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.