From Gambling to Stereotyping: The Way We See Patterns
Second-year Psychology students participating in the University Honours College follow a mini-course on Blogging Science (within the Thematic Meetings course), in which they learn to communicate science to the general public, by means of informing, giving an opinion, and relating issues in science to issues in society. This year a selection of these written blog posts is published on Mindwise. This post is by Airi Yamada.
Imagine you are participating in a lottery. You look at the numbers that the last winner picked: 2, 6, 32, 24, 3 and 11. Immediately, you might think: “Well, I’m going to choose anything but 2, 6, 32, 24, 3 and 11.”
What you have unknowingly committed in this example, is known as the gambler’s fallacy . As most people would intuitively think, it would be highly unlikely for the winning numbers (or even a subset) to come up again in the next winner’s choice. Just as six consecutive heads in a coin-toss game may seem “odd”, we seem to detect patterns in a sequence of events and even ascribe meaning to them.
However, what we often seem to forget is that patterns are not always meaningful. In the aforementioned lottery example, the numbers are chosen by random chance, meaning that each possible number has an equal probability of being selected, no matter how many times the number appeared before. The gambler’s fallacy refers to this belief that a future outcome will be affected by previous results, although in reality this is not the case.
People often seem prone to perceiving erroneous statistical patterns in various contexts. For instance, many sports coaches as well as spectators believe that a player’s future chance of scoring increases following previous successful attempts, attributing the player with a“hot hand”or a “winning streak”. This belief has been studied primarily in basketball, and appears to be much less pervasive in reality. In a classic study, Thomas Gilovich and colleagues investigated this so-called “hot hand” by examining the shooting records of several basketball teams such as the 76ers and the Boston Celtics. Objective results showed that previous successful throws were not correlated with successive scoring attempts, although they may affect subjective predictions of future performance . Thus, as in the lottery example, the probability of scoring seems independent of previous outcomes. We simply draw (incorrect) probabilistic inferences of the player’s performance pattern based on past results.
Regardless of the specific context, one possible reason why people make these judgmental biases may be due to a concept known as the law of small numbers. According to this law, people assume that a small sample (three consecutive scores made by a basketball payer) is an adequate representation of a larger sample (the success rate of a player across multiple free throws) mainly because people overestimate the reliability of a single sample . Note that this is the opposite of the law of large numbers, which posits that a larger sample size will be more representative of the average, or a proportion of the actual population. The law of small numbers can lead people to impose erroneous patterns in their daily lives, simply because pattern recognition helps make sense of the world in an effortless manner.
The pattern-seeking mind in society
Although the pattern-seeking mind has its advantages, it definitely has some disadvantages in society. Say, for example, that you meet a person from a foreign country you are not quite familiar with. Everything that that individual does or says will become a reference point for a larger population of people you may meet in the future with similar backgrounds, such as:
“People from Country X are diligent workers.”
“People from Country Y are rude and impatient.”
Yes, I’m talking about stereotyping.
The cognitive process involved seems surprisingly comparable to that of those committing the gambler’s fallacy – forming hasty expectations of future events based on past occurrences. It is undeniably true that stereotypes equip us with the ability to comprehend unfamiliar contexts. However, imagine if the next person you meet from Country X was laid back and disorganized, and if another individual from Country Y was patient and polite. Would you not be disappointed and pleasantly surprised in both cases, respectively? Whether the initial stereotype is positive or negative, it poses a social pressure on the one being evaluated – an implicit expectation to be a certain way.
The same could be said of a basketball player who scores consecutive free throws; he will be stereotyped as a “good”player, constantly expected to produce successful results. People will soon become less accepting of his failures because they not only commit the hot hand fallacy but also believe in the law of small numbers – that a small sample of his performance is representative of his general ability.
Is generalization an impulse too great for us to control?
It is interesting to note that both the gambler’s fallacy and stereotyping happen at a subconscious level. If brought to attention, we know that we have committed an error, and we know that it does not make sense logically to generalize from one small event. But why then, do we keep on making these errors? Is generalization an impulse too great for us to control?
As constant“judges”of society, we should keep in mind how random chance plays a role in the various patterns that we see around us. Just like individual numbers drawn in a lottery, there is also an equal amount of chance for a person to produce certain results or behave in a certain way.
Probability allows us to predict, but not to predetermine. Hence, avoiding jumping to conclusions may be our safest bet after all.
Relevant links and publications
 Clotfelter, C., & Cook, P. (1991). The “Gambler’s Fallacy” in Lottery Play. NBER Working Papers Series, (3769).
 Gilovich, T., Vallone, R., & Tversky, A. (1985). The hot hand in basketball: On the misperception of random sequences. Cognitive psychology, 17(3), 295-314.
 Tversky, A., & Kahneman, D. (1971). Belief in the Law of Small Numbers. Psychological Bulletin, 76(2), 105-110.
NOTE: Image by conorwithonen, licenced under CC BY 2.0