambled upon. While games of skill provide a significant edge for the gambler, serious gamblers need more than an edge – they need an opponent who can be exploited. Serious gamblers gravitate towards types of gambling that provide an appropriate mix of chance and skill. This is one of the reasons why sports betting – and in particular horse-race betting – is so popular for gamblers. In the most recent British Gambling Prevalence Survey published in 2011, the results indicated that betting on horse-races in the past year had slightly decreased to 16% (down from 17% in the 2007 survey) with men (21%) being more likely than women (13%) to have bet on horse-races. The survey also showed that 7% of the sample had gambled on horse-races in the past week. The survey also indicated that horse-race bettors were more likely to be classed as ‘high spenders’ compared to most other types of gambler.

The edge available in horse-race gambling can be sufficient to fully support professional gamblers as they bring their wide range of knowledge to the activity. There is the complex interplay of factors that contributes to the final outcome of the race. There is the form of the horse, the length of the race, the reputation of the jockey, trainer and stable, breeding, weight, the conditions of the racetrack, etc. From this mix of information the horse-race bettor will, broadly speaking, do one of two things. Either they try to select a winner, or they try to select a horse that offers the best odds in terms of its true chances. Assessing these odds (i.e., handicapping), is done by developing ratings based on the available information. Precisely how all these factors can be combined to select a horse is a matter about which most gamblers disagree, but it is reasonable to assume that many punters believe that their knowledge of these factors gives them an edge over other punters that they are competing against.

Individuals clearly differ in how they use complex information to select horses. There has been some interesting research on the psychology of handicapping particularly in whether good handicappers are more intelligent. For instance, American psychologists, Dr. Steve Ceci and Dr. Jeffrey Liker studied a group of experienced horse-race gamblers all of who had been serious gamblers for over eight years and who attended racetracks most days. In a paper that had published in the Journal of Experimental Psychology, they divided the gamblers into experts and non-experts on the basis of predicting the favourite and the rank order according to odds of the three most favoured horses. Expert gamblers were those who correctly picked the favourite in at least nine out of ten races and correctly picked the top three horses in rank order in at least five out of ten races. In contrast, the best of the non-experts correctly identified the favourite in only five out of ten races, and selected the top three in only two of the ten races. The two groups were then given a number of intelligence quotient (IQ) tests. Ceci and Liker predicted that the experts would have higher IQs on the basis of their handicapping ability but was very surprised to find no difference at all between the two groups’ intelligence levels.

When the psychologists did some follow-up interviewing, they found that one of the best handicappers was a construction worker with a low IQ (of 85). He managed to pick the top horse in terms of post-time odds 100% of the time and picked the top three horses in correct order in five out of ten races. They also highlighted the case of a high IQ lawyer who picked the top horse only 30% of the time and got the rank ordering of the top three horses correct only once. One of the things concluded was that there is probably more than one type of intelligence and that the IQ test that was used may not have measured the types of skill needed in the handicapping of horses. At least Ceci and Liker’s findings give some hope to us all!

Psychologists have also shown that gamblers (including those who bet on horse racing) can be very biased in their thinking. The occasional punter expects to lose but this isn’t the case for serious gamblers. Each bet is part of a pattern of bets that the gambler expects to yield a positive return overall. To the gambler, winning bets confirm that their system is successful. However, losing bets do not convince gamblers that their system is a failure. Gamblers may explain losing bets as an error in implementing their system or to factors beyond their control. In essence, (and as I have shown in some of my own research studies) many gamblers attribute wins to their skilful gambling but explain away losses as something due to external factors or the environment that they gamble in. On a psychological level, the serious gambler is able to maintain their belief that they have a winning system despite mounting losses through biased evaluations of the outcomes. Since winning is central to the gambler’s self-concept and self-esteem, they cannot quit while losing as this would invalidate the core of the self-concept and initiate intense negative effects (such as depression).

Although horse-race gamblers treat their pastime as a skilful activity, it has been estimated that at least 40% of the relevant information that determines the winner of a race is not accessible to any gamblers. Furthermore, despite years of practice, frequent gamblers may still be very poor at assessing the chances of different horses.

Dr Mark Griffiths, Professor of Gambling Studies, International Gaming Research Unit, Nottingham Trent University, Nottingham, UK

Further reading

Ceci, S. J., & Liker, J. K. (1986). A day at the races: A study of IQ, expertise, and cognitive complexity. Journal of Experimental Psychology: General, 115, 255-266.

Griffiths, M.D. (1994). The role of cognitive bias and skill in fruit machine gambling. British Journal of Psychology, 85, 351-369.

Griffiths, M.D. (2010). The psychology of sports betting: What should affiliates know? i-Gaming Business Affiliate, August/September, 46-47.

Griffiths, M.D. (2011). Mobile sportsbetting: A view from the social sciences. i-Gaming Business, 69, 64-65.

Parke, A., Griffiths, M.D. & Irwing, P. (2004). Personality traits in pathological gambling: Sensation seeking, deferment of gratification and competitiveness as risk factors, Addiction Research and Theory, 12, 201-212.

Parke, J., Griffiths, M.D. & Parke, A. (2007). Positive thinking among slot machine gamblers: A case of maladaptive coping? International Journal of Mental Health and Addiction, 5, 39-52.

Wardle, H., Moody, A., Spence, S., Orford, J., Volberg, R., Jotangia, D., Griffiths, M., Hussey, D. & Dobbie, F. (2011). British Gambling Prevalence Survey 2010. London: The Stationery Office.

Wardle, H., Sproston, K., Orford, J., Erens, B., Griffiths, M.D., Constantine, R. & Pigott, S. (2007). The British Gambling Prevalence Survey 2007. London: The Stationery Office

Problem thinking: Heuristics and cognitive bias in gambling

Once when I was playing roulette at my local casino, there was a run of seven reds in a row. I rarely bet by colour myself, but while I was laying my many 50 pence chips all over the roulette number grid, I told a friend standing next to me that many people would put a lot of their chips on black on the next spin of the wheel. And they did! I am no mind reader but what I do know about is the gambler’s fallacy. The gambler’s fallacy is a well-known psychological ‘rule of thumb’ where gamblers apply the law of averages to very small number sequences. Put very simply, I knew that most people would be thinking “by the law of averages the black is supposed to come up 50% of the time and hasn’t done so for the last seven spins”. While the 50% probability is true, the probability is based on very large sequences of numbers and not a few spins of the roulette wheel. What’s more, the roulette ball has no memory of where it landed before and every spin is independent of the last one. As it turned out, red came up again and there were some disgruntled and disbelieving gamblers. On the ninth spin, a black number finally came up.

The gambler’s fallacy is one of many psychological thinking patterns that are known as ‘heuristics’ (and sometimes called cognitive biases). The psychological effect of heuristics is to reduce uncertainty for the gambler. Open up any textbook on gambling and you will find that the gambler’s fallacy is referred to as the ‘representativeness bias’. This is because people expect to find a representative relationship between samples drawn from a small number of events (for example, eight spins on the roulette wheel), and the complete set of events (in this case, all the spins ever on all roulette wheels). When we gamble, we constantly process information (often unconsciously) in a consistently biased way. Humans tend to exhibit consistent biases when cognitively processing information in gambling situations. For instance, in psychological gambling experiments where people are asked to create a random sequence of imaginary coin tosses, they tend to produce sequences where the proportion of heads in a short segment is closer to 50% than chance would predict.

Over the last 35 years, psychologists have written about many different heuristics that gamblers use. One of the better known ones is the ‘availability bias’. This occurs when a person evaluating the probability of a chance event makes the judgement in terms of the ease with which relevant instances or associations come to mind. For instance, pools winners are highly publicised to invoke the idea that big wins are regular and commonplace when in fact they are rare. Availability biases can also be found when people actually gamble in lotteries. For instance, when selecting numbers, some people will pick (‘hot’) numbers that have come up more often and avoid the (‘cold’) numbers that by chance have not come up as often. For instance, during the week of the first ever triple rollover on the UK National Lottery it was noted by a number of newspapers that the number ‘13’ had come up much less than any other number in almost 10 years of lottery draws. Those gamblers prone to the ‘availability bias’ would be unlikely to pick this number. Of course, those prone to the ‘representativeness bias’ would be more likely to pick it! And that is one of the problems with ‘rules of thumb’ – it is almost impossible to know which heuristic will be applied in a given situation and it is quite possible for the same person to use a different heuristic in the same situation on different occasions.

Some of my favourite heuristics are those involving ‘illusory correlations’. These are superstitious behaviours where people believe two actions are related when in fact they are not. For instance, one seminal 1960s study of ‘craps’ players in US casinos (published by Dr. J. Henslin in the American Journal of Sociology) showed that players rolled the dice softly to get low numbers and rolled harder for higher ones. Other spurious examples are those people who have ritualised routines before they gamble, have ‘lucky chairs’ at the bingo hall, or those who carry lucky charms when they gamble. Most of these illusory correlations start by associative accident. For instance, a gambler might have three big wins at the roulette table and then notice that on all three of those occasions they wore the same pair of trousers. As a consequence, they might start to think that the trousers are somehow lucky and wear them on subsequent visits to the casino. When they win while wearing them, it bolsters the bias. The relationship between the winning and the trousers wearing is illusory but many gamblers display such irrational biases.

Psychological biases provide some insight into why some gamblers don’t learn from past losses and helps explain supposedly ‘irrational’ behaviour in the gambling process. Some psychologists claim that problem gambling is caused by defective reasoning, rather than personality traits, education or social environment.  They also claim that gamblers gamble, not because they have a bigger repertoire of heuristics, but because they select heuristics on the wrong occasions.

Dr Mark Griffiths, Professor of Gambling Studies, International Gaming Research Unit, Nottingham Trent University, Nottingham, UK

Further reading

Griffiths, M.D. (1994). The role of cognitive bias and skill in fruit machine gambling. British Journal of Psychology, 85, 351-369.

Griffiths, M.D. (1997). Selling hope: The psychology of the National Lottery. Psychology Review, 4, 26-30.

Griffiths, M.D. & Bingham, C. (2002). Bingo playing in the UK: The influence of demographic factors on play.  International Gambling Studies, 2, 51-60.

Griffiths, M.D. & Wood, R.T.A. (2001). The psychology of lottery gambling. International Gambling Studies, 1, 27-44.

Henslin, J. (1967) Craps and magic. American Journal of Sociology, 73, 316-330.

Kahneman, D. & Tversky, A. (1973). Availability: A heuristic for judging frequency and probability. Cognitive Psychology, 5, 207-233.

Langer, E.J. (1975). The illusion of control. Journal of Personality and Social Psychology, 32, 311-328.

Langer, E.J. & Roth, J. (1975). The effect of sequence outcome in a chance task on the illusion of control. Journal of Personality and Social Psychology, 32, 951-955.

Parke, J., Griffiths, M.D. & Parke, A. (2007). Positive thinking among slot machine gamblers: A case of maladaptive coping? International Journal of Mental Health and Addiction, 5, 39-52.

Tversky, A. & Kahneman, D. (1971). Belief in the law of small numbers. Psychological Bulletin, 76, 105-110.

Walker, M.B. (1992). The Psychology of Gambling. Pergamon, Oxford.

Wagenaar, W. (1988). Paradoxes of Gambling Behaviour. Erlbaum, London.

Everyone’s a winner? The role of cognitive biases in lottery playing

Earlier this week, I was interviewed by the Metro newspaper about the psychology of playing the National Lottery.  One reader of the article had a somewhat sarcastic dig at me:

“I happened to glance through the Metro today, whilst waiting for an appointment, and noticed a feature on lotteries. It actually draws on Prof Mark Griffiths from Nottingham Trent University, to deliver this shocking statement ‘Prof Griffiths believes lotteries are a form of gambling’”

Out of context, the statement does sound somewhat banal. However, the point that I was making to the journalist was that many lottery players don’t believe that buying a lottery ticket is really gambling. Studies have shown that if you ask “pure lottery players” (i.e., those people who only play the lottery and don’t engage in any other form of gambling) if they gamble, a large proportion typically answer that they don’t. Lottery players often refer to their behaviour as nothing more than a ‘harmless flutter’. Given that very few people develop problems from weekly or bi-weekly lotteries is a fair and accurate comment. Other lottery players will claim that the activity is not really a form of gambling because the money goes to good causes (which while partly true) doesn’t negate the fact that playing the lottery is a form of gambling.

Over the years I have written many papers and articles on lottery play. In today’s blog I briefly examine some of the cognitive biases and heuristics that have been applied to lottery gambling (excluding the psychology of the near miss that I examined in a previous blog). Heuristics are usually defined as ‘rules-of-thumb’ (i.e. simple ‘if-then’ rules or norms). There are many heuristics (e.g., the illusion of control, the availability bias, the sunk cost bias, the representativeness bias, etc.) that may help explain why lotteries are so appealing to the general public – beyond the basic reason that playing the lottery provides the chance to win a life-changing amount of money (millions of pounds) for a low cost (typically £1). Although the following heuristics are not an exhaustive list, they do contain those cognitive biases and heuristics that are probably most salient to the psychology of lottery gambling:

Illusion of control: Ellen Langer, a very well know American psychologist at Harvard University, defined the illusion of control is an expectancy of success higher than the objective probability would warrant. In essence, her basic assumption was that in some chance settings (e.g., buying a lottery ticket), those conditions that involved factors of choice, involvement, familiarity and/or competition stimulate the illusion of control to produce skill orientations. These observations have been confirmed in both laboratory and natural setting based experiments. For instance, Langer’s seminal 1970s experiments showed that participants would sell previously bought lottery tickets for a higher price if they had picked it themselves as opposed to having it ‘assigned’ by someone else.

Flexible attributions: Flexible attributions are cognitive distortions in which gamblers attribute their successes as due to their own skill and failures as due to some external influence. Research by US psychologixt Thomas Gilovich (Cornell University) demonstrated that gamblers transform their losses into ‘near wins’ and spend far more time discussing their losses and discounting them while bolstering their wins. Professor Gilovich also showed that gamblers display hindsight bias (i.e. they are not surprised by the outcome of a gamble and report they predicted it after the event has happened).

Representativeness bias: The classic work on representativeness bias – by Israeli-US psychologists Daniel Kahneman and Amos Tversky – applies to random samples of data and is where people expect to find a representative relationship between samples drawn from the population and the population itself. For instance, when subjects are asked to create a random sequence of imaginary coin tosses they tend to produce sequences where the proportion of ‘tails’ in a short segment is closer to 0.5 than chance would predict. This particular mechanism may well explain the ‘gambler’s fallacy’, (i.e., the expectation that the probability of winning will increase with the length of an ongoing run of losses).

Availability bias: The availability bias occurs when a person evaluating the probability of a chance event makes the judgment in terms of the ease with which relevant instances come to mind. With regards to the lotteries, winners are often highly publicised. These both give the idea that wins are regular and commonplace when in fact they are rare. A vividly presented case study or example can make a lasting impression.

Sunk cost bias: Another factor that may be important in why lotteries have been so financially successful is the sunk cost bias (also known as entrapment). Entrapment refers to a commitment to a goal that has not yet been reached. The basic premise is to get the person committed to the cause or product as soon as possible. Once a commitment is made, the nature of thought changes. To the converted (in this case the lottery ticket buyer), careful and considered analysis of the situation is likely to be minimal. Lotteries have one great advantage over many other forms of gambling in that many people pick exactly the same numbers each week. In the UK, a newspaper survey reported that 67% of people choose the same numbers each week. Of this figure, the survey reported that 30% chose their regular numbers after an initial random selection and 37% chose the same numbers each week based on birthday dates, house numbers, favourite numbers, etc. However, no details were given about demography of the participants or the sample size.

By picking the same numbers the person may become ‘entrapped’. Each week the player thinks they are coming closer to winning. The winning day is impossible to predict but should the lottery player decide to stop and cut their losses, they are faced with the prospect that the very next week their numbers might come up. The player is thus entrapped and the entrapment become greater as the weeks go by. According to Australian psychologist Dr Michael Walker, people can reach a point where holidays cannot be taken unless arrangements are made for the weekly ticket to be completed and entered. The ‘entrapment’ process is not only known as the ‘sunk cost bias’ but is also another ‘foot-in-the-door’ technique.

These heuristics and biases give some insight into why gamblers do not learn from their past losses and help to explain supposedly ‘irrational’ behaviour. However, heuristics and biases have no predictive value. It is almost impossible to know which heuristic will be applied in a given situation and it is quite possible for the same person to use a different heuristic in the same situation on different occasions.

Dr Mark Griffiths, Professor of Gambling Studies, International Gaming Research Unit, Nottingham Trent University, Nottingham, UK

Further reading

Arkes, H.R. & Blumer, C. (1985). The psychology of sunk cost.  Organizational Behavior and Human Decision Processes, 35, 124-140.

Griffiths, M.D. (1997). The National Lottery and instant scratchcards: A psychological perspective. The Psychologist: The Bulletin of the British Psychological Society, 10, 26-29.

Griffiths, M.D. (1997). Selling hope: The psychology of the National Lottery. Psychology Review, 4, 26-30.

Griffiths, M.D. (2008). Problem gambling and European lotteries. In M. Viren (Ed.), Gaming in New Market Environment. pp. 126-159. New York: Macmillan Palgrave.

Griffiths, M.D. & Wood, R.T.A. (2001). The psychology of lottery gambling. International Gambling Studies, 1, 27-44.

Kahneman, D. & Tversky, A. (1973). Availability: A heuristic for judging frequency and probability. Cognitive Psychology, 5, 207-233.

Langer, E.J. (1975). The illusion of control. Journal of Personality and Social Psychology, 32, 311-328.

Langer, E.J. & Roth, J. (1975). The effect of sequence outcome in a chance task on the illusion of control. Journal of Personality and Social Psychology, 32, 951-955.

Tversky, A. & Kahneman, D. (1971). Belief in the law of small numbers. Psychological Bulletin, 76, 105-110.

Walker, M.B. (1992). The Psychology of Gambling. Pergamon, Oxford.

Wagenaar, W. (1988). Paradoxes of Gambling Behaviour. Erlbaum, London.

Wood, R.T.A. & Griffiths, M.D. (2004). Adolescent lottery and scratchcard players: Do their attitudes influence their gambling behaviour? Journal of Adolescence, 27, 467-475.