Show
The gambler’s fallacy is the mistaken belief that if an event occurred more frequently than expected in the past then it’s less likely to occur in the future (and vice versa), in a situation where these occurrences are independent of one another. For example, the gambler’s fallacy can cause someone to mistakenly assume that if a coin that they tossed landed on heads twice in a row, then it’s likely to land on tails next. It’s important to understand the gambler’s fallacy, since it plays a crucial role in people’s thinking, both when it comes to gambling as well as when it comes to other areas of life. As such, in the following article you will learn more about the gambler’s fallacy, understand the psychology behind it, and see what you can do to avoid it. Explanation of the gambler’s fallacyThe gambler’s fallacy involves manifests in two connected ways:
These beliefs both represent an underlying expectation of systematic reversal in random sequences of independent events, which is mistaken, since when events are independent of one another, their future occurrences are unaffected by their past occurrences by definition, even if people’s intuition leads them to expect otherwise. For example, consider a situation where you roll a pair of dice, which both land on 6. The odds of this happening in a fair roll are 1/36, since the odds of each die landing on a 6 are 1/6. Here, the gambler’s fallacy could cause someone to assume that the odds of both dice landing on 6 again on the next roll are lower than 1/36. However, in reality, on each individual roll, the odds of the dice landing on double 6’s are still 1/36. This continues to be true regardless of how many times we roll the dice, since the dice can’t remember what they landed on last time. Essentially, there is no way for the last dice roll to affect the next one, which is why it’s incorrect to assume that these independent events affect each other. When considering this, it helps to understand the difference between the odds of getting a certain string of outcomes, and the odds of getting a certain outcome given an independent prior string of outcomes. For example, the odds of having a fair coin land on heads 5 times in a row are 0.5^5; this represents the odds of getting a certain string of outcomes. However, the odds of having a fair coin land on heads any single time are always 0.5, regardless of what number toss it is, since each toss is independent of the prior string of outcomes, meaning that it is unaffected by the previous tosses. As one book on the topic explains:
Examples of the gambler’s fallacyOne example of the gambler’s fallacy is the mistaken belief that if a coin lands on heads multiple times in consecutive coin tosses, then it’s due to land on “tails” next. A similar example of the gambler’s fallacy is the mistaken belief that if a die landed on the same number (e.g. 6) multiple times in a row, then it’s less likely to land on that same number the next time. In general, as its name suggests, the gambler’s fallacy is most commonly associated with how people think when they gamble. Beyond the previous examples of this, with coins and dice, another example of this is the incorrect belief that if a certain number was recently drawn in a lottery, then it’s less likely to be drawn again in an upcoming draw. In addition, another notable example of the gambler’s fallacy in the context of gambling occurred in a 1913 incident, at a roulette game at the Monte Carlo Casino, where the ball fell on the color black 26 times in a row since this was such a rare occurrence, gamblers lost millions of dollars betting that the ball will fall on red throughout this streak, in the mistaken belief that the ball was due to land on it soon. As one book notes on this phenomenon:
Furthermore, the gambler’s fallacy can also influence people’s thinking and decision making in other areas of life beyond gambling. For example, in the case of childbirth, the gambler’s fallacy means that people often believe that someone is “due” to give birth to a baby of a certain gender, if they have previously given birth to several babies of the opposite gender. A similar phenomenon was described by French scholar Pierre-Simon Laplace, in the first published account of the gambler’s fallacy:
Finally, the gambler’s fallacy has been shown to affect the judgment, decision-making, and behavior of various professionals, such as loan officers, sports referees, judges, and even psychologists, despite the fact that many of them are well aware of its influence. Note: the gambler’s fallacy is sometimes referred to as the Monte Carlo Fallacy, as a result of the aforementioned incident at the Monte Carlo casino, or as the doctrine of the maturity of chances. The psychology behind the gambler’s fallacyThe gambler’s fallacy is a cognitive bias, meaning that it’s a systematic pattern of deviation from rationality, which occurs due to the way people’s cognitive system works. It is primarily attributed to the expectation that even short sequences of outcomes will be highly representative of the process that generated them, and to the view of chance as a fair and self-correcting process. Essentially, people often assume that streaks of outcomes will even out in the short-term in order to be representative of what an ideal and fair random streak should look like. In the case of a fair coin toss, for example, the gambler’s fallacy can cause people to assume if a coin just landed on heads twice in a row, then it will now land on tails in order to even out the streak and maintain an equal ratio of heads to tails. As one key study notes:
As this shows, the issue underlying the gambler’s fallacy is the incorrect belief in local representativeness, which is people’s expectation that small samples (or small parts of large samples) will be representative of their parent population, since they expect the essential characteristics of the population to be represented not only globally in the entire population (or in large samples), but also locally in all its parts. This is also referred to as the law of small numbers, which is the incorrect belief that small samples are likely to be highly representative of the populations from which they are drawn, similarly to large samples. Furthermore, additional explanations have been proposed for the gambler’s fallacy. This includes, for example, a gestalt approach to assessing strings of events, which involves the belief that upcoming independent random events will be connected to prior ones, as a result of the tendency to perceive patterns and connections where there are none. These explanations, together with the representativeness explanation, generally revolve around the concept of heuristics, which are mental shortcuts that can be beneficial in some cases, but that can also lead to erroneous judgments in others. Because of this, and because the gambler’s fallacy occurs as a result of belief in local representativeness, this bias is closely associated with the representativeness heuristic, which is the tendency to evaluate probabilities by the degree to which one thing is representative of another (i.e., the degree to which a sample is representative of its parent population or an event is representative of the process that generated it). How to avoid the gambler’s fallacyTo avoid the gambler’s fallacy, you must first be aware that it’s about to be used, in your reasoning or in someone else’s, or that it has been used already. However, research shows that simply being aware of the gambler’s fallacy is often not enough, by itself, in order to avoid it, which suggests that additional debiasing techniques are needed. One such technique is to emphasize the independence of the different events in question, by highlighting their inability to affect each other. For example, when it comes to the odds of a pair of dice landing on double 6’s in an upcoming roll, after they have landed on double 6’s in the previous roll, you should internalize the fact that the second roll is independent of the previous one, by considering that:
When doing this, you can either explain this issue when it comes to the specific scenario under consideration, or you can illustrate the concept of event independence using a simple and intuitive generic example, such as that of a dice roll or a coin toss. In addition, you can further internalize this concept by asking yourself or whomever you’re trying to help avoid this fallacy to explain how the dice might be able to influence the roll. This can be beneficial, since asking people to think through the process, instead of simply explaining it to them, can increase the likelihood that they will understand why this belief is false. Finally, you can also benefit from other, more generalized debiasing techniques. This can involve, for example, slowing down the reasoning process, or optimizing the decision-making environment by removing distractions that make it harder for people to think clearly. Overall, to avoid the gambler’s fallacy, you should become aware that it’s playing a role in someone’s thinking, and then demonstrate the independence of the events in questions, by showing that they cannot possibly affect each other. You can also explain why this type of reasoning is flawed, illustrate its issues using relevant examples, and implement general debiasing techniques, such as slowing down the reasoning process. Remember that events aren’t always independentIt’s important to keep in mind that, in some cases, an unlikely outcome suggests that events aren’t truly random and independent from one another. For example, consider the example of a coin flip. The odds of a fair coin landing on heads 5 times in a row are roughly 3 in 100. This isn’t too unlikely, and so, if we toss a coin and it ends up landing on heads 5 times in a row, it shouldn’t necessarily cause us to be suspicious. Furthermore, even if you keep tossing a coin, and it lands on heads 10 times in a row, this doesn’t mean that you should necessarily assume that it’s not a fair coin, since the odds of a fair coin doing that are approximately 1 in 1,000. However, let’s say you keep tossing the coin, until you get 50 tosses in a row. Since the odds that the coin will keep landing on heads 50 times in a row are about 1 in 1,126,000,000,000,000 (1 in 1.126 quadrillion), if this outcome occurs then it’s reasonable to assume that the coin isn’t a fair one, since the likelihood of receiving this outcome is so low otherwise. Accordingly, you can be relatively certain that the next time you toss that coin, it’s still going to land on heads, as it will the next time after that, based on the previous tosses. As such, while it’s important to be aware of the gambler’s fallacy, and to avoid assuming that independent events can affect one another, it’s also important to remember that in some cases, certain unlikely outcomes suggest that events aren’t truly independent of one another, which you should take into account when making decisions. Note: there are various statistical approaches, such as Bayesian inference, that can be used to assess the likelihood that supposedly independent events are not actually independent of one another. Related conceptsThe inverse gambler’s fallacyThe inverse gambler’s fallacy (sometimes referred to as the retrospective gambler’s fallacy) is the mistaken belief that a random process is likely to have occurred many times in the past, after an outcome of it that is perceived as rare is observed. For example, the inverse gambler’s fallacy can cause someone who sees a pair of dice landing on double 6’s to assume that the person rolling them has rolled them several times beforehand, just because this outcome is perceived as rare, and as unlikely to occur on the first roll. The gambler’s fallacy fallacyOne study on the topic of the gambler’s fallacy, proposes several variants of this fallacy, which are defined as follows:
Type I and Type II gambler’s fallaciesA distinction is sometimes drawn between two different types of the gambler’s fallacy:
The hot-hand fallacyThe hot-hand fallacy is the mistaken belief that a string of similar outcomes signals that additional similar outcomes are likely to follow, in a situation where these outcomes are independent of one another. For example, the hot-hand fallacy can cause someone to believe that if they rolled double 6’s twice in a row, then they are likely to get double 6’s again if they roll the dice a third time. Though this phenomenon appears to represent an opposite effect than the gambler’s fallacy, the two are not always viewed as contradictory or as a simple inverse of one other, and various distinctions have been drawn between them. For example, one study states the following:
Independent and identically distributed variablesThe gambler’s fallacy is often mentioned in the context of variables that are independent and identically distributed (i.i.d.), such as coin tosses and dice rolls. In this context, independent means that the variables (e.g. coin tosses) do not influence one another, and identically distributed means that the variables have the same probability distribution (i.e. the same likelihood of resulting in the same outcomes). However, note that the outcomes of i.i.d. variables do not have to be equiprobable, which means that they do not need to have an equal probability of occurring. For example, even if a coin is unfair because it’s more likely to land on heads than tails, a series of tosses of this coin is still identically distributed, because the coin has the same probability of landing on heads each time. Summary and conclusions
|