Don’t count on the gambler’s fallacy

Don’t count on the gambler’s fallacy
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First Published: Sun, Sep 14 2008. 09 58 PM IST
Updated: Sun, Sep 14 2008. 09 58 PM IST
Let’s say you flip a fair coin a thousand times. Apart from getting a very sore thumb, what outcome would you expect from this exercise? As the coin is fair, one would expect to see roughly equal numbers of heads and tail outcomes. Now, let’s take the same fair coin and start flipping it again. On the first 19 flips, you get all tails. Now, if you have an opportunity to bet on the 20th flip, should you bet on heads or tail? Which of the two outcomes has a higher probability of occurrence, given that the previous 19 flips have resulted in an unbroken string of tails? If the coin is fair, wouldn’t the chances of heads increase to balance out the unusual streak of tails in the previous flips? In other words, won’t the “random generator” kick in to produce more heads to balance out the tail outcomes? The answer is a surprising no. The odds of getting heads on the 20th flip are exactly the same as they were in any of the first 19 flips (50/50).
So, why don’t the probabilities change after a lengthy streak? In statistical terms, the answer is because each flip is independent of every other flip. In layman’s terminology, the coin does not have any memory built into it. Other than you, there is nobody keeping track of outcomes. In the long run, the odds will roughly balance out, but on any given flip the probability still stays 50/50.
To give you an oft-cited example, what are the odds of someone carrying a bomb with them on a flight? Let’s say the answer is one in 1,000 (airport security folks would have to shut air travel if the odds were really this high but let’s just work with these odds to keep the discussion simple). Now, what are the odds that two individuals will independently bring bombs with them on the same flight? The odds drop to one in a million. Given the dramatic drop in probability, you decide to bring a bomb with you (how you convince the airport security to let you do this is entirely a function of your negotiation skills). Does this action of yours reduce the chances of another person carrying a bomb on the same flight from one in 1,000 to one in a million? No, it doesn’t. You have already brought one of the two bombs on board, so now the odds of another person bringing their own bomb on that flight drops back to one in 1,000.
In repeat trials of a random process, the occurrence of deviations from an expected outcome (such as a streak of consecutive heads in a coin flip) creates an expectation of a higher probability of the opposite outcome (a tail on the next flip being imminent). This false belief is commonly referred to as the gambler’s fallacy.
How does gambler’s fallacy operate in the business world? Any time managers take overall odds and apply them to a narrow situation, they run the risk of falling victim to this fallacy. For example, let’s say a quality control manager knows that the overall odds of her manufacturing plant producing a defective product are one in 100. She inspects 99 units and finds them to be defect-free. She will be committing the gambler’s fallacy if she expects the odds of the hundredth unit being defective to be higher. The odds are no different from what they were for the first 99 units (one in 100). It is important to note here that the reverse is true as well. Just because she discovers three defective pieces in a row does not change the probability of encountering yet another defective piece in the short run.
A note of caution to managers: The gambler’s fallacy assumes that events are independent. If they were not, then there could be reasons to believe that the odds would change over time. Here’s an example. Let’s say the average rate of new product failure for your industry is 80%. Eight out of every 10 new products introduced in your industry fail to survive past the first year. Your company introduced six products in the last two years, out of which five have been successful. What are the odds that your next product will be successful? In this case, it is incorrect to use the industry average because events are not independent. You could have a particularly skilful new product development team that has figured out a way to beat the industry odds. To go back to the coin analogy, the coin in this case is not fair. It is loaded in your favour and is likely to yield more successes than failures.
To summarize, the broad idea behind this fallacy is that when you are dealing with independent random events, it is imprudent to use past outcomes to predict a future outcome. You should do this only if you think the events are correlated.
Praveen Aggarwal is an associate professor of marketing at the Labovitz School of Business & Economics at the University of Minnesota Duluth and Rajiv Vaidyanathan is a professor of marketing and director of MBA programmes at the University of Minnesota Duluth.
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First Published: Sun, Sep 14 2008. 09 58 PM IST